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

12th Standard

Reg.No. :
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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?