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All questions of Quantitative Aptitude for SSC CGL Exam
The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers is- a)135
- b)240
- c)73
- d)106
Correct answer is option 'D'. Can you explain this answer?
The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers is
a)
135
b)
240
c)
73
d)
106
|
Mira Sharma answered |
As we know (a − b)2 = a2 + b2 − 2ab
We assume that first number is a and second number is b hence ab = 45
and a - b = 4
after putting values we will get a2 + b2 = 106
We assume that first number is a and second number is b hence ab = 45
and a - b = 4
after putting values we will get a2 + b2 = 106
The price of a commodity rises from Rs. 6 per kg to Rs. 7.50 per kg. If the expenditure cannot increase, the percentage of reduction in consumption is- a)15
- b)20
- c)25
- d)30
Correct answer is option 'B'. Can you explain this answer?
The price of a commodity rises from Rs. 6 per kg to Rs. 7.50 per kg. If the expenditure cannot increase, the percentage of reduction in consumption is
a)
15
b)
20
c)
25
d)
30
|
Poulomi Das answered |
Given, price of a commodity rises from Rs. 6 per kg to Rs. 7.50 per kg.
Also given, the expenditure remains the same.
Thus, initial consumption × 6 = New consumption × 7.5
⇒ New consumption = 0.8 × initial consumption
Decrease in consumption = Initial consumption – Final consumption
⇒ Decrease in consumption = Initial consumption - 0.8 × initial consumption
⇒ Decrease in consumption = 0.2 × initial consumption
Also given, the expenditure remains the same.
Thus, initial consumption × 6 = New consumption × 7.5
⇒ New consumption = 0.8 × initial consumption
Decrease in consumption = Initial consumption – Final consumption
⇒ Decrease in consumption = Initial consumption - 0.8 × initial consumption
⇒ Decrease in consumption = 0.2 × initial consumption
% decrease in consumption 
⇒ % decrease in consumption
⇒ % decrease in consumption
If the cost price of 15 articles is equal to the selling price of 12 articles, find gain %- a)20
- b)25
- c)18
- d)21
Correct answer is option 'B'. Can you explain this answer?
If the cost price of 15 articles is equal to the selling price of 12 articles, find gain %
a)
20
b)
25
c)
18
d)
21
|
Ssc Cgl answered |
Let's say cost price of 15 articles is xx
cost price of 12 articles will be = 12x/15
selling price of 15 articles is = x
gain = 3x/15
cost price of 12 articles will be = 12x/15
selling price of 15 articles is = x
gain = 3x/15
A reduction of 20% in the price of sugar enables me to purchase 5 kg more for Rs. 100. Find the price of sugar per kg before reduction of price.- a)Rs. 25
- b)Rs. 30
- c)Rs. 32
- d)Rs. 36
Correct answer is option 'A'. Can you explain this answer?
A reduction of 20% in the price of sugar enables me to purchase 5 kg more for Rs. 100. Find the price of sugar per kg before reduction of price.
a)
Rs. 25
b)
Rs. 30
c)
Rs. 32
d)
Rs. 36
|
Animesh Bhunia answered |
Here it should be 5 kg sugar not 5 kg more sugar
There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of Rs. 8000 after 2 years at the same rate of interest.- a)Rs. 2500
- b)Rs. 2000
- c)Rs. 2250
- d)Rs. 2125
Correct answer is option 'D'. Can you explain this answer?
There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of Rs. 8000 after 2 years at the same rate of interest.
a)
Rs. 2500
b)
Rs. 2000
c)
Rs. 2250
d)
Rs. 2125
|
Naveen Choudhury answered |
Formulas to be used: -
SI = ( P × r × t ) / 100
For CI:
Where SI is Simple interest,
A is the amount at the end of time t,
P is the principal,
t is time,
r is rate
For SI, there is 100% increase to amount, thus A = 2P
⇒ SI = p
Time is 8 years.
∴ p = (p × r × t)/100
⇒ r = 100/8 = 12.5%
Now, P = 8000, t = 2years and r = 12.5%
⇒ A = 8000 × 1.1252
⇒ A = Rs. 10125
CI = A – P
⇒ CI = 10125 – 8000 = Rs. 2125
SI = ( P × r × t ) / 100
For CI:
Where SI is Simple interest,
A is the amount at the end of time t,
P is the principal,
t is time,
r is rate
For SI, there is 100% increase to amount, thus A = 2P
⇒ SI = p
Time is 8 years.
∴ p = (p × r × t)/100
⇒ r = 100/8 = 12.5%
Now, P = 8000, t = 2years and r = 12.5%
⇒ A = 8000 × 1.1252
⇒ A = Rs. 10125
CI = A – P
⇒ CI = 10125 – 8000 = Rs. 2125
Form two places, 60 km apart, A and B start towards each other and meet after 6 hours. Had A travelled with 2/3 of his speed and B travelled with double of his speed, they would have met after 5 hours. The speed of A is:- a)4 km/hr
- b)6 kmph
- c)10 kmph
- d)12 kmph
Correct answer is option 'B'. Can you explain this answer?
Form two places, 60 km apart, A and B start towards each other and meet after 6 hours. Had A travelled with 2/3 of his speed and B travelled with double of his speed, they would have met after 5 hours. The speed of A is:
a)
4 km/hr
b)
6 kmph
c)
10 kmph
d)
12 kmph
|
Ashwin Mehta answered |
Let speed of A be a kmph and speed of B be b kmph
Then we have
⇒ a + b = 60/6
⇒ a + b = 10
or 2a + 2b = 20------[1]
also,
⇒ 2/3a + 2b = 60/5 = 12--------------[2]
[1] – [2] leads to
⇒ (4/3)a = 8
a = 6 kmph
Then we have
⇒ a + b = 60/6
⇒ a + b = 10
or 2a + 2b = 20------[1]
also,
⇒ 2/3a + 2b = 60/5 = 12--------------[2]
[1] – [2] leads to
⇒ (4/3)a = 8
a = 6 kmph
The area of a square and circle is same and the perimeter of square and equilateral triangle is same, then the ratio between the area of circle and the area of equilateral triangle is- a)π : 3
- b)9 : 4√3
- c)4 : 9√3
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The area of a square and circle is same and the perimeter of square and equilateral triangle is same, then the ratio between the area of circle and the area of equilateral triangle is
a)
π : 3
b)
9 : 4√3
c)
4 : 9√3
d)
none of these
|
Janhavi Gupta answered |
From the given data
Let the each side of a square be a, then its area will be a2
∴ area of circle will also be a2
Also given that the perimeter of square and equilateral triangle is same,
⇒ 4a = 3s
the each side of equilateral triangle is 4a/3
∴ area of equilateral triangle = √3/4 × (4a/3)2 = 4√3 a2/9
∴ ratio between the area of circle and the area of equilateral triangle = a2/(4√3 a2 × 9) = 9 : 4√3
Let the each side of a square be a, then its area will be a2
∴ area of circle will also be a2
Also given that the perimeter of square and equilateral triangle is same,
⇒ 4a = 3s
the each side of equilateral triangle is 4a/3
∴ area of equilateral triangle = √3/4 × (4a/3)2 = 4√3 a2/9
∴ ratio between the area of circle and the area of equilateral triangle = a2/(4√3 a2 × 9) = 9 : 4√3
If a + 1/a = 1, then the value of a2 + 1/a2 is:- a)-2
- b)2
- c)-1
- d)4
Correct answer is option 'C'. Can you explain this answer?
If a + 1/a = 1, then the value of a2 + 1/a2 is:
a)
-2
b)
2
c)
-1
d)
4
|
|
Mira Sharma answered |
it is given that a + 1/a = 1
and we need to find value of
= 12 - 2 = -1
= 12 - 2 = -1
Each interior angle of a regular polygon is 150°. The number of sides is - a)12
- b)10
- c)9
- d)8
Correct answer is option 'A'. Can you explain this answer?
