GA Questions 1 to 10 Solutions
Q.1-Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: 1/3).
Q.1 The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
a) 9,92,500
b) 9,95,006
c) 10,00,000
d) 12,51,506
Ans: c) 10,00,000
Solution:- GIven that the current population of the city is 11,02,500. It is increasing by 5% every year.
We know that finding population ‘n’ years ago the formula is given by,
P=P_{o}\left [ 1+\frac{R}{100} \right ]^{n}So, in the problem P=1102500 , R= 5 , n=Time period = 2 and consider Po=Population ‘n’ years before or after n= x
Now putting values in the formula
1102500=x\left [ 1+\frac{5}{100} \right ]^{2}1102500= x \frac{21}{20}^2
x=10,00,000
So, option (c) is correct.
Q.2 p and q are positive integers and \frac pq+\frac qp=3, then, \frac{p^2}{q^2}+\frac{q^2}{p^2}=
a) 3
b) 7
c) 9
d) 11
Ans: b) 7
Solution:- It is given that \frac pq+\frac qp=3,
So, squaring both sides of the equation we get,
\left ( \frac{p}{q}+\frac{q}{p} \right )^{2}=3^{2} \frac{p^{2}}{q^{2}}+\frac{q^{2}}{p^{2}}+2=9 \frac{p^{2}}{q^{2}}+\frac{q^{2}}{p^{2}}=9-2 = 7So, option (b) is coreect.
Q.3 The least number of squares that must be added so that the line P-Q becomes the line of symmetry is _______
a) 4
b) 3
c) 6
d) 7
Ans: c) 6
Solution:- Symmetrey means when one part of the figure becomes exactly same as second part of the figure while folding it along the line.
So, for making P-Q as symmetric line . the minimum number of squares that should be added is 6. So, option (c) is the correct answer.
Q.4 Nostalgia is to anticipation as ______ is to ________ Which one of the following options maintain a similar logical relation in the above sentence?
a) Present, past
b) Future, past
c) Past, future
d) Future, present
Ans: c) Past, future
Solution:- In general Nostalgia means feeling of pleasure, mixed with sadness when you think of happy times in the past and anticipation means the state of expecting something to happen . This both words resembles the past and future relation. So. option (c) is the correct answer.
Q.5 Consider the following sentences:
(i) I woke up from sleep.
(ii) I woked up from sleep.
(iii) I was woken up from sleep.
(iv) I was wokened up from sleep.
Which of the above sentences are grammatically CORRECT?
a) (i) and (ii)
b) (i) and (iii)
c) (ii) and (iii)
d) (i) and (iv)
Ans: b) (i) and (iii)
Solution:- The option (b) is correct because wake-woke-woken are the three forms of verb and the option (i) and (iii) are grammatically correct as they indicates the form of verb.
Q.6-Q.10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer:-2/3).
Q.6 Given below are two statements and two conclusions.
Statement 1: All purple are green.
Statement 2: All black are green.
Conclusion I: Some black are purple.
Conclusion II: No black is purple.
Based on the above statements and conclusions, which one of the following option is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Ans: (C) Either conclusion I or II is correct.
Solution:- We will solve this problem by drawing the Venn diagram. So the following statement can have possible cases as,
From the venn diagram we can depict that either conclusion (1) or (ii) is correct.
Q.7 Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.
Which of the following can be deduced from the above passage?
(i) Nowadays, computers are present in almost all places.
(ii) Computers cannot be used for solving problems in engineering.
(iii) For humans, there are both positive and negative effects of using computers.
(iv) Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Ans: (D) (i) and (iii)
Solution:- The term ubiquitous means seeming to be everywhere or in several places at the same time. This ubiquitous word is analogically compared to computers. By reading the paragraph the statements (i) and (iii) can be deduced from the above passage.
Q.8 Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is_____
a) \frac\pi3
b) \frac{2\pi}3
c) \frac{3\pi}2
d) 3\pi
Ans: a) \frac\pi3
Solution:- The square sheet is cut along the main diagonal to get two large triangles. It is also given solid cone is formed by revolving about its short edge.
Hence the radius and height of the cone is r=1 and h=1.
Volume of the cone = V=\frac{1}{3}\pi r^{2}h=\frac{\pi }{3}(1)^{2}(1)=\frac{\pi }{3}
So, option (a) is correct.
Q.9 The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
a) 4
b) 5
c) 6
d) 7
Ans: c) 6
Solution:- The number of minutes exercising every day in a given week is calculated by the formula. Percentage = (Obtained value/Maximum value)x 100
From the graph , calculating the percentage on each day ,
On sunday the percentage = \frac{65-55}{55}\times 100=18.18%
On saturday the percentage = \frac{60-50}{50}\times 100=20%
On Friday , the percentage = \frac{35-20}{20}\times 100=75%
On Thursday , the percentage = \frac{60-55}{55}\times 100=9.09%
On Wednesday , the percentage = \frac{60-50}{20}\times 100=20%
On Tuesday , the percentage = \frac{65-55}{55}\times 100=18.18%
On Monday , the percentage = \frac{70-45}{45}\times 100=55.56%
So, from this evaluation, we can see that total six days are spent when one of the students spent a minimum of 10% more than the other student. So, option (c) is the correct answer.
Q.10 Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure.
The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
a) 2:3
b) 3:4
c) 4:5
d) 5:6
Ans: a) 2:3
Solution:- The given figure indicates that the corners of equilateral triangle produce a regular hexagon,
We know that, hexagon has 6 sides.
So, Consider side of equilateral triangle as ‘a ‘
Side of regular hexagon = \frac{a}{3}
The area of regular hexagon is given by, A=6\times \frac{\sqrt{3}}{4}\left ( \frac{a}{3} \right )^{2}
where a/3 is the side of hexagon.
Area of triangle = \frac{\sqrt{3}}{4}(a)^{2}
Now, finding the ratio=Area of regular hexagon/Area of triangle
= \frac{\frac{6\sqrt{3}}{4}\times \frac{a^{2}}{9}}{\frac{\sqrt{3}}{4}a^{2}}=\frac{6}{9} = 2:3
The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle .
So, option (a) is the correct answer.