CUET Mathematics - Calculus - Integrals | Free Questions

Q1:

3 June Shift 2

Calculus

>

Medium

Common

Q1:

$a$

$\frac{a}{2}$

$\frac{a}{3}$

$2a$

Correct Answer

Option 2

Correct Answer

Explanation →

Q2:

3 June Shift 2

Calculus

>

Medium

Common

Q2:

$\frac{28}{3}$

$\frac{25}{3}$

$\frac{184}{3}$

$\frac{136}{5}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q3:

3 June Shift 2

Calculus

>

Medium

Core

Q3:

$-\frac{1}{2}e^{2x}\cos x + C$ , C is an arbitrary constant

$\frac{1}{2}e^{2x}\sin x + C$ , C is an arbitrary constant

$e^{2x}\sin x + C$ , C is an arbitrary constant

$-e^{2x}\cos x + C$ , C is an arbitrary constant

Correct Answer

Option 2

Correct Answer

Explanation →

Q4:

3 June Shift 2

Calculus

>

Medium

Core

Q4:

(B) and (D) only

(A) and (C) only

(A) and (D) only

(B) and (C) only

Correct Answer

Option 2

Correct Answer

Explanation →

Q5:

3 June Shift 2

Calculus

>

Medium

Applied

Q5:

$\frac{1}{2}\log_e(\frac{17}{5})$

$\frac{1}{5}\log_e(\frac{17}{5})$

$\log_e(\frac{17}{5})$

$2\log_e(\frac{17}{5})$

Correct Answer

Option 1

Correct Answer

Explanation →

Q6:

3 June Shift 1

Calculus

>

Medium

Common

Q6:

$\frac{1}{9}[\frac{9}{2}\log|x + \sqrt{x^2 + 9}| + \frac{x}{2}\sqrt{x^2 + 9}] + C$

$3[\frac{9}{2}\log|x + \sqrt{x^2 + 9}| + \frac{x}{2}\sqrt{x^2 + 9}] + C$

$[\frac{9}{2}\log|x + \sqrt{x^2 + 9}| + \frac{x}{2}\sqrt{x^2 + 9}] + C$

$\frac{1}{3}[\frac{9}{2}\log|x + \sqrt{x^2 + 9}| + \frac{x}{2}\sqrt{x^2 + 9}] + C$

Correct Answer

Option 4

Correct Answer

Explanation →

Q7:

3 June Shift 1

Calculus

>

Medium

Common

Q7:

$\frac{3}{2}$

$\frac{1}{2}$

1

0

Correct Answer

Option 2

Correct Answer

Explanation →

Q8:

3 June Shift 1

Calculus

>

Medium

Core

Q8:

$\sin^{-1}(\frac{x + 2}{3}) + C$ ; C is an arbitrary constant

$\frac{1}{3}\sin^{-1}(\frac{x + 2}{3}) + C$ ; C is an arbitrary constant

$3\sin^{-1}(\frac{x + 2}{3}) + C$ ; C is an arbitrary constant

$\frac{1}{3}\sin^{-1}(x + 2) + C$ ; C is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q9:

3 June Shift 1

Calculus

>

Medium

Core

Q9:

$\frac{1}{(1 + \log_e x)^2} + C$ , where C is constant of integration

$\frac{x}{1 + \log_e x} + C$ , where C is constant of integration.

$\frac{x}{(1 + \log_e x)^2} + C$ , where C is constant of integration

$\frac{1}{1 + \log_e x} + C$ , whereC is constant of integration

Correct Answer

Option 2

Correct Answer

Explanation →

Q10:

3 June Shift 1

Calculus

>

Medium

Core

Q10:

(A) - (I), (B) - (IV), (C) - (III), (D) - (II)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Correct Answer

Option 4

Correct Answer

Explanation →

Q11:

3 June Shift 1

Calculus

>

Medium

Applied

Q11:

$\frac{4}{15}(1 - \frac{1}{x^3})^{5/4} + C$

$\frac{4}{15}(1 + \frac{1}{x^3})^{5/4} + C$

$\frac{4}{15}(1 - \frac{1}{x^3})^{4/5} + C$

$\frac{4}{15}(1 + \frac{1}{x^3})^{4/5} + C$

Correct Answer

Option 1

Correct Answer

Explanation →

Q12:

2 June Shift 1

Calculus

>

Medium

Common

Q12:

1

0

3/2

$\log 2$

Correct Answer

Option 2

Correct Answer

Explanation →

Q13:

2 June Shift 1

Calculus

>

Medium

Common

Q13:

$\frac{1}{2}\log_e|e^{2x} - e^{-2x}| + C$ , where $C$ is an arbitrary constant.

$\log_e|e^{2x} - e^{-2x}| + C$ , where $C$ is an arbitrary constant.

$\frac{1}{2}\log_e|e^{2x} + e^{-2x}| + C$ , where $C$ is an arbitrary constant.

$\log_e|e^{2x} + e^{-2x}| + C$ , where $C$ is an arbitrary constant.