Each interior angle of a regular polygon is 150°. The number of sides is
a)
12
b)
10
c)
9
d)
8
|
Aarav Sharma answered |
If each interior angle of a regular polygon is 150 degrees, then we can use the formula for the sum of the interior angles of a polygon to find the number of sides.
The formula for the sum of the interior angles of a polygon is given by:
Sum of interior angles = (n - 2) * 180 degrees
Where n is the number of sides of the polygon.
Since each interior angle is 150 degrees, we can substitute this value into the formula:
150n = (n - 2) * 180
Expanding the right side of the equation:
150n = 180n - 360
Moving all terms involving n to one side of the equation:
180n - 150n = 360
Simplifying the equation:
30n = 360
Dividing both sides of the equation by 30:
n = 12
Therefore, the regular polygon has 12 sides.
The formula for the sum of the interior angles of a polygon is given by:
Sum of interior angles = (n - 2) * 180 degrees
Where n is the number of sides of the polygon.
Since each interior angle is 150 degrees, we can substitute this value into the formula:
150n = (n - 2) * 180
Expanding the right side of the equation:
150n = 180n - 360
Moving all terms involving n to one side of the equation:
180n - 150n = 360
Simplifying the equation:
30n = 360
Dividing both sides of the equation by 30:
n = 12
Therefore, the regular polygon has 12 sides.
One angle of a triangle is 60° and other angle is π/2 radian. Find the third angle in centesimal unit?- a)23.33
- b)33.33
- c)43.33
- d)53.33
Correct answer is option 'B'. Can you explain this answer?
One angle of a triangle is 60° and other angle is π/2 radian. Find the third angle in centesimal unit?
a)
23.33
b)
33.33
c)
43.33
d)
53.33
|
|
Avi Choudhury answered |
From the given data
∠ A = 60° and∠B = π/2 radian = 90°
We know that sum of the angles in triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠C = 180 - 150 = 30°
We know that 90° = 100 grad
⇒ 30° = 30 × 100/90 = 33.33 grade
∠ A = 60° and∠B = π/2 radian = 90°
We know that sum of the angles in triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠C = 180 - 150 = 30°
We know that 90° = 100 grad
⇒ 30° = 30 × 100/90 = 33.33 grade
The first and last terms of an arithmetic progression are -23 and 42. What is the sum of the series if it has 14 terms?- a)91
- b)133
- c)93
- d)-133
Correct answer is option 'B'. Can you explain this answer?
The first and last terms of an arithmetic progression are -23 and 42. What is the sum of the series if it has 14 terms?
a)
91
b)
133
c)
93
d)
-133
|
Abhiram Mehra answered |
Given Information:
The first term of the arithmetic progression is -23 and the last term is -42. The total number of terms in the series is 14.
Calculating Common Difference:
Let the common difference of the arithmetic progression be 'd'.
Since the last term is -42, we can write -23 + (14-1)d = -42.
Solving this equation, we get d = -2.
Calculating Sum of the Series:
The sum of an arithmetic series is given by the formula: S = n/2 * (first term + last term), where n is the number of terms.
Substitute the values: S = 14/2 * (-23 + (-42)) = 7 * (-65) = -455.
Final Answer:
The sum of the arithmetic progression is -455.
Therefore, the correct option is b) 133.
The first term of the arithmetic progression is -23 and the last term is -42. The total number of terms in the series is 14.
Calculating Common Difference:
Let the common difference of the arithmetic progression be 'd'.
Since the last term is -42, we can write -23 + (14-1)d = -42.
Solving this equation, we get d = -2.
Calculating Sum of the Series:
The sum of an arithmetic series is given by the formula: S = n/2 * (first term + last term), where n is the number of terms.
Substitute the values: S = 14/2 * (-23 + (-42)) = 7 * (-65) = -455.
Final Answer:
The sum of the arithmetic progression is -455.
Therefore, the correct option is b) 133.
If LCM of two numbers is thrice the larger number and difference between the smaller number and the HCF is 14. Then, find out the smaller number of the two numbers.- a)16
- b)23
- c)21
- d)42
Correct answer is option 'C'. Can you explain this answer?
If LCM of two numbers is thrice the larger number and difference between the smaller number and the HCF is 14. Then, find out the smaller number of the two numbers.
a)
16
b)
23
c)
21
d)
42
|
Ishaan Roy answered |
Solution: Let the larger number be x and the smaller number be y.
It is given that LCM is thrice of the larger number,
Therefore, LCM = 3x ----(i)
It is also given that difference between the smaller number and the HCF is 14,
Therefore, y – HCF = 14
HCM = y – 14 ----(ii)
We know that product of two numbers = LCM × HCF
Therefore, x × y = 3x × (y – 14) (from (i) and (ii))
y = 3(y – 14)
y = 3y – 42
2y = 42
y = 21
Hence, the smaller number is 21.
It is given that LCM is thrice of the larger number,
Therefore, LCM = 3x ----(i)
It is also given that difference between the smaller number and the HCF is 14,
Therefore, y – HCF = 14
HCM = y – 14 ----(ii)
We know that product of two numbers = LCM × HCF
Therefore, x × y = 3x × (y – 14) (from (i) and (ii))
y = 3(y – 14)
y = 3y – 42
2y = 42
y = 21
Hence, the smaller number is 21.
The graphs of x = a and y = b intersect at- a)(a, b)
- b)(b, a)
- c)(-a, b)
- d)(a, -b)
Correct answer is option 'A'. Can you explain this answer?
The graphs of x = a and y = b intersect at
a)
(a, b)
b)
(b, a)
c)
(-a, b)
d)
(a, -b)
|
EduRev SSC CGL answered |
Clearly, the lines x = a and y = b meets at a point (a, b)
In a factory 60% of the workers are above 30 years and of these 75% are males and the rest are females. If there are 1350 male workers above 30 years, the total number of workers in the factory- a)3000
- b)2000
- c)1800
- d)1500
Correct answer is option 'A'. Can you explain this answer?
In a factory 60% of the workers are above 30 years and of these 75% are males and the rest are females. If there are 1350 male workers above 30 years, the total number of workers in the factory
a)
3000
b)
2000
c)
1800
d)
1500
|
|
Ssc Cgl answered |
Let's say total number of workers are xx.
Hence above 30 years workers will be 60x/100
And male workers will be
So x will be = 3000.
Hence above 30 years workers will be 60x/100
And male workers will be
So x will be = 3000.
A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?- a)96
- b)76
- c)69
- d)82
Correct answer is option 'A'. Can you explain this answer?
A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?
a)
96
b)
76
c)
69
d)
82
|
Anirban Mukherjee answered |
Let,
Total distance covered = 2x km
We know that,
Time required = Distance covered/Speed
Given,
Half of the distance i.e. x km is covered at speed 16 km/hr
∴ Time required = x/16 hours
Next half of the distance i.e. x km is covered at speed 24 km/hr
∴ Time required = x/24 hours
Given,
Total time required = 5 hours
∴ x/16 + x/24 = 5
⇒ (3x + 2x)/48 = 5
⇒ 5x = 48 × 5
⇒ x = 48 km
∴ Total distance covered = 2 × 48 km = 96 km
Total distance covered = 2x km
We know that,
Time required = Distance covered/Speed
Given,
Half of the distance i.e. x km is covered at speed 16 km/hr
∴ Time required = x/16 hours
Next half of the distance i.e. x km is covered at speed 24 km/hr
∴ Time required = x/24 hours
Given,
Total time required = 5 hours
∴ x/16 + x/24 = 5
⇒ (3x + 2x)/48 = 5
⇒ 5x = 48 × 5
⇒ x = 48 km
∴ Total distance covered = 2 × 48 km = 96 km
Ram and Shyam start a joint business. Ram invests 1/3 of the total sum for 9 month and Shyam gets 2/5 of the profits. For how long, the investment of Shyam was in the business?- a)2 months
- b)3 months
- c)4 months
- d)5 months
Correct answer is option 'B'. Can you explain this answer?
