All India CAT Group

What is the remainder when 36001 + 76000 is divided by 13?
  • a)
    9
  • b)
    10
  • c)
    4
  • d)
    3
Correct answer is option 'C'. Can you explain this answer?

Kunaal Satija answered
36001 = 3 ⋅ (36000) = 3 ⋅ (36)1000 = 3 ⋅ (729)1000 = 3(728 + 1)1000
728 is divisible by 13, so the remainder is 3.
76000 = (74)1500 = (2401)1500 = (2392 + 9)15002392 is divisible by 13, so we have to find the remainder when 91500 is divided by 13.
91500 = (36)500 = (729)500 = (728 + 1)500
since 728 is divisible by 13, therefore the remainder is 1.
So the net remainder = 3 + 1 = 4

a, b and c are positive real numbers such that a + b + c = p, where 'p' is a constant. Find the maximum value of (p - a) (p - b)(p - c).
  • a)
    (p3 - abc)
  • b)
    8p3/27
  • c)
    5p3/16
  • d)
    9p3/8
Correct answer is option 'B'. Can you explain this answer?

Kunaal Satija answered
(p − a), (p − b) and (p − c) all are positive numbers.
∴ AM ≥ GM
Hence (b) is the correct answer.
Alternative Method:
(p − a) + (p − b) + (p − c) = 2p(constant)
⇒ (p − a)⋅(p − b)⋅(p − c) will be maximum when
p − a = p − b = p − c = 2p/3
Maximum value of the product

How many integers “a” are there such that 9x2 + 3ax + (a + 5) > 0 for all values of x ?
  • a)
    7
  • b)
    8
  • c)
    9
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?

Kunaal Satija answered
If 9x2 + 3ax + (a + 5) > 0 for all values of x, then the discriminant of this quadratic expression must be negative.
⇒ (3a)2 -4(9) (a + 5) < 0="" or="" />2 - 4a - 20 < 0="" or="" r="" (a="" -="" />2 < />
⇒ -2.89
⇒ a = -2, -1,0, 1, 2, 3, 4, 5, 6
⇒ there are 9 such integral values.
Hence (c) is the correct option.

A manufacturing company conducted workshops on three techniques namely designing, formatting and testing for its executives. The number of executives who attended the workshop on designing is twice and thrice of the number of executives who attended the workshops on formatting and testing respectively. 42 executives attended the workshop on formatting. The aggregate number of executives who attended the workshops on exactly two techniques is at most 25% of the aggregate number of executives who attended the workshops on exactly one technique. Workshops on any combination of exactly two techniques were attended by more than 1 executive.
If the minimum possible executives attended the workshop on all three techniques, then find the minimum possible number of executives who attended the workshop on designing only.
  • a)
    56
  • b)
    61
  • c)
    62
  • d)
    63
Correct answer is option 'B'. Can you explain this answer?

Kunaal Satija answered
Minimum possible number of executives who attended the workshop on all three techniques = 0.
Since we have to minimise the number of executives who attended the workshop on only designing, we have to maximise the number of executives who attended the workshop on designing, formatting and testing.
A minimum number of employees who attended the workshop on formatting and testing = 2.
A + 2B = 154.
Maximum possible value of B = 25 (Since maximum possible value of B = 0.25A)
The minimum possible value of the number of executives who attended the workshop on only designing.
= 84-(25 - 2) = 61.

Find all the values of p, such that 6 lies some where between the roots of the equation
x2 + 2(p - 3)x + 9 = 0. (‘x’ is a real number).
  • a)
    p < />
  • b)
    P > 6
  • c)
    0 < p="" />< />
  • d)
    0 < p="" />< />
Correct answer is option 'A'. Can you explain this answer?

Kunaal Satija answered
Both the roots will be real as 6 lies between the roots
(i) b2 − 4ac > 0
= 4(p − 3)2 − 4 × 9 > 0P(P − 6) > 0
p > 6 or p < />
(ii), since x = 6 lies between the two roots.
so, (6)2 + 2(p − 3)6 + 9 < />
Hence the correct option is A.

