Q. Let and let
and .
Then which of the following options is/are correct?

JEE Advanced JEE Advanced 2019 Report Error

A

There exists a real number x such that PQ = QP

B

detR = det for all

C

For x = 0,if R then a + b = 5

D

For x = 1, there exists a unit vector for which

Solution:

det() = det() = (det )(det)
det

Option-1 :
for det
for equation
We will have trivial solution

Option-2 :

No value of x.
Option-3 :
det

Option-4 :

Questions from JEE Advanced 2019

1. Let be given by

Then which of the following options is/are correct?

2. Let f : ℝ ℝ be given by f(x) = (x - 1)(x - 2)(x - 5). Define

Then which of the following options is/are correct?

3. Three lines

and

are given. For which point(s) on can we find a point P on and a point R on so that P, Q and R are collinear?

4. Let f(x) = sin( cos x) and g(x) = cos(2 sin a) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:
X = {x : f'(x) — 0}, Y = {x : f(x) = 0},
Z = [x : g(x) = 0}, W = [x : g'(x) = 0}.
List -1 contains the sets X, Y, Z and W. List - II contains some information regarding these sets.

List-I List-II

(I) X (p) ⊇

(II) Y (Q) an arithmetic progression

(III) Z (R) NOT an arithmetic progression

(IV) W (S) ⊇

(T) ⊇

(U) ⊇

Question: Which of the following is the only CORRECT combination?

5. Let f(x) = sin( cos x) and g(x) = cos(2 sin a) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:
X = {x : f'(x) — 0}, Y = {x : f(x) = 0},
Z = [x : g(x) = 0}, W = [x : g'(x) = 0}.
List -1 contains the sets X, Y, Z and W. List - II contains some information regarding these sets.

List-I List-II

(I) X (p) ⊇

(II) Y (Q) an arithmetic progression

(III) Z (R) NOT an arithmetic progression

(IV) W (S) ⊇

(T) ⊇

(U) ⊇

Question : Wliich of the following is the only CORRECT combination?

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