#### 12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Two

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. If sin-1 x+cot-1$(\frac{1}{2})=\frac{\pi}{2}$, then x is equal to

(a)

$\frac{1}{2}$

(b)

$\frac{1}{\sqrt{5}}$

(c)

$\frac{2}{\sqrt{5}}$

(d)

$\frac{\sqrt3}{2}$

2. The eccentricity of the ellipse (x−3)2 +(y−4)2 =$\frac { { y }^{ 2 } }{ 9 }$ is

(a)

$\frac { \sqrt { 3 } }{ 2 }$

(b)

$\frac { 1 }{ 3 }$

(c)

$\frac { 1 }{ 3\sqrt { 2 } }$

(d)

$\frac { 1 }{ \sqrt { 3 } }$

3. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

(a)

$\frac { \sqrt { 7 } }{ 2\sqrt { 2 } }$

(b)

$\frac{7}{2}$

(c)

$\frac { \sqrt { 7 } }{ 2 }$

(d)

$\frac { 7 }{ 2\sqrt { 2 } }$

4. The maximum value of the function x2 e-2x,

(a)

$\cfrac { 1 }{ e }$

(b)

$\cfrac { 1 }{ 2e }$

(c)

$\cfrac { 1 }{ { e }^{ 2 } }$

(d)

$\cfrac { 4 }{ { e }^{ 4 } }$

5. If w (x, y, z) = x2 (v - z) + y2 (z - x) + z2(x - y), then $\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z }$ is

(a)

xy + yz + zx

(b)

x(y + z)

(c)

y(z + x)

(d)

0

6. If $\int _{ 0 }^{ x }{ f(t)dt=x+\int _{ x }^{ 1 }{ tf } (t)dt }$ then the value of f (1) is

(a)

$\frac{1}{2}$

(b)

2

(c)

1

(d)

$\frac{3}{4}$

7. 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

8. If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

(a)

0.125

(b)

0.25

(c)

0.375

(d)

0.75

9. Subtraction is not a binary operation in

(a)

R

(b)

Z

(c)

N

(d)

Q

10. The dual of ᄀ(p V q) V [p V (p ∧ ᄀr)] is

(a)

ᄀ(p ∧ q) ∧ [p V (p ∧ ᄀr)]

(b)

(p ∧ q) ∧ [p ∧ (p V ᄀr)]

(c)

ᄀ(p ∧ q) ∧ [p ∧ (p ∧ r)]

(d)

ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]