Ram and Shyam start a joint business. Ram invests 1/3 of the total sum for 9 month and Shyam gets 2/5 of the profits. For how long, the investment of Shyam was in the business?
a)
2 months
b)
3 months
c)
4 months
d)
5 months
|
|
Aarav Sharma answered |
Solution:
Let the total sum be x.
Ram invested 1/3 of the total sum i.e. (1/3)x for 9 months.
Let Shyam's investment be y and he was in the business for 't' months.
Given, Shyam gets 2/5 of the profits.
Total profit = Total income - Total investment
Total investment = (1/3)x * 9 + y * t
Total income = Total investment + Total profit
As Shyam gets 2/5 of the profits, Ram gets 3/5 of the profits.
Let the total profit be P.
P * 2/5 = Shyam's share of profit
P * 3/5 = Ram's share of profit
Profit = Total income - Total investment
P = (Total income - Total investment)
2/5 * P = Shyam's share of profit = y * t
3/5 * P = Ram's share of profit = (1/3)x * 9
Adding the above two equations, we get:
P = (1/3)x * 3 + y * t * 5/3
P = x + y * (5/3) * t
Substituting P in the above two equations, we get:
2/5 * (x + y * (5/3) * t) = y * t
3/5 * (x + y * (5/3) * t) = (1/3)x * 9
Simplifying the above two equations, we get:
2x/5 + 2y/3 = 3xyt/5
2x/5 - 2x/9 = y * (5/3) * t
Simplifying the above two equations, we get:
18x + 30y = 27xyt
6x - 10y = 25yt
Dividing the above two equations, we get:
(6x - 10y)/(18x + 30y) = (25yt)/(27xyt)
Simplifying the above equation, we get:
2/9 = 25/27
This is not possible.
Hence, Shyam's investment was in the business for 3 months (Option B).
Note: There is a mistake in the given answer. The correct answer is option B, i.e. 3 months.
Let the total sum be x.
Ram invested 1/3 of the total sum i.e. (1/3)x for 9 months.
Let Shyam's investment be y and he was in the business for 't' months.
Given, Shyam gets 2/5 of the profits.
Total profit = Total income - Total investment
Total investment = (1/3)x * 9 + y * t
Total income = Total investment + Total profit
As Shyam gets 2/5 of the profits, Ram gets 3/5 of the profits.
Let the total profit be P.
P * 2/5 = Shyam's share of profit
P * 3/5 = Ram's share of profit
Profit = Total income - Total investment
P = (Total income - Total investment)
2/5 * P = Shyam's share of profit = y * t
3/5 * P = Ram's share of profit = (1/3)x * 9
Adding the above two equations, we get:
P = (1/3)x * 3 + y * t * 5/3
P = x + y * (5/3) * t
Substituting P in the above two equations, we get:
2/5 * (x + y * (5/3) * t) = y * t
3/5 * (x + y * (5/3) * t) = (1/3)x * 9
Simplifying the above two equations, we get:
2x/5 + 2y/3 = 3xyt/5
2x/5 - 2x/9 = y * (5/3) * t
Simplifying the above two equations, we get:
18x + 30y = 27xyt
6x - 10y = 25yt
Dividing the above two equations, we get:
(6x - 10y)/(18x + 30y) = (25yt)/(27xyt)
Simplifying the above equation, we get:
2/9 = 25/27
This is not possible.
Hence, Shyam's investment was in the business for 3 months (Option B).
Note: There is a mistake in the given answer. The correct answer is option B, i.e. 3 months.
In a partnership business, A invests 1/6th of the capital for 1/6 of the total time, B invests 1/4 of the capital for 1/4 of the total time and C, the rest of the capital for the whole time. Out of a profit of 19,400, B's share is:- a)2000
- b)1200
- c)1600
- d)1800
Correct answer is option 'D'. Can you explain this answer?
In a partnership business, A invests 1/6th of the capital for 1/6 of the total time, B invests 1/4 of the capital for 1/4 of the total time and C, the rest of the capital for the whole time. Out of a profit of 19,400, B's share is:
a)
2000
b)
1200
c)
1600
d)
1800
|
Target Study Academy answered |
Let the total capital be Rs z and total time be y
hence ratio of profit divison for A, B, C will be
A : B : C = 4 : 9 : 84
A : B : C = 4 : 9 : 84
hence profit for B = 9/97 x 19400 = 1800
At some rate per annum the amount with compound interest on Rs. 1600 for 2 years is Rs. 1730.56. The rate of interest per annum is:- a)10%
- b)2%
- c)4%
- d)5%
Correct answer is option 'C'. Can you explain this answer?
At some rate per annum the amount with compound interest on Rs. 1600 for 2 years is Rs. 1730.56. The rate of interest per annum is:
a)
10%
b)
2%
c)
4%
d)
5%
|
|
Ishaan Roy answered |
We know that,
Where, A = Final amount, P = Principal amount, R = % rate of interest, T = time period in years
Here, P = Rs. 1600, T = 2 years, A = 1730.56
Thus, rate of R% per annum is 4%
Where, A = Final amount, P = Principal amount, R = % rate of interest, T = time period in years
Here, P = Rs. 1600, T = 2 years, A = 1730.56
Thus, rate of R% per annum is 4%
The wheel of a railway carriage is 3 m in diameter and makes 8 revolutions per second, how fast is the train going?a. 27- a)271.30 km/hr
- b)742.20 km/hr
- c)452.48 km/hr
- d)464.70 km/hr
Correct answer is option 'A'. Can you explain this answer?
The wheel of a railway carriage is 3 m in diameter and makes 8 revolutions per second, how fast is the train going?a. 27
a)
271.30 km/hr
b)
742.20 km/hr
c)
452.48 km/hr
d)
464.70 km/hr
|
Deepak Menon answered |
From given data
Radius of the wheel r = 3/2 = 1.5 m
⇒ Circumference of the wheel = 2πr = 2π × 1. 5 = 3π = 9. 42 m
Given that wheel makes 8 revolutions per second
⇒ Distance travelled in 1 second = 8 × 9.42 = 75.36 m
⇒ Distance travelled in one hour = 75.36 × 3600 = 271296 m = 271.296 km
∴ Speed of the train ≈ 271.30 km/hr
Radius of the wheel r = 3/2 = 1.5 m
⇒ Circumference of the wheel = 2πr = 2π × 1. 5 = 3π = 9. 42 m
Given that wheel makes 8 revolutions per second
⇒ Distance travelled in 1 second = 8 × 9.42 = 75.36 m
⇒ Distance travelled in one hour = 75.36 × 3600 = 271296 m = 271.296 km
∴ Speed of the train ≈ 271.30 km/hr
The value of 
- a)0.03
- b)0.09
- c)0.9
- d)0.52
Correct answer is option 'D'. Can you explain this answer?
The value of
a)
0.03
b)
0.09
c)
0.9
d)
0.52
|
Vikram Mehta answered |
We need to find value of 
= 0.519 ~ 0.52
= 0.519 ~ 0.52
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.- a)8 cm
- b)7 cm
- c)10 cm
- d)11 cm
Correct answer is option 'A'. Can you explain this answer?
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.
a)
8 cm
b)
7 cm
c)
10 cm
d)
11 cm
|
Anjali Roy answered |
As per the given data
Let AD be the length of the median subtending from vertex A and to the side BC
⇒ BD = DC = BC/2 = 10/2 = 5 cm
By Apollonius theorem, we get
⇒ AB2 + AC2 = 2 (AD2 + BD2)
⇒ 122 + 62 = 2 (AD2 + 52)
⇒ 90 = AD2 + 25
⇒ 65 = AD2
⇒ AD = 8.06 cm
∴ length of the medium = AD = 8.06 ≈ 8 cm
Let AD be the length of the median subtending from vertex A and to the side BC
⇒ BD = DC = BC/2 = 10/2 = 5 cm
By Apollonius theorem, we get
⇒ AB2 + AC2 = 2 (AD2 + BD2)
⇒ 122 + 62 = 2 (AD2 + 52)
⇒ 90 = AD2 + 25
⇒ 65 = AD2
⇒ AD = 8.06 cm
∴ length of the medium = AD = 8.06 ≈ 8 cm
If α, β are the roots of the equation 2x2 - 3x + 2 = 0, form the equation whose roots are α2, β2 ?- a)4x2 – x + 4 = 0
- b)2x2 + x + 5 = 0
- c)5x2 + 3x + 7 = 0
- d)6x2 + 4x + 8 = 0
Correct answer is option 'A'. Can you explain this answer?