Correct Answer

Option 3

Correct Answer

Explanation →

Q14:

2 June Shift 1

Calculus

>

Medium

Core

Q14:

$\frac{1}{2}\log_e 2 - 1$

$2\log_e 2$

$2\log_e 2 - 2$

$4\log_e 2$

Correct Answer

Option 2

Correct Answer

Explanation →

Q15:

2 June Shift 1

Calculus

>

Medium

Core

Q15:

$\frac{5\sqrt{2}}{3}$

$\frac{4\sqrt{2}}{3}$

$\frac{4\sqrt{3}}{3}$

$\frac{\sqrt{2}}{3}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q16:

2 June Shift 1

Calculus

>

Easy

Core

Q16:

0

-1

$\pi$

1

Correct Answer

Option 1

Correct Answer

Explanation →

Q17:

2 June Shift 1

Calculus

>

Medium

Applied

Q17:

$a$

$2a$

$\frac{a}{2}$

$7a$

Correct Answer

Option 1

Correct Answer

Explanation →

Q18:

2 June Shift 1

Calculus

>

Medium

Applied

Q18:

$\frac{5^x}{\log 5}e^x + C$

$5^x e^x + C$

$(5e)^x \log(5e) + C$

$\frac{(5e)^x}{\log(5e)} + C$

Correct Answer

Option 4

Correct Answer

Explanation →

Q19:

30 May Shift 2

Calculus

>

Medium

Common

Q19:

$\frac{1}{5}\log_e \left|\frac{x^5-1}{x^5}\right| + C$ ; C is an arbitrary constant

$\log_e \left|\frac{x^5-1}{x^5}\right| + C$ ; C is an arbitrary constant

$\frac{1}{5}(\log_e|x| + \log_e|x^5-1|) + C$ ; C is an arbitrary constant

$\log_e \left|\frac{x}{x^5-1}\right| + C$ ; C is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q20:

30 May Shift 2

Calculus

>

Medium

Common

Q20:

$\frac{1}{2}$

1

2

4

Correct Answer

Option 2

Correct Answer

Explanation →

Q21:

30 May Shift 2

Calculus

>

Medium

Core

Q21:

0

1

2

4

Correct Answer

Option 4

Correct Answer

Explanation →

Q22:

30 May Shift 2

Calculus

>

Hard

Core

Q22:

$2\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \log x\sqrt{16+(\log x)^2} + C$

$16\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

$8\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

$4\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

Correct Answer

Option 3

Correct Answer

Explanation →

Q23:

30 May Shift 2

Calculus

>

Medium

Core

Q23:

$\frac{\pi}{4}$

$\frac{\pi}{12}$

0

$\pi$

Correct Answer

Option 3

Correct Answer

Explanation →

Q24:

30 May Shift 2

Calculus

>

Easy

Applied

Q24:

$\frac{\pi}{3}$

$\frac{2\pi}{3}$

$\frac{\pi}{6}$

$\frac{\pi}{12}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q25:

30 May Shift 2

Calculus

>

Medium

Applied

Q25:

$x^6 + x^4 + x^2 + C$

$\frac{x^6}{6} + \frac{x^4}{4} + \frac{x^2}{2} + C$

$\frac{x^6}{3} + \frac{x^4}{2} + x^2 + C$

$x^6 + x^5 + x^4 + x^3 + x^2 + x + C$

Correct Answer

Option 3

Correct Answer

Explanation →

Q26:

30 May Shift 1

Calculus

>

Medium

Common

Q26:

$-\frac{x}{2} + c$

$\frac{x^2}{2} + c$

$\frac{x^3}{3} + c$

$\frac{x^4}{4} + c$

Correct Answer

Option 4

Correct Answer

Explanation →

Q27:

30 May Shift 1

Calculus

>

Medium

Common

Q27:

$\frac{3}{2}$

$\frac{5}{2}$

$\frac{1}{2}$

5

Correct Answer

Option 2

Correct Answer

Explanation →

Q28:

30 May Shift 1

Calculus

>

Medium

Core

Q28:

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

(A) - (IV), (B) - (I), (C) - (III), (D) - (II)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (III), (B) - (I), (C) - (IV), (D) - (II)

Correct Answer

Option 3

Correct Answer

Explanation →

Q29:

30 May Shift 1

Calculus

>

Medium

Core

Q29:

$2\sin x + 2x\cos\alpha + c$

$2\cos x + 2x\sin\alpha + c$

$x\cos x + 2\sin\alpha + c$

$x\cos x + x\sin\alpha + c$

Correct Answer

Option 1

Correct Answer

Explanation →

Q30:

30 May Shift 1

Calculus

>

Medium

Core

Q30:

$\frac{\pi}{2}$

$\frac{\pi}{4}$

0

$-\frac{\pi}{2}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q31:

30 May Shift 1

Calculus

>

Medium

Applied

Q31:

$\log_e\left|\frac{x + 2}{x + 1}\right| + C$ : where $C$ is an arbitrary constant

$\log_e\left|\frac{x + 1}{x + 2}\right| + C$ : where $C$ is an arbitrary constant

$\log_e|(x + 1)(x + 2)| + C$ : where $C$ is an arbitrary constant

$\log_e|2x + 3| + C$ : where $C$ is an arbitrary constant

Correct Answer

Option 2

Correct Answer

Explanation →

Q32:

29 May Shift 2

Calculus

>

Medium

Common

Q32:

0

1

$\frac{1}{2}$

2

Correct Answer

Option 2

Correct Answer

Explanation →

Q33:

29 May Shift 2

Calculus

>

Medium

Common

Q33:

$\frac{a^x}{\log a} + \frac{x^{a+1}}{a+1} + C$ ; C is an arbitrary constant

$(\log a) a^x + \frac{x^{a+1}}{a+1} + C$ ; C is an arbitrary constant

$\frac{a^x}{a+1} + \frac{x^{a+1}}{\log a} + C$ ; C is an arbitrary constant

$(a + 1)a^x + (\log a)x^{a+1} + C$ ; C is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q34:

29 May Shift 2

Calculus

>

Medium

Core

Q34:

(A) - (I), (B) - (IV), (C) - (III), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

Correct Answer

Option 2

Correct Answer

Explanation →

Q35:

29 May Shift 2

Calculus

>

Medium

Core

Q35:

$\sqrt{6}\cot^{-1}(\sqrt{6}\cot x) + C$ ; C is an arbitrary constant

$\sqrt{6}\cot^{-1}(\sqrt{6} \tan x) + C$ ; C an arbitrary constant

$\frac{1}{\sqrt{6}} \tan^{-1}(\sqrt{6}\cot x) + C$ ; C an arbitrary constant

$\frac{1}{\sqrt{6}} \tan^{-1}(\sqrt{6} \tan x) + C$ ; C an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q36:

29 May Shift 2

Calculus

>

Easy

Core

Q36:

2

10

8

5

Correct Answer

Option 1

Correct Answer

Explanation →

Q37:

27 May Shift 1

Calculus

>

Medium

Common

Q37:

$\frac{2}{9}(1 + x^3)^{3/2} - \frac{2}{3}(1 + x^3)^{1/2} + c$ : $c$ is an arbitrary constant

$\frac{2}{3}(1 + x^3)^{3/2} - \frac{2}{3}(1 + x^3)^{1/2} + c$ : $c$ is an arbitrary constant

$\frac{1}{3}(1 + x^3)^{3/2} + \frac{1}{3}(1 + x^3)^{1/2} + c$ : $c$ is an arbitrary constant

$\frac{2}{9}(1 + x^3)^{3/2} + \frac{2}{3}(1 + x^3)^{1/2} + c$ : $c$ is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q38:

27 May Shift 1

Calculus

>

Medium

Common

Q38:

0

$\frac{1}{4}$

$\frac{1}{2}$

1

Correct Answer

Option 3

Correct Answer

Explanation →

Q39:

27 May Shift 1

Calculus

>

Medium

Core

Q39:

$\log|e^x + e^{-x}| + C$ : $C$ is an arbitrary constant

$\log|e^{2x} + 1| + C$ : $C$ is an arbitrary constant

$\log|e^{2x} - e^{-x}| + C$ : $C$ is an arbitrary constant

$\log|e^{2x} - 1| + C$ : $C$ is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q40:

27 May Shift 1

Calculus

>

Medium

Core

Q40:

$e^{-x}\cot x + c$ , where $c$ is an arbitrary constant.

$-e^{-x}\cot x + c$ , where $c$ is an arbitrary constant.

$-e^{-x}\cosec^2 x + c$ , where $c$ is an arbitrary constant.

$e^{-x}\cosec^2 x + c$ , where $c$ is an arbitrary constant.

Correct Answer

Option 2

Correct Answer

Explanation →

Q41:

27 May Shift 1

Calculus

>

Medium

Core

Q41:

$\tan^{-1}(e^x) + c$ : $c$ is an arbitrary constant

$\tan^{-1}(e^{-x}) + c$ : $c$ is an arbitrary constant

$log(e^x - e^{-x}) + c$ : $c$ is an arbitrary constant

$log(e^x + e^{-x}) + c$ : $c$ is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q42:

27 May Shift 1

Calculus

>

Medium

Applied

Q42:

32

36

34

50

Correct Answer

Option 3

Correct Answer

Explanation →

Q43:

26 May Shift 2

Calculus

>

Medium

Common

Q43:

$\log\left(\frac{2}{3}\right)$

$\log\left(\frac{4}{3}\right)$

0

$\log\left(\frac{3}{4}\right)$

Correct Answer

Option 2

Correct Answer

Explanation →

Q44:

26 May Shift 2

Calculus

>

Medium

Common

Q44:

$xe^x + C$

$\frac{e^x}{x} + C$

$\frac{e^{-x}}{x^2} + C$

$e^x + \frac{1}{x} + C$

Correct Answer

Option 2

Correct Answer

Explanation →

Q45:

26 May Shift 2

Calculus

>

Hard

Core

Q45:

$\frac{e^x}{1+x^2} + C$ ; $C$ is an arbitrary constant

$\frac{e^x}{(1+x^2)^2} + C$ ; $C$ is an arbitrary constant

$\frac{-e^x}{(1+x^2)^2} + C$ ; $C$ is an arbitrary constant

$\frac{-e^x}{1+x^2} + C$ ; $C$ is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q46:

26 May Shift 2

Calculus

>

Medium

Core

Q46:

$a\int_{0}^{a} f(x)dx$

$a\int_{0}^{a} g(x)dx$

$\frac{a}{2}\int_{0}^{a} f(x)dx$

$\frac{a}{2}\int_{0}^{a} g(x)dx$

Correct Answer

Option 3

Correct Answer

Explanation →

Q47:

26 May Shift 2

Calculus

>

Medium

Core

Q47:

$\pi/2$

$\pi/3$

$\pi/4$

$\pi/6$

Correct Answer

Option 3

Correct Answer

Explanation →

Q48:

26 May Shift 2

Calculus

>

Medium

Applied

Q48:

$\log|e^{2x} - 1| + C$ ; $C$ is an arbitrary constant

$\log\left|\frac{e^{2x}-1}{e^{2x}+1}\right| + C$ ; $C$ is an arbitrary constant

$\log\left|\frac{e^{2x}}{e^{2x}-1}\right| + C$ ; $C$ is an arbitrary constant

$\log\left|\frac{e^{2x}-1}{e^{2x}}\right| + C$ ; $C$ is an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q49:

22 May Shift 2

Calculus

>

Medium

Common

Q49:

$\sin^{-1}\left(\frac{\cos^2 x}{3}\right) + C$ ; $C$ is an arbitrary constant.