How many sets of three distinct factors of the number N = 26 x 34 x 52 can be made such that the factors in each set have a highest common factor of 1 with respect to every other factor in that set?
  • a)
    236
  • b)
    360
  • c)
    104
  • d)
    380
Correct answer is option 'A'. Can you explain this answer?

Kunaal Satija answered
N = 26 × 34 × 52
Case: [A]
when none of the elements is 1 ⇒ the three factors must be some powers of 2, 3, 5 respectively.
⇒ total number of such sets = 6 × 4 × 2 = 48
Case: [B]
when one of the elements is 1
⇒ the other two factors could be of the form (2a), (3b) − number of sets = 6 × 4 = 24
(26), (52) − number of sets = 6 × 2 = 12
(34),(52) − number of sets = 4 × 2 = 8
(26 × 34 × 52) − number of sets = 6 × 4 × 2 = 48
(26 × 52 × 34) − number of sets = 6 × 2 × 4 = 48
(34 × 52 × 26) − number of sets = 4 × 2 × 6 = 48
∴ total number of such sets = 188
combining both the cases, total sets possible
= 188 + 48 = 236

A combo pack having a bulb and a tube light costs Rs. 52. If the cost of the bulb drops by 20% and the cost of the tube light escalates by 50%. the pack would cost Rs. 50. Find the price of a tube light?
  • a)
    Rs.8
  • b)
    Rs.9
  • c)
    Rs.10
  • d)
    Rs.10
Correct answer is option 'D'. Can you explain this answer?

Kunaal Satija answered
Cost of a tubelight = t and cost of a bulb = b.
t + b = 52
cost of bulb drops by 20% and cost of tubelight increases by 50%
⇒1.5t + 0.8b = 50
Solving the two equations in t and b
t + b = 52.......(i)
1.5t + 0.8b = 50.......(ii)
Multiplying (i) equation by 4 and (ii) equation by 5
4t + 4b = 2087.5t + 4b = 250
Subtracting
3.5 t = 42
⇒ t = 12
Thus, the cost of a tube light = Rs. 12

Answer the questions on the basis of the information given below:
A, B, C. D and E are five brothers. They have assets in the form of flats and cash only. Together they have 9 flats and each brother has at least 1 flat. Value (in terms of rupees) of all flats is equal and constant. Cash with each brother is an integral multiple of Rs. 10 lakhs. The amount of cash with B is just enough to buy one more flat, all the other brothers have cashless than that of B. E has got the maximum number of flats. A number of flats with A is equal to the sum of the number of flats with B and C. Amount of cash with B is double of that with D, but D has got assets worth Rs. 20 lakhs more than that of B.
For how many brothers is it possible to find out the exact value of their total assets?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Kunaal Satija answered
E has got the maximum number of flats and number of flats with A is equal to the sum of a number of flats with B and C. As there are 9 flats, so possible solutions are when E, A, B, C and D have 3, 2, 1, 1 and 2 or 4, 2, 1. 1 and 1 flats respectively.
Case I:B and D have one flat and two flats respectively.
Let the value of a flat be Rs. x. So, the amount of cash with B = x.
So total assets of B = 2x
Total assets of As D has got assets worth 20 lakhs more than that of B
Case II:
B and D have one flat each.
Let value of a flat be Rs. x. So, amount of cash with B = x
⇒ Total assets of B = 2x
Total assets of
As D has got assets worth 20 lakhs more than B
Here the value of x is coming as negative. So this case is not possible.
We can collate the final distribution of assets in the following table:
According to the table B and D buy 1 and 2 flat respectively.
So, Only for B and D, it is possible to find the exact value of their total assets.​
Only 2 brothers find out the exact value of their total assets.
Hence the correct option is B.

All natural numbers that give remainders 1 and 2 when divided by 6 and 5, respectively, are written in ascending order, side by side from left to right. What is the 99th digit from the left?
  • a)
    2
  • b)
    7
  • c)
    1
  • d)
    0
Correct answer is option 'D'. Can you explain this answer?

