#### Model questions

11th Standard

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Maths

Use blue pen Only
Time : 00:50:00 Hrs
Total Marks : 55

Part A

10 x 1 = 10
1. ${d\over dx}({2\over \pi}sin \ x^o)$is

(a)

${\pi\over 180}cos \ x^o$

(b)

${1\over 90} cos \ x^o$

(c)

${\pi\over 90}cos \ x^o$

(d)

${2\over \pi}cos \ x^o$

2. If y= f(x2+2) and f'(3)=5,then ${dy\over dx}$ at x=1 is

(a)

5

(b)

25

(c)

15

(d)

10

3. If x=a sin $\theta$ and y= b cos $\theta$,then ${d^2y\over dx^2}$is

(a)

${a \over b^2}sec^2 \theta$

(b)

$-{b \over a}sec^2 \theta$

(c)

$-{b \over a^2}sec^3 \theta$

(d)

$-{b^2\over a^2}sec^3 \theta$

4. The differential coefficient of log10 x with respect to logx10 is

(a)

1

(b)

-(log10 x)2

(c)

(logx 10)2

(d)

$x^2\over100$

5. If f(x)=x+2, then f'(f(x)) at x= 4 is

(a)

8

(b)

1

(c)

4

(d)

5

6. If is differentiable at x = 1, then

(a)

$a={1\over2},b={-3\over 2}$

(b)

$a={-1\over2},b={3\over 2}$

(c)

$a=-{1\over2},b=-{3\over 2}$

(d)

$a={1\over2},b={3\over 2}$

7. The number of points in R in which the function $f(x)=|x-1|+|x-3|+sin \ x$ is not differentiable, is

(a)

3

(b)

2

(c)

1

(d)

4

8. $\int sin^3 \ xdx$ is

(a)

${-3\over 4}cos \ x-{cos \ 3x\over 12}+c$

(b)

${3\over 4}cos \ x-{cos \ 3x\over 12}+c$

(c)

${-3\over 4}cos \ x+{cos \ 3x\over 12}+c$

(d)

${-3\over 4}sin \ x-{sin \ 3x\over 12}+c$

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

(a)

x+c

(b)

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

(c)

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

(d)

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

10. $\int {sec \ x\over \sqrt{cos 2x}}dx$ is

(a)

tan-1 (sin x)+c

(b)

2sin-1(tan x)+c

(c)

tan-1(cos x)+c

(d)

sin -1(tan x)+c

11. Part B

10 x 2 = 20
12. Find the derivatives of the following functions using first principle.f(x)=-x2+2

13. Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1? f(x) = |x - 1|

14. Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1? f(x)=$\sqrt{1-x^2}$.

15. Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?
f(x)={$\begin{matrix} x, & x\le 1 \\ -x^{ 2 } & x<0 \end{matrix}$

16. Differentiate the following with respect to x: y=x3+5x2+3x+7

17. Differentiate the following with respect to x: y=ex+sin x+2

18. Differentiate the following with respect to x: y=4cosec x-log x-2ex

19. Differentiate the following with respect to x :$y=(x-{1\over x})^2$

20. Differentiate the following: y=(x2+4x+6)5

21. Differentiate the following: y = tan3x

22. Part C

5 x 5 = 25
23. Differentiate the following: $y=\sqrt{1+2 \ tan \ x}$

24. Differentiate the following: y=sin3 x+cos3 x

25. Integrate the following with respect to x: ex

26. Integrate the following with respect to x:$(1+x^2)^{-1}$

27. Integrate the following with respect to x:$(1+x^2)^{-{1\over 2}}$