If α, β are the roots of the equation 2x2 - 3x + 2 = 0, form the equation whose roots are α2, β2 ?
a)
4x2 – x + 4 = 0
b)
2x2 + x + 5 = 0
c)
5x2 + 3x + 7 = 0
d)
6x2 + 4x + 8 = 0
|
|
Prateek Mehta answered |
As per the given data
⇒ α + β = - b/a = - ( - 3)/2 = 3/2
⇒ αβ = c/a = 2/2 = 1
For the new equation roots are α2 and β2
∴ sum of the roots α2 + β2 = (α + β)2 - 2αβ = (3/2)2 - 2(1) = 9/4 – 2 = ¼
Product of the roots = α2β2 = (αβ)2 = 12 = 1
⇒ Required equation = x2 – (sum of the roots)x + product of the roots = 0
⇒ x2 – (1/4)x + 1 = 0
⇒ 4x2 - x + 4 = 0
⇒ α + β = - b/a = - ( - 3)/2 = 3/2
⇒ αβ = c/a = 2/2 = 1
For the new equation roots are α2 and β2
∴ sum of the roots α2 + β2 = (α + β)2 - 2αβ = (3/2)2 - 2(1) = 9/4 – 2 = ¼
Product of the roots = α2β2 = (αβ)2 = 12 = 1
⇒ Required equation = x2 – (sum of the roots)x + product of the roots = 0
⇒ x2 – (1/4)x + 1 = 0
⇒ 4x2 - x + 4 = 0
A shop keeper sells an article at 20% loss. If he sells it for 100 more, he would earn a profit of 10%.The cost price is - a)Rs. 333.33
- b)Rs. 666.66
- c)Rs. 166.25
- d)Rs. 150.25
Correct answer is option 'A'. Can you explain this answer?
A shop keeper sells an article at 20% loss. If he sells it for 100 more, he would earn a profit of 10%.The cost price is
a)
Rs. 333.33
b)
Rs. 666.66
c)
Rs. 166.25
d)
Rs. 150.25
|
|
Anjali Roy answered |
As per the given data
Let the cost price be x and selling price be y
Given that shopkeeper sells an article at 20% loss
⇒ x – 20x/100 = y
⇒ 80x/100 = y
⇒ x = 5y/4
⇒ 4x - 5y = 0.…eq 1
Also given that if he sells it for 100 more, he would earn a profit of 10%
⇒ x + 10/100 x = y + 100
⇒ 11x = 10y + 1000
⇒ 11x - 10y = 1000.…eq 2
Multiply eq 1 with 2 , we get
⇒ 8x – 10 y = 0 …eq 3
⇒ subtract eq 3 from eq 2 , we get
⇒ 3x = 1000
⇒ x = 333.33
Therefore cost price of the article = Rs.333.33
Let the cost price be x and selling price be y
Given that shopkeeper sells an article at 20% loss
⇒ x – 20x/100 = y
⇒ 80x/100 = y
⇒ x = 5y/4
⇒ 4x - 5y = 0.…eq 1
Also given that if he sells it for 100 more, he would earn a profit of 10%
⇒ x + 10/100 x = y + 100
⇒ 11x = 10y + 1000
⇒ 11x - 10y = 1000.…eq 2
Multiply eq 1 with 2 , we get
⇒ 8x – 10 y = 0 …eq 3
⇒ subtract eq 3 from eq 2 , we get
⇒ 3x = 1000
⇒ x = 333.33
Therefore cost price of the article = Rs.333.33
Four identical circles of radius 4 cm each touch each other externally. The area of the region bounded by the four circles (in cm2) is
- a)16 π
- b)4(4 – π)
- c)16(4 – π)
- d)64(4 – π)
Correct answer is option 'C'. Can you explain this answer?
Four identical circles of radius 4 cm each touch each other externally. The area of the region bounded by the four circles (in cm2) is
a)
16 π
b)
4(4 – π)
c)
16(4 – π)
d)
64(4 – π)
|
Yash Saini answered |
Area of a square = side2
Area of a circle = πr2
The radius of each circle in the figure (r) = 4 cm.
We have constructed a square by joining the centers of 4 circles.
∴ Each side of the square = (4+4) cm. = 8 cm.
Now, if we consider any one of the circles it is clearly visible that the square includes ¼ th of each circle.
Now total area of all circles included inside the square
= 4 × [¼ × area of one circle]
= area of one circle
= 16 × π cm2 [∵ area of circle = π × r2]
The area of the square = 82 = 64 cm2
From the figure, the area of the region bounded by the four circles = the area of the square - total area of all circles included inside the triangle
⇒ The area of the region bounded by the four circles:
= [64 - 16 × π] cm.2
= 16 × [4 – π] cm.2
By selling cloth at Rs. 9 per metre, a shopkeeper loses 10%. Find the rate at which it should be sold so as to earn profit of 15%- a)Rs. 11.20
- b)Rs. 11.30
- c)Rs. 11.40
- d)Rs. 11.50
Correct answer is option 'D'. Can you explain this answer?
By selling cloth at Rs. 9 per metre, a shopkeeper loses 10%. Find the rate at which it should be sold so as to earn profit of 15%
a)
Rs. 11.20
b)
Rs. 11.30
c)
Rs. 11.40
d)
Rs. 11.50
|
|
Aarav Sharma answered |
Given:
Selling price of cloth = Rs. 9
Loss = 10%
To find:
Selling price to earn a profit of 15%
Solution:
Let the cost price of the cloth be Rs. x.
Selling price is Rs. 9, so we can write:
Selling price = Cost price - Loss
9 = x - 0.1x
x = 10
The cost price of the cloth is Rs. 10.
To earn a profit of 15%, the selling price should be:
Selling price = Cost price + Profit
Profit% is 15%, so Profit = 0.15x
Selling price = 10 + 0.15(10)
Selling price = 11.50
Therefore, the cloth should be sold at Rs. 11.50 to earn a profit of 15%. Hence, option (D) is the correct answer.
Selling price of cloth = Rs. 9
Loss = 10%
To find:
Selling price to earn a profit of 15%
Solution:
Let the cost price of the cloth be Rs. x.
Selling price is Rs. 9, so we can write:
Selling price = Cost price - Loss
9 = x - 0.1x
x = 10
The cost price of the cloth is Rs. 10.
To earn a profit of 15%, the selling price should be:
Selling price = Cost price + Profit
Profit% is 15%, so Profit = 0.15x
Selling price = 10 + 0.15(10)
Selling price = 11.50
Therefore, the cloth should be sold at Rs. 11.50 to earn a profit of 15%. Hence, option (D) is the correct answer.
ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F, G and H are the mid points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is- a)1:4
- b)2:3
- c)1:2
- d)1:3
Correct answer is option 'C'. Can you explain this answer?
ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F, G and H are the mid points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is
a)
1:4
b)
2:3
c)
1:2
d)
1:3
|
Mayank Kulkarni answered |
In Δ OAB,
Mid- point of OA = E
Mid- point of OB = H
Therefore,
EH|| AB
Therefore,
HE = AB/2
Similarly,
HG = BC/2
FG = CD/2
EF = AD/2
EF + HG + FG + EF = (1/2)(AB + BC + CD + AD)
⇒ Perimeter of EFGH = (1/2) perimeter of ABCD
So,
The ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD = 1:2
The average age of the boys in a class of 20 boys is 15.6 years. What will be the average age if 5 new boys come whose average is 15.4 years?- a)15.56 yrs
- b)15.65 yrs
- c)18 yrs
- d)16.56 yrs
Correct answer is option 'A'. Can you explain this answer?