Kunaal Satija answered
Natural numbers which when divided by 5 give a remainder 2 are given by 5K + 2 [‘k’ is a whole number].
Natural numbers which when divided by 6 give a remainder 1 are given by 6m +1 [‘m’ is a whole number].
5k + 2 = 6m + 1 or 6m - 5k = 1.
All such natural numbers are 7, 37, 67, 97,127
Numbers when written one beside the other
7, 37, 67, 97, 127, 157, 187, 217, 247, 277, 307, 337.......so on.
Observe the series.
The first 4 numbers give first 7 digits. After these 4 numbers, 3 digit numbers follow. The 3 digit numbers from an A.P. with common difference 30.
First three digit number = 127
The 30th 3-digit number is = 127 + (30 -1) × 30
= 997
=> The first 34 numbers (= 4 + 30) give 97 digits (= 7 + 3 × 30)
The next number in this A.P is 997 + 30 = 1027
=> the 99th digit is 0.
Hence answer is an option (d).

Answer the questions on the basis of the information given below:
A, B, C. D and E are five brothers. They have assets in the form of flats and cash only. Together they have 9 flats and each brother has at least 1 flat. Value (in terms of rupees) of all flats is equal and constant. Cash with each brother is an integral multiple of Rs. 10 lakhs. The amount of cash with B is just enough to buy one more flat, all the other brothers have cashless than that of B. E has got the maximum number of flats. A number of flats with A is equal to the sum of the number of flats with B and C. Amount of cash with B is double of that with D, but D has got assets worth Rs. 20 lakhs more than that of B.
What is the ratio of the maximum possible value of assets of E to the minimum possible value of assets of C?
  • a)
    5 : 2
  • b)
    4 : 1
  • c)
    2 : 1
  • d)
    3 : 1
Correct answer is option 'D'. Can you explain this answer?

Kunaal Satija answered
E has got the maximum number of flats and number of flats with A is equal to the sum of a number of flats with B and C. As there are 9 flats, so possible solutions are when E, A, B, C and D have 3, 2, 1, 1 and 2 or 4, 2, 1. 1 and 1 flats respectively.
Case I:B and D have one flat and two flats respectively.
Let the value of a flat be Rs. x. So, the amount of cash with B = x.
So total assets of B = 2x
Total assets of As D has got assets worth 20 lakhs more than that of B
Case II:
B and D have one flat each.
Let value of a flat be Rs. x. So, amount of cash with B = x
⇒ Total assets of B = 2x
Total assets of
As D has got assets worth 20 lakhs more than B
Here the value of x is coming as negative. So this case is not possible.
We can collate the final distribution of assets in the following table:
Maximum possible assets of E = 150 lakhs and minimum possible assets of C = 50 lakhs. so, Ratio is = 3 : 1​.

Answer the questions on the basis of the information given below:
A, B, C. D and E are five brothers. They have assets in the form of flats and cash only. Together they have 9 flats and each brother has at least 1 flat. Value (in terms of rupees) of all flats is equal and constant. Cash with each brother is an integral multiple of Rs. 10 lakhs. The amount of cash with B is just enough to buy one more flat, all the other brothers have cashless than that of B. E has got the maximum number of flats. A number of flats with A is equal to the sum of the number of flats with B and C. Amount of cash with B is double of that with D, but D has got assets worth Rs. 20 lakhs more than that of B.
What is the value of 1 flat?
  • a)
    Rs. 45 lakhs
  • b)
    Rs. 35 lakhs
  • c)
    Rs. 40 lakhs
  • d)
    Rs. 30 lakhs
Correct answer is option 'C'. Can you explain this answer?

Kunaal Satija answered
E has got the maximum number of flats and number of flats with A is equal to the sum of a number of flats with B and C. As there are 9 flats, so possible solutions are when E, A, B, C and D have 3, 2, 1, 1 and 2 or 4, 2, 1. 1 and 1 flats respectively.
Case I:B and D have one flat and two flats respectively.
Let the value of a flat be Rs. x. So, the amount of cash with B = x.
So total assets of B = 2x
Total assets of As D has got assets worth 20 lakhs more than that of B
Case II:
B and D have one flat each.
Let value of a flat be Rs. x. So, amount of cash with B = x
⇒ Total assets of B = 2x
Total assets of
As D has got assets worth 20 lakhs more than B
Here the value of x is coming as negative. So this case is not possible.
We can collate the final distribution of assets in the following table:
In above table B's flat is 40 lacks so,value of 1 flat is Rs 40 lacks.

