Gate 2021 : Toppers Weekly Quiz 1 (App update required to attempt this test) for ESE & GATE CE Exams

Question 1

In the following question, select the missing number from the given series.

Question 2

Alloy A contain 80% copper and rest is tin. Alloy B contain 85% copper, 10% tin & rest are impurities. In which ratio both alloys are mixed so that in new mixture percentage of tin will be 15 % ?

Question 3

The function given by y = |lxl -1|, is differentiable for all real numbers except at the points

Question 4

For the Runge kutta method of order 4, the truncation error is of order

Question 5

Eigen value of inverse of matrix A is

Question 6

In the sentence, identify the segment which contains the grammatical error. If the sentence has no error, then select 'No error'.

Although he studied regularly, his marks didn't improving.

Question 7

Find the trace of a matrix [A] of 3 × 3 if [A]^T = –[A] _______.

Question 8

One or two statements are given followed by two conclusions/assumptions, I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given conclusions/assumptions can definitely be drawn from the given statement. Indicate your answer.
Statements:
1) All mangoes are golden in colour.
2) No golden coloured things are cheap.
Conclusions:
I. All mangoes are cheap.
II. Golden-coloured mangoes are not cheap.

Question 9

If a + b + c = 7 and ab + bc + ca = -6, then the value of a³ + b³ + c³ – 3abc is:

Question 10

The system of linear equations
4x + 2y = 7
2x + y = 6
has

Question 11

Consider the following system of linear equations:

It has _______.

Question 12

A statement is given followed by two course of action. The candidate is required to grasp the statement and analyses the problem or policy it mentions and then decide which course of action logically follows.

Statement:
Raju has topped his class in the 10^th board examination.
Course of action:
I. Raju went to school regularly and studied carefully throughout the session.
II. Raju likes video games.

Question 13

A man can do a work in 10 days. With the help of a boy he can do the same work in 6 days. If they get Rs 50 for the work, what is the share of the boy?

Question 14

Identify the best way to improve the underlined part of the given sentence. If there is no improvement required, select ‘no Improvement’.

No sooner was his name called out when he was gone onto the stage to receive the award.

Question 15

While evaluating integral with Simpson’s 3/8^th rule

This question can have multiple correct solution.
The error with the integrating interval are:

Question 16

Identify the segment in the sentence which contains the grammatical error.

Even Sharat tried his best, he could not clear all the examination papers in one attempt.

Question 17

The solution of differential equation

is

Question 18

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly ‘9’ twice is

Question 19

The average age of A and B, 2 years ago was 32. If the age of A, 5 years hence is 38 years, and B is 5 years younger to C, then find the difference between the age of A and C?

Question 20

The area of the region bounded by the parabola

and the straight line x + y = 3 is