$\cos^{-1}\left(\frac{\sin^2 x}{3}\right) + C$ ; $C$ is an arbitrary constant

$\sin\left(\frac{\cos^2 x}{3}\right) + C$ ; $C$ is an arbitrary constant

$-\sin^{-1}\left(\frac{\cos^2 x}{3}\right) + C$ ; $C$ is an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q50:

22 May Shift 2

Calculus

>

Medium

Common

Q50:

8

4

2

$\frac{1}{2}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q51:

22 May Shift 2

Calculus

>

Medium

Core

Q51:

$m - e + 1$

$\frac{m}{2} + e - 1$

$m - \frac{e}{2} + 1$

$m + \frac{e}{2} - 1$

Correct Answer

Option 3

Correct Answer

Explanation →

Q52:

22 May Shift 2

Calculus

>

Medium

Core

Q52:

$\frac{1}{4x^2}\sqrt{1 + x^4} + C$ , $C$ is an arbitrary constant

$\frac{1}{x^2}\sqrt{1 + x^4} + C$ , $C$ is an arbitrary constant

$\frac{1}{2x^2}\sqrt{1 + x^4} + C$ , $C$ is an arbitrary constant

$-\frac{1}{2x^2}\sqrt{1 + x^4} + C$ , $C$ is an arbitary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q53:

22 May Shift 2

Calculus

>

Medium

Core

Q53:

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (II), (B) - (III), (C) - (I), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Correct Answer

Option 3

Correct Answer

Explanation →

Q54:

22 May Shift 2

Calculus

>

Medium

Applied

Q54:

$\frac{1}{2}$

2

-2

$-\frac{1}{2}$

Correct Answer

Option 1

Correct Answer

Explanation →

Q55:

22 May Shift 1

Calculus

>

Medium

Common

Q55:

$\log_e\left|\frac{(x-1)^2}{x-2}\right| + C$

$\log_e\left|\frac{(x-2)^2}{x-1}\right| + C$

$\log_e|(x-2)(x-1)^2| + C$

$\log_e\left|\frac{x-1}{(x-2)^2}\right| + C$

Correct Answer

Option 2

Correct Answer

Explanation →

Q56:

22 May Shift 1

Calculus

>

Medium

Common

Q56:

0

1

e

$e^2$

Correct Answer

Option 2

Correct Answer

Explanation →

Q57:

22 May Shift 1

Calculus

>

Medium

Core

Q57:

$\frac{1}{\sqrt{10}} \tan^{-1}\left(\frac{ \tan x}{\sqrt{5}}\right) + C$ ; C is an arbitrary constant

$\frac{1}{\sqrt{5}} \tan^{-1}\left(\frac{2 \tan x}{\sqrt{5}}\right) + C$ ; C is an arbitrary constant

$\frac{1}{\sqrt{2}} \tan^{-1}\left(\frac{\sqrt{2} \tan x}{\sqrt{5}}\right) + C$ ; C is an arbitrary constant

$\frac{1}{\sqrt{10}} \tan^{-1}\left(\frac{\sqrt{2} \tan x}{\sqrt{5}}\right) + C$ ; C is an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q58:

22 May Shift 1

Calculus

>

Medium

Core

Q58:

$\frac{a}{2}\int_0^a f(x)dx$

$2\int_0^a f(x)dx$

$a f(a)$

$a\int_0^a f(x)dx$

Correct Answer

Option 1

Correct Answer

Explanation →

Q59:

22 May Shift 1

Calculus

>

Medium

Core

Q59:

$\frac{x}{\log_e x} + c$ ; c is an arbitrary constant

$\frac{1}{\log_e x} + c$ ; c is an arbitrary constant

$\frac{x}{(\log_e x)^2} + c$ ; c is an arbitrary constant

$\frac{\log_e x}{x} + c$ ; c is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q60:

22 May Shift 1

Calculus

>

Medium

Applied

Q60:

2

4

6

8

Correct Answer

Option 3

Correct Answer

Explanation →

Q61:

22 May Shift 1

Calculus

>

Medium

Applied

Q61:

$\frac{e^x}{2x} + C$ , where $C$ is constant of integration.

$\frac{2e^x}{x} + C$ , where $C$ is constant of integration.

$\frac{e^x}{x} + C$ , where $C$ is constant of integration.

$\frac{e^x}{4x} + C$ , where $C$ is constant of integration.