A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:
Correct answer is '50'. Can you explain this answer?

Kunaal Satija answered
Total cost price Rs. 1600 Let CP1 = 600 and CP2 = 1000
Case I, When he sells first at 10% profit and second at 20% profit:
∴ Profit on CP1 = 10% on 600 = Rs. 60
Profit on CP2 = 20% on 1000 = Rs. 200
Total Profit = ₹ 260 ...(i) Case II, When he sells first at 20% profit and second at 10% profit:
∴ Profit on CP1 = 20% on 600 = Rs. 120
Profit on 2 = 10% on 1000 = Rs. 100
Total Profit = Rs. 220...(ii)
Difference in Profit [(i)−(ii)} = 260 − 220 Rs.
= Rs. 40
When difference in profit is Rs. 40, then difference in cost price would be Rs. (1000 − 600) = Rs. 400.
When difference in profit is Rs. 5, then difference in cost price would be:
Rs. =((400/40) × 5)
= Rs. 50.
Hence, the correct answer is 50.

A number when divided by 2567, gives a remainder of 147. If the same number is divided by 17, then what will be the remainder?
Correct answer is '11'. Can you explain this answer?

Kunaal Satija answered
We know that,
Dividend = (Quotient × Divisor) + Remainder
Let the quotient is k.
Dividend = 2567k + 147
When the number is divided by 17.
(2567k + 147/17) = 151k + (147/17)
While solving we get quotient as 8 and remainder = 11
∴ The required remainder is 11.
Hence, the correct answer is 11.

In a football World Cup several teams participated. If the last place team in the point table receive $40,000 as a prize money and the award increases by $2500 for the successive finishing places. The champion team receives $65,000. Find how many teams participated in the world cup?
Correct answer is '11'. Can you explain this answer?

Kunaal Satija answered
Given
Last team received $40,000.
Champion team received $65,000.
Award increases by $2500 for the successive finishing places.
Prizes received by the teams in increasing order are, $40,000, $42500, $4500, $47500,
This is an A.P. with a = 40,000, d = 2500 and I = 65,000
Let the number of terms be n. Then,
an = 65000
a + (n − 1)d = 65000
⇒ 40000 + (n − 1) × 2500 = 65000
⇒ (n − 1) × 2500 = 65000 − 40000
⇒ (n − 1) = 25000/2500
⇒ n − 1 = 10
⇒ n = 10 + 1
n = 11
∴ 11 teams participated in Football World Cup.
Hence, the correct answer is 11.

If 10Pr = 5040, then r = ?
Correct answer is '4'. Can you explain this answer?

Kunaal Satija answered
We know that
nPr = n!/(n−r)! = n × (n − 1)×….×(n−r+1)
Given that:
10Pr = 5040
⇒ 10Pr = 10 × 504
⇒ 10Pr = 10 × 9 × 56
⇒ 10Pr = 10 × 9 × 8 × 7
⇒ 10Pr = 10 × (10 − 1) × (10 − 2) × (10 − 4 + 1)
On comparing the above expression with nPr = n × (n − 1)×……×(n − r + 1), we get:
r = 4
Hence, the correct answer is 4.
Sushila asked a question

