#### 12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020

12th Standard

Reg.No. :
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Maths

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

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