#### 11th Standard Maths Integral Calculus English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. If $\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c$ ,then the value of k is

(a)

log 3

(b)

-log 3

(c)

$-{1\over log3}$

(d)

${1\over log3}$

2. $\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx$ is

(a)

x+c

(b)

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

(c)

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

(d)

${1\over x^2}+c$

3. $\int {sin^8x-cos^8x\over 1-2sin^2 \ x \ cos^2 \ x}dx$ is

(a)

${1\over2}sin 2x+c$

(b)

$-{1\over2}sin 2x+c$

(c)

${1\over2}cos 2x+c$

(d)

$-{1\over2}cos 2x+c$

4. $\int{x^2+cos^2x\over x^2+1}cosec^2xdx$ is

(a)

cot x+sin -1x+c

(b)

-cot x+tan-1x+c

(c)

-tan x+cot-1x+c

(d)

-cot x-tan-1x+c

5. $\int e^{-4x}cos \ x \ d x$ is

(a)

${e^{-4x}\over 17}[4cos \ x-sin \ x]+c$

(b)

${e^{-4x}\over 17}[-4cos \ x+sin \ x]+c$

(c)

${e^{-4x}\over 17}[4cos \ x+sin \ x]+c$

(d)

${e^{-4x}\over 17}[-4cos \ x-sin \ x]+c$

6. $\int {x+2\over \sqrt{x^2+1}}dx$is

(a)

$\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c$

(b)

$sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c$

(c)

$2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c$

(d)

$\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c$

7. $\int sin \sqrt{x}$ dx is

(a)

$2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c$

(b)

$2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c$

(c)

$2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c$

(d)

$2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c$

8. $\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } }$ dx = _______+C.

(a)

$\frac { \left( 1+logx \right) ^{ 3 } }{ 3 }$

(b)

3 log ( 1 + log x)

(c)

2(1 + log x)

(d)

none of these

9. $\int { \frac { 1 }{ 9x^{ 2 }-4 } }$ dx = ____________+c.

(a)

log$\left| \frac { 3x-2 }{ 3x+2 } \right|$

(b)

$\frac { 1 }{ 12 }$log$\left| \frac { 3x-2 }{ 3x+2 } \right|$

(c)

12log$\left| \frac { 3x-2 }{ 3x+2 } \right|$

(d)

$\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right|$

10. $\int { \frac { x }{ 4+{ x }^{ 4 } } }$ dx is equal to________+c.

(a)

$\frac { 1 }{ 4 }$ tan-1 (x2)

(b)

$\frac { 1 }{ 4 }$ tan-1 $\left( \frac { { x }^{ 2 } }{ 2 } \right)$

(c)

$\frac { 1 }{ 2 }$ tan-1 $\left( \frac { { x }^{ 2 } }{ 2 } \right)$

(d)

none of these