“How we spend our days is, of course, how we spend our lives,” Annie Dillard wrote in her timeless reflection on presence over productivity — a timely antidote to the central anxiety of our productivity-obsessed age. Indeed, my own New Year’s resolution has been to stop measuring my days by degree of productivity and start experiencing them by degree of presence. But what, exactly, makes that possible?
This concept of presence is rooted in Eastern notions of mindfulness — the ability to go through life with crystalline awareness and fully inhabit our experience — largely popularized in the West by British philosopher and writer Alan Watts (January 6, 1915-November 16, 1973), who also gave us this fantastic meditation on the life of purpose. In the altogether excellent 1951 volume The Wisdom of Insecurity: A Message for an Age of Anxiety (public library), Watts argues that the root of our human frustration and daily anxiety is our tendency to live for the future, which is an abstraction. What keeps us from happiness, Watts argues, is our inability to fully inhabit the present.
The “primary consciousness,” the basic mind which knows reality rather than ideas about it, does not know the future. It lives completely in the present, and perceives nothing more than what is at this moment. The ingenious brain, however, looks at that part of present experience called memory, and by studying it is able to make predictions. These predictions are, relatively, so accurate and reliable (e.g., “everyone will die”) that the future assumes a high degree of reality — so high that the present loses its value.
But the future is still not here, and cannot become a part of experienced reality until it is present. Since what we know of the future is made up of purely abstract and logical elements — inferences, guesses, deductions — it cannot be eaten, felt, smelled, seen, heard, or otherwise enjoyed. To pursue it is to pursue a constantly retreating phantom, and the faster you chase it, the faster it runs ahead. This is why all the affairs of civilization are rushed, why hardly anyone enjoys what he has, and is forever seeking more and more. Happiness, then, will consist, not of solid and substantial realities, but of such abstract and superficial things as promises, hopes, and assurances.
Q.Which of the following would weaken Watt’s argument?
... more

It takes 10 hours for a person to travel a distance. If he reduces his speed by 20%, then what is the percentage increase in the time taken to cover the same distance?
Correct answer is '25'. Can you explain this answer?

Kunaal Satija answered
Given
Let, speed be x km/hour.
It takes 10 hours to travel the distance.
That means total distance = 10x km
Latter speed =
x(100 – 20)/100 = 4x/5 km/hour
Time taken to cover the whole distance at this speed is 10x/(4x/5) = 12.5 hour
Time increase = (12.5 – 10) hours = 2.5 hours
Percentage increase in time taken =
(2.5/10) × 100 = 25%
Hence, the correct answer is 25%.

How many words can be formed with the letters of the word VOWELS that begin with O and end with E?
Correct answer is '24'. Can you explain this answer?

Kunaal Satija answered
We know that
Number of arrangement of n different objects is given by n!
n! = n×(n−1)×…×1
The word VOWELS contains 6 letters, in which all the different letters occur only once.
Now, after fixing O in first place and E in the last place, we have only 4 letters.
∴ Number of words =4!=24.
Hence, the correct answer is 24.

A train 1350 m long takes 135 seconds to cross a man running at a speed of 5kmph in a direction same to that of the train. What is the speed of the train?
Correct answer is '41'. Can you explain this answer?

Kunaal Satija answered
The length of the train = 1350 m
Speed of men = 5 km/h
Time to cross the men = 135 seconds
Let the speed of the train be x km/h
Relative speed = (x − 5)km/h
⇒ (x − 5) = (1350 × 18)/(135 × 5)
⇒ x − 5 = 36
⇒ x = 36 + 5 = 41 km/h
So, 41 km/h is the speed of train
Hence, the correct answer is 41 km/h.

The sum of radii spheres A and B is 14 cm, the radius of A being larger than that of B. The difference between their surface areas is 112π. What is the ratio of the volumes of A and B?
Correct answer is '64 : 27'. Can you explain this answer?

Kunaal Satija answered
Given
The Difference between the surface area of the spheres is 112π
The sum of the radii of spheres of A and B is 14 cm
Radius of A is larger than the radius of B
As we know,
Area of a sphere =4πr2 (where ' r′ is the radius of the sphere)
Volume of a sphere
= (4/3)πr3
Let the radius of the circle A be ′a′
Let the radius of the circle B be ' b '
Difference of the surface area of the circle is 112π
4πa2 − 4πb2 = 112π
(a + b)⋅(a − b) = 28
a − b = 2 [Given, (a + b) = 2]
a + b = 14… (i)
a − b = 2… (ii)
Solving equation (i) and (ii)
⇒ a = 8 and b = 6
So,
Volume of sphere with radius a cm : volume of sphere with radius b cm=4πa3:4πb3
= 83:63
= 512:216
= 64:27
∴ The ratio of the volume will be 64:27.
Hence, the correct answer is 64:27.

