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12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions 2020

12th Standard

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Maths

Time : 00:25:00 Hrs
Total Marks : 25

    Answer all the questions

    25 x 1 = 25
  1. The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

    (a)

    -8

    (b)

    -4

    (c)

    -2

    (d)

    0

  2. The equation of the tangent to the curve y=x2-4x+2 at (4,2) is

    (a)

    x + 4y + 12 = 0

    (b)

    4x + y + 12 = 0

    (c)

    4x - y - 14 = 0

    (d)

    x + 4y - 12 = 0

  3. In LMV theorem, we have f'(x1) =\(\frac { f(b)-f(a) }{ b-a } \) then a < x1 _________

    (a)

    <b

    (b)

    ≤b

    (c)

    =b

    (d)

    ≠b

  4. If the curves y = 2ex and y =ae-x intersect orthogonally, then a = _________

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    -\(\frac { 1 }{ 2 } \)

    (c)

    2

    (d)

    2e2

  5. If w (x, y) = xy, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

    (a)

    xy log x

    (b)

    y log x

    (c)

    yxy-1

    (d)

    x log y

  6. If u = xy + yx then ux + uy at x = y = 1 is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

  7. If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f= sin u then f is a homogeneous function of degree ..................

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    4

  8. The area between y2 = 4x and its latus rectum is

    (a)

    \(\frac{2}{3}\)

    (b)

    \(\frac{4}{3}\)

    (c)

    \(\frac{8}{3}\)

    (d)

    \(\frac{5}{3}\)

  9. For any value of n∈Z, \(\int _{ 0 }^{ \pi }{ e{ cos }^{ 2x }{ cos }^{ 3 } } [(2n+1)x]\) is

    (a)

    \(\frac{\pi}{2}\)

    (b)

    \(\pi\)

    (c)

    0

    (d)

    2

  10. \(\int _{ 1 }^{ \sqrt { 3 } }{ \frac { dx }{ 1+{ x }^{ 2 } } } \) is

    (a)

    \(\frac { \pi }{ 3 } \)

    (b)

    \(\frac { \pi }{ 6 } \)

    (c)

    \(\frac { \pi }{ 12 } \)

    (d)

    \(-\frac { \pi }{ 6 } \)

  11. The area bounded by the parabola y = x2 and the line y = 2x is

    (a)

    \(\frac43\)

    (b)

    \(\frac23\)

    (c)

    \(\frac{51}{3}\)

    (d)

    \(\frac{30}{3}\)

  12. \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

    (a)

    \(\frac { \pi }{ 2 } \)

    (b)

    0

    (c)

    \(\frac { \pi }{ 4 } \)

    (d)

    \( \pi\)

  13. The order and degree of the differential equation \(\sqrt { sin\quad x } (dx+dy)=\sqrt { cos\quad x } (dx-dy)\)

    (a)

    1,2

    (b)

    2,2

    (c)

    1,1

    (d)

    2,1

  14. The solution of \(\frac { dy }{ dx } ={ 2 }^{ y-x }\)is

    (a)

    2x+2y=C

    (b)

    2x-2y=C

    (c)

    \(\frac { 1 }{ { 2 }^{ x } } -\frac { 1 }{ { 2 }^{ y } } =C\)

    (d)

    x+y=C

  15. If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Pt=Q,\)Then P is

    (a)

    log sin x

    (b)

    cos x

    (c)

    tan x

    (d)

    cot x

  16. The general solution of \(4\frac{d^2 y}{dx^2}\)+y=0 is

    (a)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right] \)

    (b)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right] \)

    (c)

    \(y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 } \)

    (d)

    \(t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }\)

  17. The solution of log \(\left( \frac { dy }{ dx } \right) \)=ax+by is______.

    (a)

    \(\frac { { e }^{ ax } }{ a } +\frac { { e }^{ -by } }{ b } +c=0\)

    (b)

    aeax-be-by+c=0

    (c)

    aex+bey=k

    (d)

    beax+ae-by=k

  18. A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
    \(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0<x<l \\\ 0 & l \leq x<2 l \end{array}\right.\)
    The mean and variance of the shorter of the two pieces are respectively

    (a)

    \(\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 3 } \)

    (b)

    \(\\ \cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 6 } \)

    (c)

    \(l,\cfrac { { l }^{ 2 } }{ 12 } \)

    (d)

    \(\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 12 } \)

  19. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

    (a)

    i + 2n, i = 0,1,2... n

    (b)

    2i- n, i = 0,1,2... n

    (c)

    n - i, i = 0,1,2... n

    (d)

    2i + 2n, i = 0, 1, 2...n

  20. Which of the following is a discrete random variable?
    I. The number of cars crossing a particular signal in a day
    II.The number of customers in a queue-to buy train tickets at a moment.
    III.The time taken to complete a telephone call.

    (a)

    I and II

    (b)

    II only

    (c)

    III only

    (d)

    II and III

  21. If \(f(x)=\cfrac { 1 }{ 2 } \) ,\(E\left( { x }^{ 2 } \right) =\cfrac { 1 }{ 4 } \) then var(x) is 

    (a)

    0

    (b)

    \(\cfrac { 1 }{ 4 } \)

    (c)

    \(\cfrac { 1 }{ 2 } \)

    (d)

    1

  22. In the set Q define a⊙b= a+b+ab. For what value of y, 3⊙(y⊙5)=7?

    (a)

    y=\(\frac{2}{3}\)

    (b)

    y=\(\frac{-2}{3}\)

    (c)

    y=\(\frac{-3}{2}\)

    (d)

    y=4

  23. If a*b=\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \) on the real numbers then * is

    (a)

    commutative but not associative

    (b)

    associative but not commutative

    (c)

    both commutative and associative

    (d)

    neither commutative nor associative

  24. Which one of the following is not a statement?

    (a)

    2 + 3 =5

    (b)

    How beautiful is this flower?

    (c)

    Delhi is the capital of Tamil Nadu

    (d)

    A triangle has found angles.

  25. Which of the following is a statement?

    (a)

    7+2<10

    (b)

    Wish you all success

    (c)

    All the best

    (d)

    How old are you?

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