GATE ME 2021 : Toppers weekly Quiz 5 for ESE & GATE ME Exams

Question 1

A certain sum becomes 6 times at 5% rate of interest per annum. At what rate of interest, the sum will become 12 times?

Question 2

If a function is defined in the interval (0, a), then definite integral of f(x) i.e.

is called improper integral when;

Question 3

Sana is twice as efficient as Suhana. Together they finish a work in 8 days. How many days will Sana alone take to finish the work?

Question 4

How much rice at Rs. 40 a kg should be added to 20 kg of rice at Rs.50 a kg so that the mixture be worth Rs. 45 a kg ?

Question 5

Consider the following statements:

1) The vector X₁, X₂……, X_m of same order n such that K₁X₁+ K₂X₂ + _ _ _ _ + K_mX_m = 0 for ∀ K₁ = K₂ = _ _ _ _ = K_m = 0, are linearly independent.

2) Two collinear are linearly dependent.

3) Any set containing zero vector is always linearly independent.

Which of the following statements is/are correct?

Question 6

The solution of

with the condition

is

Question 7

A shopkeeper sold an item at 10% loss after giving a discount equal to half the marked price. Then the cost price is

Question 8

Piyush, Nirav and Rohit started a business with investment of Rs.10, 000, Rs.15, 000 and Rs.20, 000 respectively. At the end of the year the share of Rohit in the profit was Rs.5, 000. Find the difference between the share of Piyush and Nirav in the profit?

Question 9

Which of the following defines the graph of the continuous function?

Question 10

Probability of passing in Physics is 35%. The chance of passing in Physics and getting above 85 marks in it is 7%. Given that student passes in Physics. Find the probability that student gets above 85 marks.

Question 11

Four milkmen rented a pasture. A grazed 18 cows for 4 months, B grazed 25 cows for 2 months, C grazed 28 cows for 5 months and D grazed 21 cows for 3 months. If A’s share of rent be Rs. 360, then total rent of the field is

Question 12

For the matrix

eigen vector corresponding to eigen value −2 is ___________.

Question 13

A six- faced fair dice is rolled five times. The probability (in%)of obtaining “ONE” at least four times is

Question 14

2 men or 3 women can complete a job in 96 days. Then 6 men and 7 women will complete the same job in how many days?

Question 15

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?

Question 16

A pump can fill a tank with water in 1 hour. Because of a leak in the tank, it takes

hours to fill the tank. The leak can empty the filled tank in

Question 17

In a mixture of 75 liters, the ratio of milk and water is 2 : 1. The amount of water further to be added to the mixture so as to make the ratio of the milk to water 1: 2 will be?

Question 18

The value of

where V is the region bounded by x=0, y=0, z=0 and 2x + 2y + z = 4.

Question 19

Sand is pouring from a pipe at the rate of 12 cm³/sec. The falling sand from a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4cm?

Question 20

If a random variable X has the following probability distribution:

X:	0	1	2	3	4	5	6	7	8
P(X):	a	3a	5a	7a	9a	11a	13a	15a	17a

then value of ‘a’ is