The coefficient of the term independent of x in the expansion of is
Correct answer is '5/3'. Can you explain this answer?

Kunaal Satija answered
The (r+1) th term in the expansion of is given by
For term to be independent of x,
5 - (5r/2) = 0
⇒ r = 2
Substituting the values in (1) we get:
T3 = (−1)210C23−3= 10(9)/2(27)
= 5/3
Hence, the correct answer is 5/3.

Point Q(b,−1) is the midpoint of segment EF. Co-ordinates of point E are (−4, a) and point F are (2,0). What is the value of a and b?
Correct answer is '-2, -1'. Can you explain this answer?

Kunaal Satija answered
Given,
Point Q(b,−1) is the midpoint of segment with endpoints E(−4, a) and F(2, 0).
As we know,
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by,
On comparing, we get
b = −1, a = −2
Hence, the correct answer is a = -2, b = -1.

The range of the real-valued function f(x) = is:
Correct answer is '0,3'. Can you explain this answer?

Kunaal Satija answered
Given: f(x) =
Let, y2 = 9 - x2
⇒ x2 = 9 - y2
x = ...(1)
We know that for any function f(x)= ,y ≥ 0…. (A)
From equation (1).
9 − y2 ≥ 0
y2 − 9 ≤ 0
⇒ (y + 3)(y − 3) ≤ 0
⇒ −3 ≤ y ≤ 3
But from equation (A) y must be positive, then, y = [0, 3].
Range = the value of y = [0, 3]
Hence, the correct answer is [0, 3].

If the number 2632A4878 is completely divisible by 9 . Find the possible value of ' A′?
Correct answer is '5'. Can you explain this answer?

Kunaal Satija answered
Given,
Number 2632A4878 is divisible by 9.
The Sum of all digits should be divisible by 9.
The number is 2632 A4878.
= 2 + 6 + 3 + 2 + A + 4 + 8 + 7 + 8
= 40 + A
Put A = 5
= 40 + 5 = 45
⇒ 45 is divisible by 9.
The value of ' A′ is 5.
Hence, the correct answer is 5.

The areas of three adjacent faces of a cuboidal tank are 3 m2,12 m2 and 16 m2. The capacity of the tank, in litres, is:
Correct answer is '24000'. Can you explain this answer?

Kunaal Satija answered
Given
Areas of 3 adjacent faces of cuboidal tank = 3 m2,12 m2,16 m2
As we know,
1 m3 = 1000 Litres
If areas of 3 adjacent faces of a cuboid are x,y and z respectively, then
Volume of cuboid =
Areas of 3 adjacent faces of cuboidal tank = 3 m2, 12 m2, 16 m2
Volume of cuboid =
Capacity of tank =
Capacity of tank = 24 m3
1 m3=1000 Litres
Capacity of tank = 24 × 1000 lites
Capacity of tank = 24000 litres
∴ The capacity of the tank, (in litres) is 24000 litres.
Hence, the correct answer is 24000.

If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:
Correct answer is 'Q'. Can you explain this answer?

Kunaal Satija answered
Intersection
Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.
The intersection of A and B is denoted by A ∩ B
i.e., A ∩ B = {x : x ∈ A and x ∈ B}
The Venn diagram for intersection is as shown below:
Union:
Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B.
The union of A and B is denoted by A ∪ B.
i.e., A ∪ B = {x : x ∈ A or x ∈ B}
The Venn diagram for the union of any two sets is shown below:
A ∪ B = A + B - A ∩ B
As we know,
P ∪ Q = P + Q - P ∩ Q
Putting the values given in the question,
P = P + Q - P ∩ Q
P ∩ Q = Q
Hence, the correct answer is Q.

A, B, and C play cricket. If the ratio of the number of runs scored by A to that scored by B and the number of runs scored by B to that scored by C is 3:2. The total number of runs is 342. The number of runs scored by A was?
Correct answer is '162'. Can you explain this answer?

