JEE Main Test 61

Result

JEE Main Test 61

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Weekly Quiz Competition

Question 1
4 / -1

If A is a skew-symmetric matrix of order 3, then which of the following terms can be used for the matrix A⁴?

A
Skew symmetric

B
Symmetric

C
Diagonal

D
None of these

Solution

We have, A^T = -A

(A⁴)^T = (A.A.A.A.)^T

= A^TA^TA^TA^T

^⇒(-A)(-A)(-A)(-A)

= (-1)⁴A⁴

= A⁴

(A⁴)^T = A⁴, then A⁴ is symmetric.
Question 2
4 / -1

A bicycle is in motion. The force of friction exerted by the ground on its wheel is such that it acts

A
in backward direction on the front wheel and in forward direction on the rear wheel when it is accelerating

B
in forward direction on the front wheel and in backward direction on the rear wheel when brakes are applied on the rear wheel only

C
in backward direction on the front wheel and in forward direction on the rear wheel when brakes are applied on the rear wheel only

D
in backward direction on both the wheels when brakes are applied on both the wheels

Solution

When cycle accelerates, the rear wheel accelerates forward due to rotation. Hence, friction is forward. The front wheel tries to accelerate translationally without rotational motion hence friction is backward. When breaks are applied to the rear wheel, the conditions are reversed.

If breaks are applied on both wheels, they try to skid over the road in forward direction. Hence, friction is in the backward direction for both the wheels.
Question 3
4 / -1

An unknown alcohol is treated with Lucas' reagent to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts the fastest and by what mechanism?

A
Tertiary alcohol by SN¹

B
Secondary alcohol by SN²

C
Tertiary alcohol by SN²

D
Secondary alcohol by SN¹

Solution

The reaction proceeds through a carbocation intermediate.

Since 3° carbocation is highly stable and hence, the reaction proceeds through SN¹with 3° alcohol and white precipitate of horn silver is obtained instantly.