Test: Elementary Mathematics - 7 - CDS MCQ

Given: (1 -)(1 +)(1 +)(1 +)
We can write:
(1 -) = ()
(1 +) = ()
(1 +) = ()
(1 +) = ()
Now, combine all equations.
= ()()()()
= ()()()()
= ()

In triangle ABC,
A – B = π/2 radian ...(1)
Also,
A + B + C = π radian ...(2)
Subtracting (1) from (2), we get
C + 2B = π/2 radian

Let the original SP be Rs. x.
According to the given data,
x – (25/100)x  = Rs. 4,875
(3/4)x = 4875
x = (4875 x 4)/3 
x = Rs. 6,500

Let the average speed of the cyclist be x kmph.
According to the given condition,

x² - x = 42
x = 7, -6
Since x cannot be negative
So, x = 7
So, the speed of cyclist = 7 km/h

If a sum of money at a certain rate of simple interest per year doubles in 5 years, then the rate of interest (R) = 100/5 = 20%.
If a sum of money at certain rate of simple interest per year becomes three times in 12 years, then the rate of interest = 200/12 = 16.67%.
Difference = 20 - 16.67 = 3.33 = 3(1/3)%

We already know the radii of the circles, and the triangle is formed by the diameter of each circle, so the perimeter of the triangle would be double the sum of the radii of all the circles.
Perimeter = 2 × (sum of radii of all the circles)
= 2 × (12 + 16 + 10)
= 2 × (38)
= 76 cm

1 litre of liquid cost = Rs. 12
Let l litre of water be added.
Then, cost price = Rs. 12
Selling price = Rs. 13.75(1 + l)
So, 13.75 x (1 + l) = 1.25 x 12
13.75 + 13.75l = 15
l = 1.25/13.75 = 1/11
Required ratio = 1 : 11

The side length of the square is 2 units; thus, the diameter of the circle has length 2√2 units.
This is also the length of the diagonal AC (or BD). The area of the circle is thus π(√2)² = 2π sq. units.
Since the side length of the square is 2 units, it will have an area of 4 sq. units. From this, we calculate the area of the circle outside the square to be (2π - 4) sq units. To calculate the shaded area, we first calculate the area of each semicircle. Each of the semicircles has a radius of 1 unit, meaning that each semicircle will have an area of π sq. units. In total, the four semicircles have an area of 2π sq. units. Thus, the shaded area has an area of 2π - (2π - 4) = 4 sq. units.

Suppose the number is in the form of 10a + b.
So,
So, 1(10b + a) + 18 = 10a + b
a - b = 2 ... (1)
Now, 10a + b + 33 = a² + b²
10a + (a - 2) + 33 = a² + (a - 2)² [From (1)]
2a(a - 9) + 3(a - 9) = 0
(a - 9) (2a + 3) = 0
So, a = 9 (valid) or -(3/2) (invalid)
And b = 7
Hence, required number = 97.

Average speed = Total distance/Total time taken

Thus, the average speed was 4.4 km/hr.

Given: = 6
xy = 36 ... (i)
And
⇒ xyz = 216 ... (ii)
On dividing equation (ii) by equation (i), we have

⇒ z = 6
This is the correct answer.

Clearly,
Mean =
Now, to find the median, arrange the data in ascending or descending order, as shown below:
144, 150, 155, 161, 165
Here, n = 5, which is odd.
∴ Median = observation = 3^rd observation = 155
Thus, Median = 155 and Mean = 155
This is correct answer.

Let x and y be the two positive numbers [x < y].
y – x = 16 ... (1)
x = (3/5)y
Putting in (1),
y – (3/5)y = 16
5y – 3y = 80
2y = 80
y = 40
40 – x = 16
x = 40 – 16
x = 24

Let r₁ and r₂ be the radii of two circles such that r₁ : r₂ = 16 : 9.
Then, ratio of expenditures of A and B = Ratio of areas of corresponding circles

= 256/81
= 25600/8100
The appropriate data used the above mentioned pie diagram is: Rs. 25,600 and Rs. 8,100.

Joining the lines as shown in the figure, we get two quadrilaterals.
Sum of 4 angles of a quadrilateral = 360º
Required sum = 360º × 2 = 720º

2x - ky = k - 1
3x - 15y = 2k - 7
Comparing above equations by 
a₁x + b₁y = c₁
a₂x + b₂y = c₂
we get,

For unique solution,

k ≠ 10

a² + b² = 2ab
⇒ a² + b² – 2ab = 0
(a – b)² = 0
a – b = 0
a = b
Therefore, option 3 is correct.

Let DC = x
BD = 2x (Given: BD = 2DC)
Since ED || AB
ΔEDC is similar to ΔABC.
=
⇒ = 9
= = 9
⇒ = 9 {Here, y sq. cm = area of triangle EDC}
⇒ 64 + y = 9y
⇒ 64 = 8y
⇒ y = 8 sq. cm

We know that if and are the respective means (average) of n₁ and n₂ observations, then the combined mean (average) is:

Total number of students = n₁ + n₂ = 22 + 28 = 50

Required average = = = = 146.72 cm

Sum of zeros =
3 = -(b/1)
b = -3
Product of zeros =
-24 = (-d)/1
d = 24
Sum of product of zeros taken two at a time =
-10 = c/1
c = -10
Hence, (4) is the correct option.

ax + by + c = 0 …. (1)
px + my + n = 0 .… (2)
Using cross-multiplication method:

Or

Or

Also,

Hence, the denominator of x and y is (am – bp).

We know, Time = distance/speed
^{Distance between policeman and thief = 100 m;}
Since speed of the thief is 8 km/hr and that of the policeman is 10 km/hr;
∴ Relative speed = 10 – 8 = 2 km/hr = 2 × (5/18) = 5/9 m/s
∴ Time taken by police to overtake the thief = (100/5)× 9 = 180 s
Hence,
Distance travelled by the thief in 180 sec= 8 × (5/18)m/s = (20/9)m/s × 180 s = 400 m

= 1 ...(1)
= 1 ...(2)
Squaring both equations and adding, we get

So,

Here, tanθ + cotθ = 4/√3

sinθ x cosθ =
Let sinθ = x.
x =
On comparing with , we get x = .
Thus, sinθ =
So, sinθ + cosθ = (For both values of x).

Let DC = x
BD = 2x (Given: BD = 2DC)
Since ED || AB
ΔEDC is similar to ΔABC.
=
⇒ = 9
Hence, 9 : 1.