Correct Answer

Option 1

Correct Answer

Explanation →

Q62:

21 May Shift 2

Calculus

>

Medium

Common

Q62:

$\frac{x}{logx} + c$ , where c is an arbitrary constant

$x\,logx + c$ , where c is an arbitrary constant

$\frac{1}{logx} + c$ , where c is an arbitrary constant

$\frac{e^x}{logx} + c$ , where c is an arbitrary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q63:

21 May Shift 2

Calculus

>

Medium

Common

Q63:

$\frac{1}{3}\log 26$

$\log 14$

$\frac{1}{3}\log 14$

$\log 56$

Correct Answer

Option 3

Correct Answer

Explanation →

Q64:

21 May Shift 2

Calculus

>

Medium

Core

Q64:

0

$\frac{1}{2}$

1

5

Correct Answer

Option 2

Correct Answer

Explanation →

Q65:

21 May Shift 2

Calculus

>

Medium

Core

Q65:

$2(\sqrt{2} - 1)$

$2(\sqrt{2} + 1)$

2

$2\sqrt{2}$

Correct Answer

Option 1

Correct Answer

Explanation →

Q66:

21 May Shift 2

Calculus

>

Medium

Core

Q66:

$\log\left|\frac{x}{x - \sin x}\right| + C$

$\log\left|\frac{x}{x + x\sin x}\right| + C$

$\log\left|\frac{x}{x + \sin x}\right| + C$

$\log\left|\frac{x + \sin x}{x}\right| + C$

Correct Answer

Option 3

Correct Answer

Explanation →

Q67:

21 May Shift 2

Calculus

>

Medium

Core

Q67:

$p > q > r > s > t$

$q > r > p > t > s$

$r > t > s > p > q$

$t > p > q > r > s$

Correct Answer

Option 4

Correct Answer

Explanation →

Q68:

21 May Shift 2

Calculus

>

Hard

Applied

Q68:

$\frac{e}{2}$

$\frac{e}{2} - 1$

$\frac{e}{2} + 1$

$2e + 1$

Correct Answer

Option 2

Correct Answer

Explanation →

Q69:

21 May Shift 1

Calculus

>

Medium

Common

Q69:

$-2 \log_e |\sqrt{x} - 1| + C$ ; C is an arbitrary constant

$4 \log_e |\sqrt{x} - 1| + C$ ; C is an arbitrary constant

$\log_e |\sqrt{x} - 1| + C$ ; C is an arbitrary constant

$2 \log_e |\sqrt{x} - 1| + C$ ; C is an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q70:

21 May Shift 1

Calculus

>

Medium

Common

Q70:

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (II), (B) - (III), (C) - (I), (D) - (IV)

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

Correct Answer

Option 1

Correct Answer

Explanation →

Q71:

21 May Shift 1

Calculus

>

Medium

Core

Q71:

$x \log_e x + c$ ; where c is an arbitrary constant

$e^x \log_e x + c$ ; where c is an arbitrary constant

$\frac{e^x}{\log_e x} + c$ ; where c is an arbitrary constant

$\frac{x}{\log_e x} + c$ ; where c is an arbitrary constant

Correct Answer

Option 4

Correct Answer

Explanation →

Q72:

21 May Shift 1

Calculus

>

Medium

Core

Q72:

0

1

2

$\pi$

Correct Answer

Option 1

Correct Answer

Explanation →

Q73:

21 May Shift 1

Calculus

>

Easy

Core

Q73:

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (IV), (B) - (I), (C) - (III), (D) - (II)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

Correct Answer

Option 4

Correct Answer

Explanation →

Q74:

19 May Shift 1

Calculus

>

Medium

Common

Q74:

$\frac{1}{e}$

$e$

$1$

$-1$

Correct Answer

Option 3

Correct Answer

Explanation →

Q75:

19 May Shift 1

Calculus

>

Medium

Common

Q75:

$\log\left|\frac{x-3}{x+1}\right| + C$

$\log\left|\frac{\sqrt{x-1}-2}{\sqrt{x+1}}\right| + C$

$\frac{1}{2}\log\left|\frac{\sqrt{x+1}-1}{\sqrt{x+1}+1}\right| + C$

$\log\left|\frac{\sqrt{x+1}-2}{\sqrt{x+1}+2}\right| + C$

Correct Answer

Option 4

Correct Answer

Explanation →

Q76:

19 May Shift 1

Calculus

>

Hard

Core

Q76:

$\frac{1}{3}\left(\frac{2}{3}x^3 + \frac{1}{x} + x\right) + C$

$\frac{2}{3}x^3 - \frac{1}{x} + x + C$

$\frac{x^3}{3} + x + C$

$\frac{1}{3}\left(\frac{2}{3}x^3 - x\right) + C$

Correct Answer

Option 1

Correct Answer

Explanation →

Q77:

19 May Shift 1

Calculus

>

Medium

Core

Q77:

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

Correct Answer

Option 1

Correct Answer

Explanation →

Q78:

19 May Shift 1

Calculus

>

Hard

Core

Q78:

$(x+1) \tan^{-1}\sqrt{x} - \sqrt{x} + C$

$x \tan^{-1}\sqrt{x} - \sqrt{x} + C$

$\sqrt{x} - x \tan^{-1}\sqrt{x} + C$

$\sqrt{x} - (x+1) \tan^{-1}\sqrt{x} + C$

Correct Answer

Option 1

Correct Answer

Explanation →

Q79:

19 May Shift 1

Calculus

>

Medium

Applied

Q79:

$\frac{16}{15\sqrt{2}}$

$\frac{16\sqrt{3}}{15}$

$\frac{16\sqrt{2}}{15}$

$\frac{5\sqrt{2}}{7}$

Correct Answer

Option 3

Correct Answer

Explanation →

Q80:

16 May Shift 1

Calculus

>

Medium

Common

Q80:

$\frac{1}{2}$

2

1

0

Correct Answer

Option 4

Correct Answer

Explanation →

Q81:

16 May Shift 1

Calculus

>

Medium

Common

Q81:

$\frac{e^x}{(x-1)} + C$ , C is an arbitary constant

$\frac{e^x}{(x-3)^2} + C$ , C is an arbitary constant

$\frac{e^x}{(x-1)^2} + C$ , C is an arbitary constant

$\frac{e^x}{(x-1)^3} + C$ , C is an arbitary constant

Correct Answer

Option 3

Correct Answer

Explanation →

Q82:

16 May Shift 1

Calculus

>

Hard

Core

Q82:

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

Correct Answer

Option 2

Correct Answer

Explanation →

Q83:

16 May Shift 1

Calculus

>

Medium

Core

Q83:

$2 \sin x + 2x \cos α + C$ , where C is an arbitary constant

$2 \sin x + 2 \sin α + C$ , where C is an arbitary constant

$\frac{\sin 2x}{2} + x \cos 2α + C$ , where C is an arbitary constant

$\frac{\sin 2x}{2} + \frac{\sin 2α}{2} + C$ , where C is an arbitary constant

Correct Answer

Option 1

Correct Answer

Explanation →

Q84:

16 May Shift 1

Calculus

>

Medium

Core

Q84:

$\frac{\pi}{8}$

$-\frac{\pi}{8}$

$\frac{\pi}{4}$

$-\frac{\pi}{4}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q85:

16 May Shift 1

Calculus

>

Medium

Applied

Q85:

1

1/2

3/2

5/2

Correct Answer

Option 4

Correct Answer

Explanation →

Q86:

15 May Shift 2

Calculus

>

Medium

Common

Q86:

$f(x) \cdot log_e[f(x)] + C$ ; $C$ is a constant of integration

$\frac{log_e[f(x)]}{f(x)} + C$ ; $C$ is a constant of integration

$log_e(log_e[f(x)]) + C$ ; $C$ is a constant of integration

$\frac{log_e(log_e[f(x)])}{f(x)} + C$ ; $C$ is a constant of integration

Correct Answer

Option 3

Correct Answer

Explanation →

Q87:

15 May Shift 2

Calculus

>

Hard

Common

Q87:

$\frac{4}{15}\left(1 - \frac{1}{x^3}\right)^{5/4} + C$ ; $C$ is a constant of integration

$\frac{4}{3}\left(1 - \frac{1}{x^3}\right)^{5/4} + C$ ; $C$ is a constant of integration

$\frac{4}{15}\left(1 - \frac{1}{x^3}\right)^{3/4} + C$ ; $C$ is a constant of integration

$\frac{4}{15}\left(1 - \frac{1}{x^3}\right)^{1/5} + C$ ; $C$ is a constant of integration

Correct Answer

Option 1

Correct Answer

Explanation →

Q88:

15 May Shift 2

Calculus

>

Medium

Core

Q88:

0

2

4

$\frac{5}{2}$

Correct Answer

Option 3

Correct Answer

Explanation →

Q89:

15 May Shift 2

Calculus

>

Medium

Core

Q89:

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

Correct Answer

Option 2

Correct Answer

Explanation →

Q90:

15 May Shift 2

Calculus

>

Medium

Core

Q90:

$\frac{x^3}{3} + \frac{x^2}{2} + C$ ; $C$ is a constant of integration

$\frac{x^3}{3} - \frac{x^2}{2} + C$ ; $C$ is a constant of integration

$\frac{x^3}{6} + \frac{x^2}{4} + C$ ; $C$ is a constant of integration

$\frac{x^3}{6} - \frac{x^2}{4} + C$ ; $C$ is a constant of integration

Correct Answer

Option 1

Correct Answer

Explanation →

Q91:

15 May Shift 2

Calculus

>

Medium

Applied

Q91:

0

1

2

3

Correct Answer

Option 2

Correct Answer

Explanation →

Q92:

15 May Shift 2

Calculus

>

Medium

Applied

Q92:

$\alpha = 2\beta$

$2\alpha = \beta$

$\alpha = \beta$

$\alpha = 3\beta$

Correct Answer

Option 3

Correct Answer

Explanation →

Q93:

15 May Shift 1

Calculus

>

Medium

Common

Q93:

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Correct Answer

Option 4

Correct Answer

Explanation →

Q94:

15 May Shift 1

Calculus

>

Medium

Common

Q94:

0

1

2

3

Correct Answer

Option 3

Correct Answer

Explanation →

Q95:

15 May Shift 1

Calculus

>

Hard

Core

Q95:

$\sin^{-1}(\sin 2x) + C$ , C is an arbitary constant

$\sin^{-1}(\cos x - \sin x) + C$ , C is an arbitary constant

$\sin^{-1}(\sin x - \cos x) + C$ , C is an arbitary constant

$\sin^{-1}(\sin x + \cos x) + C$ , C is an arbitary constant

Correct Answer

Option 3

Correct Answer

Explanation →

Q96:

15 May Shift 1

Calculus

>

Medium

Core

Q96:

(A) and (C) only

(B) only

(B) and (D) only

(A) and (D) only

Correct Answer

Option 3

Correct Answer

Explanation →

Q97:

15 May Shift 1

Calculus

>

Medium

Core

Q97:

$\frac{1}{2}\log\left|\frac{ \tan x + 2}{ \tan x - 2}\right| + C$ , where C is constant of integration

$\frac{1}{2}\log\left|\frac{\tan x}{ \tan x + 2}\right| + C$ , where C is constant of integration

$\frac{1}{2}\log\left|\frac{\tan x + 2}{ \tan x}\right| + C$ , where C is constant of integration

