Question 1 :
${ _{  }^{ 15 }{ C } }_{ 3 }+{ _{  }^{ 15 }{ C } }_{ 5 }+....+{ _{  }^{ 15 }{ C } }_{ 15 }$ will be equal to

Question 2 :
What is $\displaystyle\sum _{ r=0 }^{ n }{ C\left( n,r \right)  } $ equal to?

Question 3 :
If $A$ is the sum of the odd terms and $B$ the sum of even terms in the expansion of ${ \left( x+a \right)  }^{ n }$, then ${ A }^{ 2 }-{ B }^{ 2 }=$

Question 4 :
If ${ \left( 8+3\sqrt { 7 }&nbsp; \right)&nbsp; }^{ n }=\alpha +\beta $&nbsp; where $n$ and $\alpha$ are positive integers and $\beta$ is a positive proper fraction,then<br>

Question 6 :
The point which does not belong to the feasible region of the LPP:<br>Minimize: $Z=60x+10y$<br>subject to $3x+y \ge 18$<br>$2x+2y \ge 12$<br>$x+2y\ge 10$<br>$x,y \ge 0$ is

Question 7 :
<span>In a certain group of 75 students, 16&#160; students are taking physics, geography&#160; and English; 24 students are taking&#160; physics and geography, 30 students are&#160; taking physics and English; and 22 students are taking geography and&#160; English. However, 7 students are taking only physics, 10 students are taking only geography and 5 students are taking only English.&#160;</span>How many of these students are taking physics?<br/>

Question 8 :
Find the complex number $z$ satisfying the equation<br/>$ \left |\dfrac {z - 4}{z - 8}\right | = 1$ and $|z|=10$ .

Question 9 :
<b><u>Assertion(A):</u></b> $ f(x) = \log(x-2)+\log(x-3)$ and $ g(x)=\log(x-2)(x-3)$ then $ f(x)=g(x)$<br/><br/><b><u>Reason (R):</u></b> <b><u></u></b>Two functions $f (x)$ and $g (x)$ &#160;are said to be equal if they are defined on the same domain $A$ and the co-domain $B$ as $ f(x)=g(x)\forall x \in A$

Question 10 :
The distance between two straight lines $y=mx+c_1$ and $y=mx+c_2$ is $|c_1-c_2|$. Then the value of $m$ is&#160;

Question 11 :
If $A, B$ are the feet of the perpendiculars from $(2, 4, 5)$ to the $x$-axis, $y$-axis respectively, then&#160;the distance $AB$ is<br/>

Question 12 :
If $\displaystyle \lim_{x\rightarrow 0}(f(x)\:g(x))$ exists for any functions $f$ and $g$ then<br>

Question 13 :
A three-digit code for certain locks uses the digits $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ according to the following&#160;constraints. The first digit cannot be $0$ or $1$, the&#160;second digit must be $0$ or $1$, and the second and third&#160;digits cannot both be $0$ in the same code. How many&#160;<span>different codes are possible?</span>

Question 15 :
If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ is equal to square of distance between centre and one focus of hyperbola,then ${ e }^{ 3 }$ is (e is eccentricity of hyperbola)

Question 16 :
In a simultaneous throw of two dice, what is the number of exhaustive events?<br>

Question 17 :
There are $3$ red, $3$ white and $3$ green balls in a bag. One ball is drawn at random from a bag:<br/>$P$ is the event that ball is red.<br/>$Q$ is the event that ball is not green.<br/>$R$ is the event that ball is red or white.<div>$S$ is the sample space.</div><div>Which of the following options is correct?</div>

Question 19 :
Suppose that $\displaystyle F(n+1)=\frac{2F(n)+1}{2}$ for $ n=1,2,3...., $ and $ F(1)=2 $. Then $ F(101)$ equals<br>

Question 20 :
For each $n\, \epsilon\, N$, then $3^{2n\, +\, 1}\, +\, 1$ is divisible by -