The average age of the boys in a class of 20 boys is 15.6 years. What will be the average age if 5 new boys come whose average is 15.4 years?
a)
15.56 yrs
b)
15.65 yrs
c)
18 yrs
d)
16.56 yrs
|
Aaditya Shah answered |
We have, Average age = Sum of all ages/No. of persons
∴ 15.6 = Sum of 20 boys ages/ 20
⇒ Sum of ages of 20 boys = 20 × 15.6 = 312
After 5 new boys come, total boys = 20 + 5 = 25
Sum of ages of 5 new boys = 15.4 × 5 = 77
Sum of 25 boys ages = 312 + 77 = 389
Overall average = 389/25 = 15.56 yrs.
∴ 15.6 = Sum of 20 boys ages/ 20
⇒ Sum of ages of 20 boys = 20 × 15.6 = 312
After 5 new boys come, total boys = 20 + 5 = 25
Sum of ages of 5 new boys = 15.4 × 5 = 77
Sum of 25 boys ages = 312 + 77 = 389
Overall average = 389/25 = 15.56 yrs.
Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is- a)PT = 2PQ
- b)PT < PQ
- c)PT > PQ
- d)PT = PQ
Correct answer is option 'D'. Can you explain this answer?
Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is
a)
PT = 2PQ
b)
PT < PQ
c)
PT > PQ
d)
PT = PQ
|
|
Neha Datta answered |
We know that,
Property- If MNO is a secant to a circle intersecting the circle at M and N and OT is a tangent segment, then
OM × ON = OT2
From the diagram,
PAB is a secant to a circle with center O1 intersecting the circle at A and B and PT is a tangent segment,
∴ PA × PB = PT2 ……. (1)
Again, PAB is a secant to a circle with center O2 intersecting the circle at A and B and PQ is a tangent segment,
∴ PA × PB = PQ2 ……. (2)
From (1) and (2)
PT2 = PQ2
⇒ PT = PQ
The sum of all odd numbers between 11 and 61 is- a)818
- b)864
- c)860
- d)896
Correct answer is option 'B'. Can you explain this answer?
The sum of all odd numbers between 11 and 61 is
a)
818
b)
864
c)
860
d)
896
|
Siddharth Ghoshal answered |
Using Sum of Arithmetic Progression
Total odd numbers between 11 and 61, n = 24
Sum = n/2[a + l] = 24/2[13 + 59] (a = first term, l = last term)
= 24/2 × 72
= 864
Total odd numbers between 11 and 61, n = 24
Sum = n/2[a + l] = 24/2[13 + 59] (a = first term, l = last term)
= 24/2 × 72
= 864
Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?- a)56
- b)54
- c)36
- d)18
Correct answer is option 'B'. Can you explain this answer?
Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?
a)
56
b)
54
c)
36
d)
18
|
|
Neha Datta answered |
Let the total work be W units.
Amount of work done by Aman in one day = Am units
Amount of work done by Akbar in one day = Ak units
W = (Am + Ak) 18
Now this piece of work has been started, but both worked for only 4 days, after which Aman took over,
⇒ W = (Am + Ak) 4 + (Am) 42
⇒ (Am + Ak) 18 = (Am + Ak) 4 + (Am)42
⇒ (Am + Ak) 14 = (Am) 42
⇒ Am + Ak = 3 Am
⇒ Ak = 2 Am
Substituting the value of Ak in the very first equation, we have
W = (Am + 2 Am)18
⇒ W = 54 Am
Hence, Aman alone would have taken 54 days to complete the work.
Amount of work done by Aman in one day = Am units
Amount of work done by Akbar in one day = Ak units
W = (Am + Ak) 18
Now this piece of work has been started, but both worked for only 4 days, after which Aman took over,
⇒ W = (Am + Ak) 4 + (Am) 42
⇒ (Am + Ak) 18 = (Am + Ak) 4 + (Am)42
⇒ (Am + Ak) 14 = (Am) 42
⇒ Am + Ak = 3 Am
⇒ Ak = 2 Am
Substituting the value of Ak in the very first equation, we have
W = (Am + 2 Am)18
⇒ W = 54 Am
Hence, Aman alone would have taken 54 days to complete the work.
A kite is flying at a height of 80 m from the level ground, attached to a string inclined at 30° to the horizontal. The length of the string is?- a)160 m
- b)150 m
- c)180 m
- d)200 m
Correct answer is option 'A'. Can you explain this answer?
A kite is flying at a height of 80 m from the level ground, attached to a string inclined at 30° to the horizontal. The length of the string is?
a)
160 m
b)
150 m
c)
180 m
d)
200 m
|
|
Ashutosh Basu answered |
From the diagram,
Height of the kite = AB = 80 m
Angle of inclination of the string with horizontal = ∠ ACB = 30°
Length of the string = AC
From ΔABC,
sin ∠ACB = Perpendicular/Hypotenuse
⇒ sin 30° = AB/AC
⇒ 1/2 = 80/AC
⇒ AC = 160 m
A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?- a)110 minutes
- b)115 minutes
- c)120 minutes
- d) 121 minutes
Correct answer is option 'B'. Can you explain this answer?
A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?
a)
110 minutes
b)
115 minutes
c)
120 minutes
d)
121 minutes
|
|
Anirban Mukherjee answered |
Given, A can fill it in 20 minutes and B can empty it in 30 minutes
Pipe A's work for one minute=1/20
Pipe B's work for one minute=1/30
∴ Total work done in two minute
In every 2 minute, 1/60th work is done, which means upto 114th minute, amount of work done will be = 57 × 1/60 = 57/60
Now the remaining work i.e. 3/60 (=1/20th) will be done by A in next 1 minute.
∴ Total time required = 114 + 1 = 115 minutes
Pipe A's work for one minute=1/20
Pipe B's work for one minute=1/30
∴ Total work done in two minute
In every 2 minute, 1/60th work is done, which means upto 114th minute, amount of work done will be = 57 × 1/60 = 57/60
Now the remaining work i.e. 3/60 (=1/20th) will be done by A in next 1 minute.
∴ Total time required = 114 + 1 = 115 minutes
The side AC of the ΔABC is produced to D, such that CD = CB. If ∠ACB = 70°, then the value of ∠ADB is- a)35°
- b)40°
- c)45°
- d)55°
Correct answer is option 'A'. Can you explain this answer?
The side AC of the ΔABC is produced to D, such that CD = CB. If ∠ACB = 70°, then the value of ∠ADB is
a)
35°
b)
40°
c)
45°
d)
55°
|
|
Saikat Singh answered |
Now we see that Δ ADB is isosceles as CD = CB and the sum of ∠ CBD and ∠ CDB is 70° (exterior angle property of a triangle). So,
∠CBD = ∠CDB (isosceles triangle)
∠CBD + ∠CDB = 70°
⇒ 2 × ∠CDB = 70°
⇒ ∠ CDB = 35°
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number?- a)349
- b)546
- c)234
- d)179
Correct answer is option 'A'. Can you explain this answer?
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number?
a)
349
b)
546
c)
234
d)
179
|
|
Aarav Sharma answered |
To solve this problem, we need to find a number that satisfies the given conditions. Let's analyze the problem step by step.
Step 1: Understand the problem
We are given that when a certain number is divided by 13, the remainder is 11. This can be represented as:
Number = 13a + 11, where 'a' is an integer.
Similarly, when the same number is divided by 17, the remainder is 9. This can be represented as:
Number = 17b + 9, where 'b' is an integer.
Step 2: Set up the equations
We now have two equations based on the given conditions:
Equation 1: Number = 13a + 11
Equation 2: Number = 17b + 9
Step 3: Solve the equations
To find the value of the number, we can equate Equation 1 and Equation 2:
13a + 11 = 17b + 9
Step 4: Simplify the equation
Let's simplify the equation by rearranging the terms:
13a - 17b = 9 - 11
13a - 17b = -2
Step 5: Find a solution
To find a solution to this equation, we need to find values of 'a' and 'b' that satisfy it. We can do this by trial and error or by using the method of finding the least common multiple (LCM) of 13 and 17.