Kunaal Satija answered
A : B : : 3 : 2
B : C :: 3 : 2
Let B = X
⇒A = 3X/2
and,
C = 2X/3
⇒ A + B + C = 342
⇒ 3X/2 + X + 2X/3 = 342
⇒ 9X + 6X + 4X = 342 × 6
⇐ 19X = 342 × 6
⇒ X = 108
⇒ Runs scored by A = (3(108))/2 = 162
Hence, the correct answer is 162.

If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log2 a) - 3]?
Correct answer is '4'. Can you explain this answer?

Kunaal Satija answered
Given, ax = 1/8, x = 3/2[(log2 a) - 3]
⇒ a3/2[(log2 a) - 3] = ⅛
Applying log to base 2 in both sides, we get,
3/2[(log2 a) - 3] log2 a = log2(⅛)
⇒ 3/2[(log2 a) - 3] log2 a = -3
Let log2 a = x
⇒ (x - 3) x = -2
⇒ x2 -3x + 2 = 0
⇒ (x - 1)(x - 2) = 0
⇒ x = 1 or 2
⇒ log2 a = 1 or log2 a = 2
⇒ a = 2 or a = 4
As given 'a' is a perfect square ⇒ a = 4
Hence, the correct answer is 4.

Time taken by two trains running in opposite directions to cross a man standing near a pole is 48 seconds and 38 seconds respectively and it took 42 seconds for the trains to cross each other. What is the ratio of the speed of the trains?
Correct answer is '2 : 3'. Can you explain this answer?

Kunaal Satija answered
Both trains running in the opposite direction
Both trains cross the man in 48 seconds and 38 seconds
Speed = Distance/Time
Relative speed = when train in opposite direction = (x + y)m/s
Let the speed of trains be x m/s and y m/s respectively,
Length of the first train = speed × time = 48x
Length of the second train = speed × time = 38y
(48x + 38y)/(x + y) = 42
⇒ 48x + 38y = 42x + 42y
⇒ 6x = 4y
⇒ x/y = 2/3
∴ The ratio of the speed of the trains is 2 : 3
Hence, the correct answer is 2 : 3.

Direction: Complete the paragraph given below.
'How did you relax on Sunday?' 'What was your last holiday like?' Simple though these questions sound, your next job might depend on how you answer them. _______. Instead of the usual laborious online questionnaires or psychometric tests, some recruiters are asking job candidates to call a phone number, key in a personal pin code and respond to a string of questions posed by a computer.
  • a)
    How you answer is always more important than what your answer is
  • b)
    Computers are changing the world
  • c)
    And it won't be a human you're talking to, but a computer
  • d)
    It's how you say it
Correct answer is option 'C'. Can you explain this answer?

Kunaal Satija answered
The correct answer is 'And it won't be a human you're talking to, but a computer'.
The given passage talks about how some recruiters are exploring novel technological techniques to assess the suitability of candidates.
Option (C): i.e., 'And it won't be a human you're talking to, but a computer' is the correct answer because it adds the required meaning and completes the passage.
Option (A): i.e., 'How you answer is always more important than what your answer is' is not the answer even though it is mildly related to the passage because it draws the attention to the questions asked in the interview rather than the changing recruitment process itself.
Option (B): 'Computers are changing the world' do not contribute any meaning to the passage.
Option (D): i.e., 'It's how you say it' are both very vague sentences and do not contribute any meaning to the passage.
The complete paragraph- 'How did you relax on Sunday?' 'What was your last holiday like?' Simple though these questions sound, your next job might depend on how you answer them. And it won't be a human you're talking to, but a computer. Instead of the usual laborious online questionnaires or psychometric tests, some recruiters are asking job candidates to call a phone number, key in a personal pin code and respond to a string of questions posed by a computer.
Hence, the correct option is (C).

Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its long-term goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocket-spacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eye-catching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life- support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future two-way missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargo-only flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a million-person colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
Which of the following is/are not inferred by the term “Red Planet”?
... more

Kunaal Satija answered
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said.
The entire passage talks about Mars and journey to Mars. Nowhere is Venus or Jupiter mentioned. “Red Planet”, in this passage refers to Mars only.
Hence, the correct option is (D).

Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its long-term goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocket-spacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eye-catching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life- support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future two-way missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargo-only flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a million-person colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
As per the passage, which rocket is used by SpaceX to send cargo to the International Space Station?
I. Falcon 9
II. Falcon Heavy
III. Starship
... more

Kunaal Satija answered
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocket-spacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Hence, the correct option is (A).

Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its long-term goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocket-spacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eye-catching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life- support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future two-way missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargo-only flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a million-person colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
According to Elon Musk, when could the first Mars base be operational?
... more

Kunaal Satija answered
Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028.
Hence, the correct option is (C).

Direction: Complete the paragraph given below.
Malaria is a life-threatening mosquito-borne blood disease caused by a Plasmodium parasite. It is transmitted to humans through the bite of the Anopheles mosquito. Once an infected mosquito bites a human, the parasites multiply in the host's liver before infecting and destroying red blood cells. ______. However, some countries lack the resources to do this treatment effectively.
  • a)
    There are many pharmacy shops in the area where malaria spreads
  • b)
    In some places, malaria can be treated and controlled with early diagnosis
  • c)
    Plenty of fluids must be taken to ensure dehydration does not occur
  • d)
    There are many multi-specialty hospitals in Delhi
Correct answer is option 'B'. Can you explain this answer?

Kunaal Satija answered
It is clear from the sentence following the blank that the preceding sentence should relate to treatment of malaria. Thus, option (B) is the correct option. The other options are out of context and irrelevant.
The complete paragraph- Malaria is a life-threatening mosquito-borne blood disease caused by a Plasmodium parasite. It is transmitted to humans through the bite of the Anopheles mosquito. Once an infected mosquito bites a human, the parasites multiply in the host's liver before infecting and destroying red blood cells. In some places, malaria can be treated and controlled with early diagnosis. However, some countries lack the resources to do this treatment effectively.
Hence, the correct option is (B).

Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water- bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rock-nectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
The tiny spring issuing from the rock is hidden by:
... more

Kunaal Satija answered
According to the passage, 'I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rock-nectar for the thirsty traveller.'
Upon the perusal of the above statement, it can be concluded that the tiny spring issuing from the rock is hidden by maidenhair fern.
Hence, the correct option is (B).

Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water- bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rock-nectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
To become part of a river, a tiny drop has to:
... more

Kunaal Satija answered
According to the passage, 'I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks.'
From the lines, it is evident that every drop of rain has its own identity which it represents and to become a part of the river it has to merge its identity.
Hence, the correct option is (D).

Direction: Find out which part has an error and mark it as your answer. If there is no error, mark ‘No error’ as your answer.
Everybody understands that (A)/ Australian continent is reeling under the worst B)/ forest fires of its history, don't they? C)/ No error D).
  • a)
    (A)
  • b)
    (B)
  • c)
    (C)
  • d)
    (D)
Correct answer is option 'D'. Can you explain this answer?

Kunaal Satija answered
The given sentence has no error.
There are some nouns that are singular in a sense but take plural question tag, e.g:- Everyone, each, every, nobody, none, everybody, no one, etc.
The pattern of a question tag is:
  • I. Auxiliary (e.g. do, did, is etc.) + not + subject (if the statement is affirmative)
  • II. Auxiliary (e.g. do, did, is, etc.) + subject (if the statement is negative)
Hence, the correct option is (D).

Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Buildings must ______ be examined and certified for safety, and those that fail to _____ to the NBC must be demolished.
  • a)
    surely, stick
  • b)
    intermittently, respect
  • c)
    intensely, purview
  • d)
    periodically, conform
Correct answer is option 'D'. Can you explain this answer?

Kunaal Satija answered
The sentence refers to the fact that buildings should be examined ‘from time to time’. In the context of the sentence, "intermittently" or "periodically" can fit the first blank and this eliminates options (A) and (C). Further, as buildings that fail ‘obey’ the standards must demolished, "conform" is the most appropriate choice for the second blank. Thus, option (B) gets eliminated as well.
Buildings must periodically be examined and certified for safety, and those that fail to conform to the NBC must be demolished.
Hence, the correct option is (D).
Fetching relevant content for you