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12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 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 value of the limit \(\\ \\ \\ \underset { x\rightarrow 0 }{ lim } \left( cotx-\cfrac { 1 }{ x } \right) \) 

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

  3. 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

  4. If u (x, y) = ex2+y2, then \(\frac { \partial u }{ \partial x } \) is equal to

    (a)

     ex2+y2

    (b)

    2xu

    (c)

    x2u

    (d)

    y2u

  5. If loge4 = 1.3868, then loge4.01 =

    (a)

    1.3968

    (b)

    1.3898

    (c)

    1.3893

    (d)

    none

  6. If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

    (a)

    -y sin (xy) + z2 cos (xz)

    (b)

    y sin (xy) - z2 cos (xz)

    (c)

    y sin (xy) + z2 cos (xz)

    (d)

    -y sin (xy) - z2 cos (xz)

  7. The approximate value of (627)\(\frac14\) is ................

    (a)

    5.002

    (b)

    5.003

    (c)

    5.005

    (d)

    5.004

  8. If u = \((\frac{y}{x})\) then x \(x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \) = .....................

    (a)

    0

    (b)

    1

    (c)

    2u

    (d)

    u

  9. If \(f(x)=\int _{ 0 }^{ x }{ t\ cos\ t\ dt,\ then\ \frac { dx }{ dx } } \)

    (a)

    cos x-x sin x

    (b)

    sin x+x cos x

    (c)

    x cos x

    (d)

    x sin x

  10. The value of \(\int _{ -1 }^{ 2 }{ |x|dx } \)

    (a)

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

    (b)

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

    (c)

    \(\frac{5}{2}\)

    (d)

    \(\frac{7}{2}\)

  11. The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is

    (a)

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

    (b)

    2

    (c)

    0

    (d)

    1

  12. The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is

    (a)

    4

    (b)

    8\(\frac23\)

    (c)

    13

    (d)

    4\(\frac{1}{3}\)

  13. \(\int _{ a }^{ b }{ f(x) } dx=\) ..............

    (a)

    \(2\int _{ 0 }^{ a }{ f(x) } dx\)

    (b)

    \(\int _{ a }^{ b }{ f(a-x) } dx\)

    (c)

    \(\int _{ b }^{ a }{ f(b-x) } dx\)

    (d)

    \(\int _{ a }^{ b }{ f(a+b-x) } dx\)

  14. The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

    (a)

    \(\frac { x }{ { e }^{ \lambda } } \)

    (b)

    \(\frac { { e }^{ \lambda } }{ x } \)

    (c)

    \({ \lambda e }^{ x }\)

    (d)

    ex

  15. The differential equation of the family of parabolas y2=4ax is

    (a)

    \(2y=x\left( \frac { dy }{ dx } \right) \)

    (b)

    \(y=2x\left( \frac { dy }{ dx } \right) \)

    (c)

    \(y={ 2x }^{ 2 }\left( \frac { dy }{ dx } \right) \)

    (d)

    \({ y }^{ 2 }=2x\left( \frac { dy }{ dx } \right) \)

  16. The transformation y=vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \)

    (a)

    \(\frac { 3av }{ 4v+1 } =\frac { dx }{ x } \)

    (b)

    \(\frac { 3dv }{ v+1 } =\frac { dx }{ x } \)

    (c)

    \(2x\frac { dv }{ dx } =v\)

    (d)

    \(\frac { 3dv }{ 1-2v } ==\frac { dx }{ x } \)

  17. The differential equation corresponding to xy=c2 where c is an arbitrary constant is ________.

    (a)

    xy"+x=0

    (b)

    y"=0

    (c)

    xy'+y=0

    (d)

    xy"-x=0

  18. The general solution of x \(\frac{dy}{dx}\)=y is _________.

    (a)

    y=cx

    (b)

    x2+y2=c

    (c)

    x2-y2=c

    (d)

    y=cx

  19. The differential equation associated with the family of concentric circles having their centres at the origin is _________.

    (a)

    \(\frac { dy }{ dx } =\frac { -x }{ y } \)

    (b)

    \(\frac { dy }{ dx } =\frac { -y }{ x } \)

    (c)

    \(\frac { dy }{ dx } =\frac { x }{ y } \)

    (d)

    \(\frac { dy }{ dx } =\frac { y }{ x } \)

  20. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  21. If X is a binomial randam variable with expected value 6 and variance 2.4, then P(X=5) is 

    (a)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 6 }\left( \cfrac { 2 }{ 5 } \right) ^{ 4 }\) 

    (b)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 10 }\)

    (c)

    \(\left( \cfrac { 10 }{ 5 } \right) { \left( \cfrac { 3 }{ 5 } \right) }^{ 4 }\left( \cfrac { 2 }{ 5 } \right) ^{ 6 }\)

    (d)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 5 }\left( \cfrac { 2 }{ 5 } \right) ^{ 5 }\)

  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. Which of the following is a contradiction?

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    q v ~ q

    (d)

    q ∧ ~ q

  24. Let p: Kamala is going to school
    q: There are 20 students in the class. Then Kamala is not going to school or there are 20 students in the class is represented by

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    ~ p

    (d)

    ~ p v q

  25. In (S, *), is defined by x * y = x where x, y \(\in \) S, then

    (a)

    associative

    (b)

    Commutative

    (c)

    associative and commutative

    (d)

    neither associative nor commutative

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