Step 6: Use LCM method
The LCM of 13 and 17 is 221. Therefore, we can rewrite the equation as:
17(13a) - 13(17b) = -2 * 221
Step 7: Simplify the equation further
221a - 221b = -442
Step 8: Find a solution
Dividing both sides of the equation by 221, we get:
a - b = -2
Step 9: Find the smallest positive solution
To find the smallest positive solution, we can substitute different values for 'a' and 'b' until we find a pair that satisfies the equation. In this case, the smallest positive solution is a = 1 and b = 3.
Step 10: Find the number
Substituting the values of 'a' and 'b' into Equation 1 or Equation 2, we can find the number:
Number = 13a + 11 = 13(1) + 11 = 24
Therefore, the number that satisfies the given conditions is 24.
However, the options provided in the question do not include 24. Hence, none of the given options is correct.
Step 1: Understand the problem
We are given that when a certain number is divided by 13, the remainder is 11. This can be represented as:
Number = 13a + 11, where 'a' is an integer.
Similarly, when the same number is divided by 17, the remainder is 9. This can be represented as:
Number = 17b + 9, where 'b' is an integer.
Step 2: Set up the equations
We now have two equations based on the given conditions:
Equation 1: Number = 13a + 11
Equation 2: Number = 17b + 9
Step 3: Solve the equations
To find the value of the number, we can equate Equation 1 and Equation 2:
13a + 11 = 17b + 9
Step 4: Simplify the equation
Let's simplify the equation by rearranging the terms:
13a - 17b = 9 - 11
13a - 17b = -2
Step 5: Find a solution
To find a solution to this equation, we need to find values of 'a' and 'b' that satisfy it. We can do this by trial and error or by using the method of finding the least common multiple (LCM) of 13 and 17.
Step 6: Use LCM method
The LCM of 13 and 17 is 221. Therefore, we can rewrite the equation as:
17(13a) - 13(17b) = -2 * 221
Step 7: Simplify the equation further
221a - 221b = -442
Step 8: Find a solution
Dividing both sides of the equation by 221, we get:
a - b = -2
Step 9: Find the smallest positive solution
To find the smallest positive solution, we can substitute different values for 'a' and 'b' until we find a pair that satisfies the equation. In this case, the smallest positive solution is a = 1 and b = 3.
Step 10: Find the number
Substituting the values of 'a' and 'b' into Equation 1 or Equation 2, we can find the number:
Number = 13a + 11 = 13(1) + 11 = 24
Therefore, the number that satisfies the given conditions is 24.
However, the options provided in the question do not include 24. Hence, none of the given options is correct.
Three students A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 2. B’s runs to C’s runs are also in the same ratio. Together they score 342 runs. Then the runs scored by B are- a)216
- b)108
- c)90
- d)171
Correct answer is option 'B'. Can you explain this answer?
Three students A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 2. B’s runs to C’s runs are also in the same ratio. Together they score 342 runs. Then the runs scored by B are
a)
216
b)
108
c)
90
d)
171
|
Subhankar Kumar answered |
Given, runs scored by A and B respectively are in the ratio 3 : 2.
∴ A’s score
Also B’s runs to C’s runs are also in the same ratio.
∴ B’s score : C’s score = 3 : 2
Together they scored 342 runs.
∴ A’s score + B’s score + C’s score = 342
⇒ B’s score = 108
∴ A’s score
Also B’s runs to C’s runs are also in the same ratio.
∴ B’s score : C’s score = 3 : 2
Together they scored 342 runs.
∴ A’s score + B’s score + C’s score = 342
⇒ B’s score = 108
Area of the circle inscribed in a square of diagonal 4 cm is- a)5 π
- b)4 π
- c)2 π
- d)√2 π
Correct answer is option 'C'. Can you explain this answer?
Area of the circle inscribed in a square of diagonal 4 cm is
a)
5 π
b)
4 π
c)
2 π
d)
√2 π
|
|
Sreemoyee Yadav answered |
Let, the side of square be a
Given,
Diagonal of square (d) = 4 cm
⟹ Side of square = Diameter of inscribed circle
Using Pythagoras theorem:
⟹ d2 = a2 + a2
⟹ (4)2 = 2a2
⟹ a = 2√2cm
∴ Radius of circle = √2cm
⟹ Area of circle = π × r2
∴ Area of circle = π × (√2)2 = 2π
Given,
Diagonal of square (d) = 4 cm
⟹ Side of square = Diameter of inscribed circle
Using Pythagoras theorem:
⟹ d2 = a2 + a2
⟹ (4)2 = 2a2
⟹ a = 2√2cm
∴ Radius of circle = √2cm
⟹ Area of circle = π × r2
∴ Area of circle = π × (√2)2 = 2π
If the diagonals of a rhombus are 24 and 10, then the value of thrice its side is- a)39
- b)36
- c)33
- d)42
Correct answer is option 'A'. Can you explain this answer?
If the diagonals of a rhombus are 24 and 10, then the value of thrice its side is
a)
39
b)
36
c)
33
d)
42
|
|
Sanaya Choudhary answered |
Half of each of the two diagonal forms the two sides of a right - angled triangle whose hypotenuse is the side of the rhombus.
Length of Diagonal 1 = 24
Length of Diagonal 2 = 10
⇒ Sides of the triangle = 12 and 5
Length of Diagonal 1 = 24
Length of Diagonal 2 = 10
⇒ Sides of the triangle = 12 and 5
Since it’s a right - angled triangle, it should follow Pythagoras theorem.
⇒ (Side)2 = (12)2 + (5)2
⇒ Side = 13
∴ Side of the rhombus = 13.
⇒ Thrice the value of the side = 3 × 13 = 39
⇒ (Side)2 = (12)2 + (5)2
⇒ Side = 13
∴ Side of the rhombus = 13.
⇒ Thrice the value of the side = 3 × 13 = 39
A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of top of the pole from each corner of the park is same, then in Δ ABC, the foot of the pole is at the- a)Centroid
- b)Circumcenter
- c)Incenter
- d)Orthocenter
Correct answer is option 'B'. Can you explain this answer?
A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of top of the pole from each corner of the park is same, then in Δ ABC, the foot of the pole is at the
a)
Centroid
b)
Circumcenter
c)
Incenter
d)
Orthocenter
|
|
Sagar Sharma answered |
Order to determine the height of the pole, we need more information about the park or the angles of elevation.
A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for is- a)20 days
- b)18 days
- c)16 days
- d) 24 days
Correct answer is option 'B'. Can you explain this answer?
A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for is
a)
20 days
b)
18 days
c)
16 days
d)
24 days
|
|
Nilesh Datta answered |
Given,
A can do a piece of work in 18 days
∴ Part of work done by A in 1 day = 1/18
B can do a piece of work in 36days
∴ Part of work done by B in 1 day = 1/36
C can do a piece of work in 72 days
∴ Part of work done by C in 1 day = 1/72
Let,
Total number of days they work = x days
Number of days A work = 8 days
∵ B leaves7 days before the completion of the work
Number of days B work = (x – 7) days
And, Number of days C work= x days
∴ {(1/18) × 8 } + {(1/36) × (x – 7)} + {(1/72) × x} = 1
⇒ 4/9 + (x – 7)/36 + x/72 = 1
⇒ (32 + 2x -14 + x)/72 = 1
⇒ 18 + 3x = 72
⇒ 3x = 54
⇒ x = 18 days
A can do a piece of work in 18 days
∴ Part of work done by A in 1 day = 1/18
B can do a piece of work in 36days
∴ Part of work done by B in 1 day = 1/36
C can do a piece of work in 72 days
∴ Part of work done by C in 1 day = 1/72
Let,
Total number of days they work = x days
Number of days A work = 8 days
∵ B leaves7 days before the completion of the work
Number of days B work = (x – 7) days
And, Number of days C work= x days
∴ {(1/18) × 8 } + {(1/36) × (x – 7)} + {(1/72) × x} = 1
⇒ 4/9 + (x – 7)/36 + x/72 = 1
⇒ (32 + 2x -14 + x)/72 = 1
⇒ 18 + 3x = 72
⇒ 3x = 54
⇒ x = 18 days
If the length of a chord is 24 cm which is at a certain distance from the centre of a circle of radius 13cm. Find distance between chord from centre of the circle?- a)8 cm
- b)4 cm
- c)5 cm
- d)10 cm
Correct answer is option 'C'. Can you explain this answer?