$\frac{1}{2}\log\left|\frac{\tan x + 1}{\tan x + 2}\right| + C$ , where C is constant of integration

Correct Answer

Option 2

Correct Answer

Explanation →

Q98:

15 May Shift 1

Calculus

>

Medium

Applied

Q98:

0

1

2

3

Correct Answer

Option 4

Correct Answer

Explanation →

Q99:

15 May Shift 1

Calculus

>

Medium

Applied

Q99:

$\log\left(\frac{2 + \sqrt{6}}{1 - \sqrt{3}}\right)$

$\log\left(\frac{2 + \sqrt{6}}{1 + \sqrt{3}}\right)$

$\log\left(\frac{5 + \sqrt{6}}{1 + \sqrt{3}}\right)$

$\log(5 + \sqrt{6})$

Correct Answer

Option 2

Correct Answer

Explanation →

Q100:

14 May Shift 2

Calculus

>

Medium

Common

Q100:

$\frac{1}{4}\log_e\left|\frac{x^4}{1-x^4}\right| + c$ : where $c$ is constant of integration.

$-\frac{1}{4}\log_e\left|\frac{x^4}{1-x^4}\right| + c$ : where $c$ is constant of integration.

$4\log_e\left|\frac{x^4}{1-x^4}\right| + c$ : where $c$ is constant of integration.

$-4\log_e\left|\frac{x^4}{1-x^4}\right| + c$ : where $c$ is constant of integration.

Correct Answer

Option 1

Correct Answer

Explanation →

Q101:

14 May Shift 2

Calculus

>

Easy

Common

Q101:

0

1

2

4

Correct Answer

Option 3

Correct Answer

Explanation →

Q102:

14 May Shift 2

Calculus

>

Hard

Core

Q102:

$\tan(e^x) + c$ , where $c$ is constant of integration.

$-\cot(ex^x) + c$ , where $c$ is constant of integration.

$\cot(e^x) + c$ , where $c$ is constant of integration.

$\tan(xe^x) + c$ , where $c$ is constant of integration.

Correct Answer

Option 4

Correct Answer

Explanation →

Q103:

14 May Shift 2

Calculus

>

Medium

Core

Q103:

0

$\frac{\pi}{2}$

$\pi$

$\frac{\pi}{4}$

Correct Answer

Option 3

Correct Answer

Explanation →

Q104:

14 May Shift 2

Calculus

>

Hard

Core

Q104:

$\frac{1}{2025}$

$\frac{1}{2027}$

$\frac{1}{2023}$

$\frac{2}{2025}$

Correct Answer

Option 1

Correct Answer

Explanation →

Q105:

14 May Shift 2

Calculus

>

Hard

Applied

Q105:

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(C) and (D) only

Correct Answer

Option 4

Correct Answer

Explanation →

Q106:

14 May Shift 2

Calculus

>

Medium

Applied

Q106:

3/2

$\frac{3}{2}\log 2 - \frac{1}{2}\log 5$

$\frac{5}{2}\log 3 - \frac{1}{2}\log 5$

$\frac{5}{2}\log 3 + \log 5$

Correct Answer

Option 2

Correct Answer

Explanation →

Q107:

14 May Shift 1

Calculus

>

Medium

Common

Q107:

5

$\frac{7}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q108:

14 May Shift 1

Calculus

>

Medium

Common

Q108:

$\frac{x}{2} + C$ , where C is the constant of integration

$\frac{x^2}{2} + C$ , where C is the constant of integration

$\frac{x^3}{3} + C$ , where C is the constant of integration

$\frac{x^4}{4} + C$ , where C is the constant of integration

Correct Answer

Option 3

Correct Answer

Explanation →

Q109:

14 May Shift 1

Calculus

>

Medium

Core

Q109:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

(A) - (III), (B) - (I), (C) - (IV), (D) - (II)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Correct Answer

Option 4

Correct Answer

Explanation →

Q110:

14 May Shift 1

Calculus

>

Medium

Core

Q110:

$\frac{1}{3}\left(\frac{x^2}{2} - x\right) + C$ , where C is constant of integration

$\left(\frac{x^2}{2} - x\right)e^x + C$ , where C is constant of integration

$\frac{1}{3x^2}e^x + C$ , where C is constant of integration

$\frac{1}{3x}e^x + C$ , where C is constant of integration

Correct Answer

Option 4

Correct Answer

Explanation →

Q111:

14 May Shift 1

Calculus

>

Medium

Core

Q111:

$\frac{\pi}{4}$

0

$\frac{\pi}{6}$

$\frac{\pi}{12}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q112:

14 May Shift 1

Calculus

>

Hard

Applied

Q112:

$e^x$

$\log x$

$\frac{1}{x}$

$\frac{1}{x^2}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q113:

13 May Shift 2

Calculus

>

Medium

Common

Q113:

$\frac{1}{log_e t} + C$ , where C is constant of integration

$\frac{t}{log_e t} + C$ , where C is constant of integration

$\frac{-t}{log_e t} + C$ , where C is constant of integration

$\frac{-1}{log_e t} + C$ , where C is constant of integration

Correct Answer

Option 2

Correct Answer

Explanation →

Q114:

13 May Shift 2

Calculus

>

Medium

Common

Q114:

$\frac{2^{n+2}(n+1)}{(n+2)(n+3)}$

$\frac{2^{n+2}(n+2)}{(n+1)(n+3)}$

$\frac{2^{n+2}}{(n+1)(n+2)}$

$\frac{2^{n+1}}{(n+1)(n+2)}$

Correct Answer

Option 3

Correct Answer

Explanation →

Q115:

