#### 12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. Let C be the circle with centre at(1,1) and radius =1. If T is the circle centered at(0, y)
passing through the origin and touching the circleC externally, then the radius of T is equal to

(a)

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

(b)

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

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 1 }{ 4 }$

2. If $\vec { a } ,\vec { b } ,\vec { c }$ are three unit vectors such that $\vec { a }$ is perpendicular to $\vec { b }$ and is parallel to $\vec { c }$ then $\vec { a } \times (\vec { b } \times \vec { c } )$ is equal to

(a)

$\vec { a }$

(b)

$\vec { b}$

(c)

$\vec { c }$

(d)

$\vec { 0 }$

3. If the distance of the point (1,1,1) from the origin is half of its distance from the plane x + y + z + k =0, then the values of k are

(a)

$\pm 3$

(b)

$\pm 6$

(c)

-3, 9

(d)

3, 9

4. One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

(a)

(2,0)

(b)

$\left( \sqrt { 5 } ,1 \right)$

(c)

$\left( 3,\sqrt { 5 } \right)$

(d)

$\left( \sqrt { 13 } ,-\sqrt { 3 } \right)$

5. If u(x, y) = x2+ 3xy + y - 2019, then $\frac { \partial u }{ \partial x }$(4, -5) is equal to

(a)

-4

(b)

-3

(c)

-7

(d)

13

6. If $\int _{ a }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } }$then a is

(a)

4

(b)

1

(c)

3

(d)

2

7. The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

(a)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$

(b)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }+y=0$

(c)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }=0$

(d)

$\frac { { d }^{ 2 }x }{ { dy }^{ 2 } }=0$

8. Integrating factor of the differential equation $\frac { dy }{ dx } =\frac { x+y+1 }{ x+1 }$ is

(a)

$\frac{1}{x+1}$

(b)

x+1

(c)

$\frac { 1 }{ \sqrt { x+1 } }$

(d)

${ \sqrt { x+1 } }$

9. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2 , where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in Rs. is

(a)

$\cfrac { 19 }{ 6 }$

(b)

$-\cfrac { 19 }{ 6 }$

(c)

$\cfrac { 3 }{ 2 }$

(d)

$-\cfrac { 3 }{ 2 }$

10. If $f(x)=\left\{\begin{array}{ll} 2 x & 0 \leq x \leq a \\ 0 & \text { otherwise } \end{array}\right.$ is a probability density function of a random variable, then the value of a is

(a)

1

(b)

2

(c)

3

(d)

4