Question 1 :
A dice is thrown once. Find the probability of getting a number greater than $4$.

Question 2 :
An experiment can result in only $3$ mutually exclusive events $A, B$ and $C$. If $P(A) = 2P(B) = 3P(C)$, then $P(A) =$<br/>

Question 3 :
A card is drawn at random from well shuffled pack of $52$ cards. Find the probability that the card drawn is a spade:

Question 4 :
Three unbiased coins are tossed, what is probability of getting exactly two heads ?

Question 5 :
Two dice are tossed once. The probability of getting an even number at the first die or a total of $8$ is

Question 6 :
$\tan\theta=-2, &#160;\theta \epsilon &#160;(0, \pi)$ then which of the following is correct

Question 7 :
Points in which abscissa and ordinate have different signs will lie in .............

Question 8 :
Solve${{{{\cos }^2}{{33}^0} - {{\cos }^2}{{57}^0}} \over {\sin {{21}^0} - \cos {{21}^0}}}$<br/><br/>

Question 9 :
The value of&#160;$\displaystyle { \sin }^{ 2 }{ 20 }^{ o }+{ \sin }^{ 2 }{ 70 }^{ o }-{ \tan }^{ 2 }{ 45 }^{ o }$ is :

Question 10 :
If $\theta \,\,\,\,$ and $\phi \,\,$ are angles in the 1st quadrant such that $\tan \theta&#160; = \dfrac{1}{7}$ and $\sin \phi&#160; = \dfrac{1}{{\sqrt {10} }}$&#160;.

Question 11 :
A wheel makes $240$ revolutions in one minute The measure of the angle it describes at the centre in $15$ seconds is ___&#160;<br/>

Question 12 :
The value of $\sqrt2 ( \cos 15^o - \sin 15^o ) $ is equal to :

Question 13 :
The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\displaystyle \frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $\displaystyle 1^{\circ}=\left ( \frac{180}{\pi } \right )^{\circ}\:\simeq 57^{\circ},17',44.{8}''$ and sum of interior angles of a $n$-sided regular polygon is $\displaystyle \left ( 2n-4 \right )\dfrac {\pi }2$. On the basis of above information, answer the following questions :The number of sides of two regular polygon are as 5 : 4 and the difference between their angles is $\displaystyle \frac{\pi }{20},$ then the number of sides in the polygons respectively are -<br/>

Question 15 :
The centre of the circle given by $\mathbf { r } \cdot ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) = 15 \text { and } | \mathbf { r } - ( \mathbf { j } + 2 \mathbf { k } ) | = 4 ,$

Question 16 :
State whether the following statements are true or false.<br/>The equation $x^{2}+y^{2} + 2x -10y + 30 = 0$ represents the equation of a circle.<br/>

Question 17 :
Find the equation of the circle passing through the origin and centre lies on the point of intersection of the lines $2x+y=3$ and $3x+2y=5$.

Question 18 :
Which of the following equations of a circle has center at (1, -3) and radius of 5?

Question 20 :
A circle has a diameter whose ends are at (-3, 2) and (12, -6) Its Equation is

Question 21 :
The circle with radius $1$ and centre being foot of the perpendicular from $(5, 4)$ on y-axis, is?

Question 22 :
The intercept on the line $y=x$ by the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x=0$ is $AB$. Equation of the circle with $AB$ as a diameter is

Question 23 :
Find the value of a if $y^2=4ax $ pases through $(8,8)$

Question 25 :
If the lines $3x-4y-7=0$ and $2x-3y-5=0$ are two diameters of a circle of area 154 square units , the equation of the circle is :<br/><br/>

Question 26 :
The equation of the circle passing through $(3,6)$ and whose centre is $(2,-1)$ is-

Question 27 :
The equation of the circle passing through $(3,6)$ and whose centre is $(2,-1)$ is

Question 28 :
The equation $y^{2} + 4x + 4y + k = 0$ represents a parabola whose latus rectum is