GA Questions 1 to 10 Solutions

Q.1 The people _______ were at the demonstration were from all sections of society.

a) whose

b) which

c) who

d) whom

Ans: c) who

Solution:- The subject of the verb is ‘who’. Therefore, option (c) is the correct answer.

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Q.2 A transparent square sheet shown below is folded along the dotted line. The folded sheet will look like ____.

Ans: c)

Solution: As the given diagram on page appears like a triangle so when it is folded along the dotted line it will turn into two traingle so option (c) is correct.

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Q.3 For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

a) 396

b) 324

c) 216

d) 144

Ans: d) 144

Solution:- We know that the interior angle of polygon is given by =\frac{(2n-4)90^{o}}{n}

n is the number of sides.

n=10,

=\frac{(2x 10 -4)90^{o}}{10} = 144^o

So, option (d) is correct.

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Q.4 Which one of the following numbers is exactly divisible by (11¹³+1)?

a) 11²⁶+1

b) 11³³+1

c) 11³⁹-1

d) 11⁵²-1

Ans: d) 11⁵²-1

Solution:- Comparing the given expression i.e. (11¹³+1) with the formula aⁿ-bⁿ

11¹³=a and 1¹³ = b

aⁿ-bⁿ is divisible by (a+b) only when n is even

Let us check by putting one by one option.

Take option (3) into consideration

\frac{11^{52}-1^{52}}{11^{13}-1^{13}}=\frac{(11^{3})^{4}-(1^{3})^{4}}{11^{13}+1^{13}} =\frac{a^{4}-b^{4}}{a+b}

So, option (d) is correct.

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Q.5 Oasis is to sand as island is to _______
Which one of the following options maintains a similar logical relation in the above sentence?

a) Stone

b) Land

c) Water

d) Mountain

Ans: c) Water

Solution: Oasis is the waterpool within the sand same as island is the piece of land within water. It is an example of analogy.

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Q. 6 — Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: — 2/3).

Q.6 The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.
Which one of the following statements is the CORRECT inference from the above passage?

a) Sleeping well alone is enough to prepare for rim exam. Studying has lesser benefit.

b) Students are efficient end ore not wrong in thinking that sleep is a waste of time.

c) If a student is extremely well prepared for rim exam, he needs little or no sleep.

d) To do well in an exam, adequate sleep must be part of the preparation.

Ans: d) To do well in an exam, adequate sleep must be part of the preparation.

Solution: It is general fact that if we will not sleep properly it will affect our mental health. Deprivation of sleep during exams have negative effect on exams. So, adequate sleep is very very important. So, option (d) is correct.

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Q.7 In the figure shown below, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm² is:

a) 12.50

b) 6.25

c) 3.125

d)1.5625

Ans: c) 3.125

Solution:- The length of the side of the larger square L₁ = 10 cm

We know that the whenever, a square is formed by joining midpoints of the next larger square, area of inner square is exactly of the area of the larger square.

The first small square cuts midway of larger square , so L_{2}=\frac{10}{\sqrt{2}} cm

The second small square also cuts midway of first small square L_{3}=\frac{10}{\sqrt{2}^{2}}

We can see taht five sqaures are made, so length of the smallest sqaure is L_{6}=\frac{10}{\sqrt{2}^{5}}

Therefore, Area of the smallest square = L_{6}^{2}=\frac{10}{\sqrt{2}^{5}}^2 = 3.125 cm²

So, the area of the smallest square (shaded) = 3.125 cm²

So, option (c)is the correct answer.

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Q.8 Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0\leq X\leq100. The mean of X is _____

a) 2.5

b) 5.0

c) 25.0

d) 50.0

Ans: d) 50.0

Solution:- The given function is f(x) = 0.01 0\leq X\leq100

The mean or expectation of a continuous random variable is given by,

E(x)=\int_{\infty }^{-\infty }x(f(x))dx

f(x) is the probability density function (PDF)

The mean or expectation of a continous random variable is given by,

E(x)=\int_{0}^{100}x(0.01)dx=50

So, option (d) is the correct answer.

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Q.9 The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.
The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are

a) 65 and 53

b) 60 and 50

c) 55 and 53

d) 55 and 48

Ans: d) 55 and 48

Solution:-

Given that Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year.

So, From the given graph, we can see that there are total 65 students appeared in the year 2 . 10 are from year 1 . So, 55 students appeared for first time in the year -2

In the year 3 53 students appeared for the exam . 5 students(failed in year 2) are from year 2.

So. from this we can say that in year 3, 48 students appeared for the first time.

Therefore, option (c) is the correct answer.

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Q.10 Seven cars P, Q, R, S, T, U and V are parked in a roe not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to
each other. R is parked to the immediate right of V. T is parked to the left of U. Based on the above statements, the only INCORRECT option given below is:

a) There are two cars parked in between Q and V.

b) Q end R are not parked together.

c) V is the only car parked in between S and R.

d) Car P is parked at the extreme end.

Ans: a) There are two cars parked in between Q and V.

Solution:- From the given condition we can get two possibilities:

1. PTUQSVR
2. TUQSVRP

Consider following statements depicted from the problem given above.

a) The car T and U should be park next to each other . This means we can park these two cars in two ways, either TU or UT.

b) The car S and V also should be parked next to each other. This means we can park these cars in two ways SV or VS .

c) The car P and Q cannot be parke next to each other This means we cannot park these cars in two ways i.e. Pq and QP.

d) R is parked to the immediate right of V.

e) T is parked to the left of U. The car Q and S must be parked next to each other.

By combining statements b and d we get two possible ways for cars Q, S and V

QSV and VSQ

If we will take one by one possibilities we can see that there can’t be two cause between Q and V .

We can see that the car P can be parked at the xtreme end in three out of the four possible combinations.

So, option a is the correct answer.