If the length of a chord is 24 cm which is at a certain distance from the centre of a circle of radius 13cm. Find distance between chord from centre of the circle?
a)
8 cm
b)
4 cm
c)
5 cm
d)
10 cm
|
Rajeev Verma answered |
From given data
Let AB = 24 cm be a chord of circle with center O and radius OA and OB equals to 13 cm
Draw OP perpendicular to AB
⇒ AP = AB/2 = 24/2 = 12 cm
From ΔOPA, we know that
⇒ OA2 = AP2 + OP2
⇒ 132 = OP2 + 122
⇒ 169 - 144 = OP2
⇒ OP = 5 cm
∴ Distance between chord from centre of the circle = OP = 5 cm
Let AB = 24 cm be a chord of circle with center O and radius OA and OB equals to 13 cm
Draw OP perpendicular to AB
⇒ AP = AB/2 = 24/2 = 12 cm
From ΔOPA, we know that
⇒ OA2 = AP2 + OP2
⇒ 132 = OP2 + 122
⇒ 169 - 144 = OP2
⇒ OP = 5 cm
∴ Distance between chord from centre of the circle = OP = 5 cm
A hollow sphere of internal and external radius 3 cm and 5 cm respectively is melted into a solid right circular cone of diameter 8 cm. The height of the cone is- a)24.5 cm
- b)25.5 cm
- c)22.5 cm
- d)23.5 cm
Correct answer is option 'A'. Can you explain this answer?
A hollow sphere of internal and external radius 3 cm and 5 cm respectively is melted into a solid right circular cone of diameter 8 cm. The height of the cone is
a)
24.5 cm
b)
25.5 cm
c)
22.5 cm
d)
23.5 cm
|
|
Naveen Roy answered |
We know that the formula of the volume of a hollow sphere is
4π(R3 – r3)
Here, R = external radius and r = internal radius
A hollow sphere of internal and external radius 3 cm and 5 cm respectively
So the volume of the hollow sphere = [4×π×(53 – 33)]/3 cc
Now, after melting this sphere, we will get a right circular cone, which’s diameter is 8 cm
So, radius of that cone = 8/2 cm = 4 cm
We know that the formula of the volume of a right circular cone is πr2h/3
Here, r is the radius of the cone and h is the height of the cone
From the question,
we can make the equation,
π × 42 × h/3 = [4×π×(53 – 33)]/3
⇒ 4h = 98
⇒ h = 24.5
So, the height of the cone is 24.5 cm
4π(R3 – r3)
Here, R = external radius and r = internal radius
A hollow sphere of internal and external radius 3 cm and 5 cm respectively
So the volume of the hollow sphere = [4×π×(53 – 33)]/3 cc
Now, after melting this sphere, we will get a right circular cone, which’s diameter is 8 cm
So, radius of that cone = 8/2 cm = 4 cm
We know that the formula of the volume of a right circular cone is πr2h/3
Here, r is the radius of the cone and h is the height of the cone
From the question,
we can make the equation,
π × 42 × h/3 = [4×π×(53 – 33)]/3
⇒ 4h = 98
⇒ h = 24.5
So, the height of the cone is 24.5 cm
In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?- a)45%
- b)35%
- c)20%
- d)40%
Correct answer is option 'D'. Can you explain this answer?
In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?
a)
45%
b)
35%
c)
20%
d)
40%
|
Pankaj Chatterjee answered |
From given data
No of students failed in Hindi n(H) = 35%
No of students failed in English n(E) = 45%
No of students failed in both n(H ∩ E) = 20%
⇒ total number of students who failed n(H ⋃ E) = n(H) + n(E) – n(H ∩ E)
⇒ n(H ⋃ E) = 35 + 45 - 20
⇒ n(H ⋃ E) = 60
No of students who passed = 100 - (total no of students who failed) = 100 – 60 = 40%
No of students failed in Hindi n(H) = 35%
No of students failed in English n(E) = 45%
No of students failed in both n(H ∩ E) = 20%
⇒ total number of students who failed n(H ⋃ E) = n(H) + n(E) – n(H ∩ E)
⇒ n(H ⋃ E) = 35 + 45 - 20
⇒ n(H ⋃ E) = 60
No of students who passed = 100 - (total no of students who failed) = 100 – 60 = 40%
A is thrice as fast as B and is therefore able to finish a work in 40 days less than that of B. Find the time in which they can do it working together.- a)20 days
- b)30 days
- c)25 days
- d)15 days
Correct answer is option 'D'. Can you explain this answer?
A is thrice as fast as B and is therefore able to finish a work in 40 days less than that of B. Find the time in which they can do it working together.
a)
20 days
b)
30 days
c)
25 days
d)
15 days
|
|
Pranjal Iyer answered |
Given,
Ratio of time taken by A and B = 1 : 3
∴ B takes 3 days to finish a unit work while A takes 1 day to finish the same work
The difference of time is 2 days
Given,
Difference of time is 40 days
∴ Time taken by B to complete the work = [(3/2) × 40] = 60 days
∴ A takes 20 days to finish a work
⇒ Work in 1 day by A = 1/20
⇒ Work in 1 day by B = 1/60
⇒ Work in 1 day by (A+B) = [(1/20) + (1/60)] = 4/60
∴ A and B will take days to complete the work = 15 days
Ratio of time taken by A and B = 1 : 3
∴ B takes 3 days to finish a unit work while A takes 1 day to finish the same work
The difference of time is 2 days
Given,
Difference of time is 40 days
∴ Time taken by B to complete the work = [(3/2) × 40] = 60 days
∴ A takes 20 days to finish a work
⇒ Work in 1 day by A = 1/20
⇒ Work in 1 day by B = 1/60
⇒ Work in 1 day by (A+B) = [(1/20) + (1/60)] = 4/60
∴ A and B will take days to complete the work = 15 days
In an examination, a student gets 20% of total marks and fails by 30 marks. Another student gets 32% of total marks which is more than the minimum pass marks by 42 marks. The pass percentage is- a)24%
- b)25%
- c)26%
- d)28%
Correct answer is option 'B'. Can you explain this answer?
In an examination, a student gets 20% of total marks and fails by 30 marks. Another student gets 32% of total marks which is more than the minimum pass marks by 42 marks. The pass percentage is
a)
24%
b)
25%
c)
26%
d)
28%
|
|
Prateek Mehta answered |
Let the total marks be X
Then, marks obtained by student 1 = 0.2X
Since, student 1 fails by 30 marks after getting 20% marks
∴ According to student1, Passing marks = 0.2X + 30
Similarly, Marks obtained by student 2 = 0.32X
And according to student 2, passing marks = 0.32X - 42;
Equating eq. 1 and 2, we get
0.2X + 30 = 0.32X - 42
⇒ X = 600
∴ Passing marks = (0.2 × 600) + 30 = 150
Passing marks %
Hence, the passing marks are 25%.
Then, marks obtained by student 1 = 0.2X
Since, student 1 fails by 30 marks after getting 20% marks
∴ According to student1, Passing marks = 0.2X + 30
Similarly, Marks obtained by student 2 = 0.32X
And according to student 2, passing marks = 0.32X - 42;
Equating eq. 1 and 2, we get
0.2X + 30 = 0.32X - 42
⇒ X = 600
∴ Passing marks = (0.2 × 600) + 30 = 150
Passing marks %
Hence, the passing marks are 25%.
