Model questions

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

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

    Part A 

    Answer all the questions

    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

    Answer all the questions

    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

    Answer all the questions

    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:\((1+x^2)^{-{1\over 2}}\)

*****************************************

TN 11th Standard Maths free Online practice tests

Reviews & Comments about 11th Maths Model Question Paper -Introduction To Probability Theory,Combinations and Mathematical Induction

Write your Comment