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# Gate 2021 : Toppers Weekly Quiz 7 (App update required to attempt this test)

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Question 1

The order and degree of following differential equation is:

Question 2

The ratio of two numbers is 3: 4 and their H.C.F. is 4. Their L.C.M. is:

Question 3

The values of function 𝑓(

using Trapezoial rule with step size or 0.1, the value or is_______

*x*) at 5 discrete poets are given below:using Trapezoial rule with step size or 0.1, the value or is_______

Question 4

A certain sum at simple interest amounts to Rs. 1586 in 2 yr and Rs. 1729 in 3 yr. Find the rate

Question 5

If (a+b) : (b+c) : (c+a) = 5 : 6 : 9 and a+b+c = 10; what is the value of: (a

^{2}+ b^{2}+ c^{2})Question 6

A boatman can row a certain distance downstream in 7 hrs and return the same distance in 21 hrs. If the stream flows at the rate of the 9 km/h find the speed of boat in still water.

Question 7

Consider matrix , then determinant of Adj (Adj A) is _________.

Question 8

The area bounded by in the third quadrant is

Question 9

Two bikers start from a point with a speed of 60 km/h but second biker starts after an interval of 10 minutes. What is the speed of a man coming from the opposite direction towards that point if the man meets the bikers at an interval of 8 minutes?

Question 10

A system of two linear equations in x and y:

px + qy = r

sx + ty = u

Has a unique solution if:

px + qy = r

sx + ty = u

Has a unique solution if:

Question 11

Which one of the following describes the relationship among the three vectors,

?

?

Question 12

Three pipes A, B & C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A & B can fill it in 7 hours after that. Number of hours taken by C to fill the cistern alone will be how much?

Question 13

Consider the system of linear equations given below:

–2x + y + z = I

x –2y + z = m

x + y – 2z = n

if I + m + n = 0, Then the system of equations has

Question 14

Two toys are sold at ₹ 504 each. One toy brings the dealer a gain of 12% and the other a loss of 4%. The gain or loss percent by selling both the toys is

Question 15

In a bag there are 150 notes which values are Rs. 100 and Rs. 50. If total value of all notes is Rs. 9000 then what is number of Rs. 100 notes?

Question 16

A can complete a piece of work in 30 days. B is two times more efficient worker than C who is 50% more efficient than A. How many days are required to complete the work if all of them work together?

Question 17

For the matrix eigen vector corresponding to eigen value −2 is ___________.

Question 18

The value of integral calculated using simpson’s 1/3

^{rd}Rule, with 10 subintervals is use the table given below.Question 19

In two mixtures respective ratio of milk and water is 3:5 and 7:5 respectively. In what ratio both mixtures should be mixed to make ratio of milk and water 1:1?

Question 20

By using Simpson's 1/3rd rule find by taking a width of 1

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Jan 30ESE & GATE CE

Posted by:

Shreya LaddhaMember since Dec 2019

M.tech from IIT Kanpur (Geotechnical Engineering)
Among top 500 in GATE 2019