13 May Shift 2

Calculus

>

Hard

Core

Q115:

-1

0

1

$\frac{\pi}{4}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q116:

13 May Shift 2

Calculus

>

Easy

Core

Q116:

$\frac{25}{4}$

0

$\frac{5}{2}$

$-\frac{5}{2}$

Correct Answer

Option 1

Correct Answer

Explanation →

Q117:

13 May Shift 2

Calculus

>

Medium

Core

Q117:

$\frac{1}{\cos x + \sin x} + C$ , where C is constant of integration

$\frac{-1}{\cos x + \sin x} + C$ , where C is constant of integration

$\frac{1}{1 + \sin 2x} + C$ , where C is constant of integration

$\frac{1}{1 - \sin 2x} + C$ , where C is constant of integration

Correct Answer

Option 2

Correct Answer

Explanation →

Q118:

13 May Shift 2

Calculus

>

Medium

Applied

Q118:

0

-1

-2

2

Correct Answer

Option 4

Correct Answer

Explanation →

Q119:

13 May Shift 1

Calculus

>

Easy

Common

Q119:

$\frac{x^2}{2} + x + c$ , Where $c$ is constant of integration

$\frac{x^2}{2} - \frac{1}{x} + c$ , Where $c$ is constant of integration

$\frac{x^2}{2} - x + c$ , Where $c$ is constant of integration

$\frac{x^2}{2} + \frac{1}{x} + c$ , Where $c$ is constant of integration

Correct Answer

Option 4

Correct Answer

Explanation →

Q120:

13 May Shift 1

Calculus

>

Medium

Common

Q120:

(B) and (D) only

(A), (B) and (C) only

(B) only

(C) and (D) only

Correct Answer

Option 1

Correct Answer

Explanation →

Q121:

13 May Shift 1

Calculus

>

Medium

Core

Q121:

$\frac{1}{24}\log_e\left|\frac{3x+4}{3x-4}\right| + C$ , Where $C$ is constant of integration

$\frac{3}{8}\log_e\left|\frac{3x+4}{3x-4}\right| + C$ , Where $C$ is constant of integration

$\frac{3}{8}\log_e\left|\frac{3x-4}{3x+4}\right| + C$ , Where $C$ is constant of integration

$\frac{1}{24}\log_e\left|\frac{3x-4}{3x+4}\right| + C$ , Where $C$ is constant of integration

Correct Answer

Option 4

Correct Answer

Explanation →

Q122:

13 May Shift 1

Calculus

>

Hard

Core

Q122:

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{6}$

$\frac{\pi}{12}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q123:

13 May Shift 1

Calculus

>

Hard

Core

Q123:

$-\frac{1}{48}(6\cos 2x + 3\cos 4x + 2\cos 6x) + C$ , Where $C$ is constant of integration

$-\frac{1}{48}(2\cos 2x + 3\cos 4x - 6\cos 6x) + C$ , Where $C$ is constant of integration

$-\frac{1}{48}(6\cos 2x + 3\cos 4x - 2\cos 6x) + C$ , Where $C$ is constant of integration

$-\frac{1}{48}(2\cos 2x + 3\cos 4x + 6\cos 6x) + C$ , Where $C$ is constant of integration

Correct Answer

Option 3

Correct Answer

Explanation →

Q124:

13 May Shift 1

Calculus

>

Medium

Applied

Q124:

16/27

8/3

2/9

8/9

Correct Answer

Option 1

Correct Answer

Explanation →

Q125:

CUET Mathematics 2024 Slot 1

Calculus

>

Medium

Common

Q125:

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}-1}{x^{n}}\right|+C$

$\quad \log _{e}\left|\frac{x^{n}+1}{x^{n}-1}\right|+C$

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}+1}{x^{n}}\right|+C$

$\pi \log _{e}\left|\frac{x^{n}}{x^{n}-1}\right|+C$

Correct Answer

Option 1

Correct Answer

Explanation →

Q126:

CUET Mathematics 2024 Slot 1

Calculus

>

Medium

Common

Q126:

$\frac{a-b}{a+b}$

$\frac{1}{a-b}$

$\frac{a+b}{2}$

$\frac{1}{a+b}$

Correct Answer

Option 4

Correct Answer

Explanation →

Q127:

CUET Mathematics 2024 Slot 1

Calculus

>

Medium

Core

Q127:

$\log _{e} 3$

$\log _{e} 4-\log _{e} 3$

$\log _{e} 9-\log _{e} 4$

$\log _{e} 3-\log _{e} 2$

Correct Answer

Option 2

Correct Answer

Explanation →

Q128:

CUET Mathematics 2024 Slot 1

Calculus

>

Medium

Core

Q128:

$0$

$\frac{\pi}{4}$

$\infty$

$\frac{\pi}{12}$

Correct Answer

Option 1

Correct Answer

Explanation →

Q129:

CUET Mathematics 2024 Slot 1

Calculus

>

Medium

Core

Q129:

$\frac{1}{2 \sqrt{\mathrm{x}}} \mathrm{e}^{\mathrm{x}}+\mathrm{C}$

$-\mathrm{e}^{\mathrm{x}} \sqrt{\mathrm{x}}+C$

$-\frac{1}{2 \sqrt{x}} e^{x}+C$

$e^{x} \sqrt{x}+C$

Correct Answer

Option 4

Correct Answer

Explanation →

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