Quiz for Sudo GATE 2021

Question 21

Choose the opposite word for ‘Paradox’ Note - This question is multiple select questions (MSQ).

• normality
• certainty
• axiom

Question 22

Which of the following is/are correct regarding uses of should/must/ought to appropriately in the sentences. Note - This question is multiple select questions (MSQ).

• Must is stronger than should and ought. It is more like an order. Should and ought to, on the other hand, are more like pieces of advice.
• Must can be used to talk about obligation. It is stronger than should and ought.
• Should and ought have very similar meanings and can often replace each other. Note that ought is followed by the infinitive with to.
• We use must in affirmative sentences to say what is necessary and to give strong advice and orders to ourselves or other people.

Question 23

There are 5 brothers in a family. All were born at a gap of 3 years. If the sum total of ages of 5 brothers is 100. Which of the following options is/are correct ? Note - This question is multiple select questions (MSQ).

• Age of 2nd most elder brother is 32
• Age of youngest brother is 14
• Difference between age of 2nd most elder brother and age of youngest brother is 9
• Addition of age of 2nd most elder brother and age of youngest brother is 46

Question 24

Consider the following graph:

If the imports of the company X in 2007 were increased by 100% then Note - This question is multiple select questions (MSQ).

• 0.625 would be the ratio of exports to the incremented imports
• 5/4 would be the ratio of exports to the incremented imports
• New import would be 8
• New import would be 9

Question 25

If mx² + nx + c = m(x - p)² then the relation between m, n, c is: Note - This question is multiple select questions (MSQ).

• mnc = 1
• n² = mc
• n² = 4mc
• 2n = m + c

Question 26

The following propositional statement is NOT equal to ((A → B) → C) → ((A → C) → B) Note - This question is multiple select questions (MSQ).

• (B → C)
• (B → C\')
• (B\' → C\')
• (B\' → C)

Question 27

Which of the following option is correct?

• (I) There are 1024 edges in the Cube graph with 8 vertices.
• (II) A Euler graph has cycle which covers every edge exactly once and does not repeat a vertex.
• (III) There are 19 edges in a connected planar graph with 12 vertices and 10 regions.

Note - This question is multiple select questions (MSQ).

• Statement I is correct
• Statement II is NOT correct
• Statement III is correct
• Only I and III are correct

Question 28

Consider following system of linear equations,

x + y + z = 6
x + 2y + 3z = 10
x + 2y + mz = n 

For what value of m and n does the system of equation has Note - This question is multiple select questions (MSQ).

• No solution if m ≠ 3 and n = 10
• Unique solution if m ≠ 3 and n ≠ 10 or m ≠ 3 and n = 10
• Infinite many solution if m = 3 and n =10
• Infinite many solution if m ≠ 3

Question 29

Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. P succeeds if he rolls either a 1 or 2. Q succeeds is he rolls either a 3, 4, or 5. If exactly 1 player succeeds on a turn, then the succeeding player wins. If neither player succeeds on a turn, another turn occurs. In case of a tie, the roll the dice repeatedly until there is no tie. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability that P will win ___________ . Note - This question is multiple select questions (MSQ).

• Out of 18 possible, and equally likely, game ends, P wins 6 times.
• 1/3
• 2/3
• 6/12

Question 30

Which of the following option(s) is/are correct ?

• (I) Function f(x) = x(x² - 27) where x is a real number. Then the function has one minima and one maxima.
• (II) The Integral value of f(x) = x * sinx within the limits [0, π] is π/2.
• (III) The mean value for the function f(x) = √(x² - 9) in the interval [3, 6] is 3/√2.

Note - This question is multiple select questions (MSQ).

• Statement I is correct
• Statement II is correct
• Statement III is correct
• Only I and II are correct