CUET · MATHS · PYQ PAPER 2023

The value of \(\int \tan ^2 x d x\) is :
where \(C\) is the constant of integration.

A \(\sec ^2 x+C\)
B \(\tan x-x+C\)
C \(\sec x+x+C\)
D \(\tan x+x+C\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\tan x-x+C\)

Step-by-step Solution

Detailed explanation

\( \int \tan^2 x \, dx = \int (\sec^2 x - 1) \, dx \) \( = \int \sec^2 x \, dx - \int 1 \, dx \) \( = \tan x - x + C \)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List - I with List - II.

LIST-I	LIST-I
(A) \(\csc ^{-1} x\)	(I) \((0, \pi)\)
(B) \(\sec ^{-1} x\)	(II) \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)
(C) \(\tan ^{-1} x\)	(III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
(D) \(\cot ^{-1} x\)	(IV) \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)

Choose the correct answer from the options given below:

CUET 2023 Easy

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=\| x \|\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=\|x+2\|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left\|x^2-4\right\|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=\|x-2\|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

CUET 2025 Easy

There is a Building which is tilted and equations of two different walls are \(2 x-y+z=4\) and \(x+y+2 z=3\). Angle between the walls is :

CUET 2023 Hard

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List - I	List - II
(A) Point of minima of \(f(x)=\|x+1\|\)	(I) 1
(B) Minimum value of \(f(x)=\|x\|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0

The value of \(\int \tan ^2 x d x\) is :where \(C\) is the constant of integration.

Step-by-step Solution

The value of \(\int \tan ^2 x d x\) is :
where \(C\) is the constant of integration.