If x = cosecθ − sinθ and y = secθ − cosθ, then the value of x2y2(x2 + y2 + 3)- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
If x = cosecθ − sinθ and y = secθ − cosθ, then the value of x2y2(x2 + y2 + 3)
a)
0
b)
1
c)
2
d)
3
|
Pranab Goyal answered |
Given:
If x = cosecθ - sinθ and y = secθ - cosθ
To find:
The value of x^2y^2(x^2 + y^2 + 3)
Solution:
Step 1: Calculate x^2 and y^2
x^2 = (cosecθ - sinθ)^2
x^2 = cosec^2θ + sin^2θ - 2cosecθsinθ
y^2 = (secθ - cosθ)^2
y^2 = sec^2θ + cos^2θ - 2secθcosθ
Step 2: Substitute x^2 and y^2 in the expression
x^2y^2(x^2 + y^2 + 3) = (cosec^2θ + sin^2θ - 2cosecθsinθ)(sec^2θ + cos^2θ - 2secθcosθ)(cosec^2θ + sin^2θ + sec^2θ + cos^2θ + 3)
Step 3: Simplify the expression
Upon simplification, the expression reduces to:
x^2y^2(x^2 + y^2 + 3) = 1
Therefore, the correct answer is option 'B' - 1.
If x = cosecθ - sinθ and y = secθ - cosθ
To find:
The value of x^2y^2(x^2 + y^2 + 3)
Solution:
Step 1: Calculate x^2 and y^2
x^2 = (cosecθ - sinθ)^2
x^2 = cosec^2θ + sin^2θ - 2cosecθsinθ
y^2 = (secθ - cosθ)^2
y^2 = sec^2θ + cos^2θ - 2secθcosθ
Step 2: Substitute x^2 and y^2 in the expression
x^2y^2(x^2 + y^2 + 3) = (cosec^2θ + sin^2θ - 2cosecθsinθ)(sec^2θ + cos^2θ - 2secθcosθ)(cosec^2θ + sin^2θ + sec^2θ + cos^2θ + 3)
Step 3: Simplify the expression
Upon simplification, the expression reduces to:
x^2y^2(x^2 + y^2 + 3) = 1
Therefore, the correct answer is option 'B' - 1.
A cricketer has a certain average of runs for his 6 innings. In the seventh inning he scores 100 runs, thereby increasing his average by 7 runs. His new average of runs is- a)52
- b)54
- c)58
- d)45
Correct answer is option 'C'. Can you explain this answer?
A cricketer has a certain average of runs for his 6 innings. In the seventh inning he scores 100 runs, thereby increasing his average by 7 runs. His new average of runs is
a)
52
b)
54
c)
58
d)
45
|
|
Juhi Nair answered |
Let the average of 6 innings be x.
Then new average can be found by (6x + 100)/7 = x + 7
⇒ 6x + 100 = 7x + 49
⇒ x = 51
∴ New average = 51 + 7 = 58
Then new average can be found by (6x + 100)/7 = x + 7
⇒ 6x + 100 = 7x + 49
⇒ x = 51
∴ New average = 51 + 7 = 58
The value of a machine depreciates every year at the rate of 10% on its value at the beginning of the year. If the current value of the machine is Rs.729, its worth 3 years ago was.- a)Rs. 1000
- b)Rs. 750.87
- c)Rs. 947.10
- d)Rs. 800
Correct answer is option 'A'. Can you explain this answer?
The value of a machine depreciates every year at the rate of 10% on its value at the beginning of the year. If the current value of the machine is Rs.729, its worth 3 years ago was.
a)
Rs. 1000
b)
Rs. 750.87
c)
Rs. 947.10
d)
Rs. 800
|
|
Aman Shah answered |
Let, x be the value of the machine 3 years ago
Since, the value of machine depreciates at the rate 10% every year
∴ its value after 1 year
Its value after 2 years
Its value after 3 years
According to the question,
0.729x = 729
x = 729/0.729 = 1000
Alternate:-
As we know that, if the value of machine depreciates by R% every year, then the value of machine after ‘t’ years will be:-
Here, P’ = future value of machine
P = current value.
Here it is given that, current value is Rs. 729 and we will have to find out the value 3 years ago.
So, here P’ = 729 and P = ?, R = 10%
⇒ P = 1000
Since, the value of machine depreciates at the rate 10% every year
∴ its value after 1 year
Its value after 2 years
Its value after 3 years
According to the question,
0.729x = 729
x = 729/0.729 = 1000
Alternate:-
As we know that, if the value of machine depreciates by R% every year, then the value of machine after ‘t’ years will be:-
Here, P’ = future value of machine
P = current value.
Here it is given that, current value is Rs. 729 and we will have to find out the value 3 years ago.
So, here P’ = 729 and P = ?, R = 10%
⇒ P = 1000
A and B can together do a piece of work in 28 days. If A, B and C can together finish the work in 14 days, how long will C take to do the work by himself?- a)7 days
- b)21 days
- c)28 days
- d)35 days
Correct answer is option 'C'. Can you explain this answer?
A and B can together do a piece of work in 28 days. If A, B and C can together finish the work in 14 days, how long will C take to do the work by himself?
a)
7 days
b)
21 days
c)
28 days
d)
35 days
|
|
Maulik Banerjee answered |
If A and B can together do a piece of work in 28 days which means in 1 day, A and B will finish 1/28th of the work.
If A, B and C can together finish the work in 14 days which means in 1 day, A, B and C will finish 1/14th of the work.
Putting the first value in second
If A, B and C can together finish the work in 14 days which means in 1 day, A, B and C will finish 1/14th of the work.
Putting the first value in second
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4 – b4) always divisible?- a)3
- b)6
- c)8
- d)12
Correct answer is option 'C'. Can you explain this answer?
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4 – b4) always divisible?
a)
3
b)
6
c)
8
d)
12
|
Anu Sarkar answered |
We know that, Summation and Subtraction between two odd integers gives an even integer.
Given, a and b are two odd positive integers.
∴ a + b = 2k1 ……(1)
And a – b = 2k2 ........(2)
Where, k1 and k2are two integers.
(1) + (2) ⇒ 2a = 2(k1 + k2) ⇒ a = k1 + k2
(1) - (2) ⇒ 2b = 2(k1 - k2) ⇒ b = k1 - k2
∴ a2 + b2
= (k1 + k2)2 + (k1 - k2)2
= k12 + k22 + 2k1k2 + k12 + k22 - 2k1k2
= 2(k12 + k22) ………..(3)
Given expression is,
a4 – b4
= (a2 – b2)(a2 + b2)
= (a + b) (a - b)(a2 + b2)
Putting values from (1), (2) and (3)
= 2k1 × 2k2 × 2(k12 + k22)
= 8× k1 × k2 × (k12 + k22)
∴ a4 – b4 = 8× k1 × k2 × (k12 + k22) is always divisible by 8.
Given, a and b are two odd positive integers.
∴ a + b = 2k1 ……(1)
And a – b = 2k2 ........(2)
Where, k1 and k2are two integers.
(1) + (2) ⇒ 2a = 2(k1 + k2) ⇒ a = k1 + k2
(1) - (2) ⇒ 2b = 2(k1 - k2) ⇒ b = k1 - k2
∴ a2 + b2
= (k1 + k2)2 + (k1 - k2)2
= k12 + k22 + 2k1k2 + k12 + k22 - 2k1k2
= 2(k12 + k22) ………..(3)
Given expression is,
a4 – b4
= (a2 – b2)(a2 + b2)
= (a + b) (a - b)(a2 + b2)
Putting values from (1), (2) and (3)
= 2k1 × 2k2 × 2(k12 + k22)
= 8× k1 × k2 × (k12 + k22)
∴ a4 – b4 = 8× k1 × k2 × (k12 + k22) is always divisible by 8.
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