Q. In a Geometric progression with common ratio less than $1$, if $n$ approaches $\infty$ then $S_{\infty }$ is

1. $a{r}^{n-1}$
2. $\frac{1-r}{a}$
3. $a{r}^0$
4. $\frac{a}{1-r}$

Q. In trapezium $ABCD,AB\parallel DC$ and the diagonals intersect at $O$, then $\frac{OD}{OC}=$ ?

1. $\frac{AB}{CD}$
2. $\frac{OB}{OA}$
3. $\frac{AC}{BD}$
4. $\frac{OC}{OD}$

Q. The L.C.M. of $(a^2-b^2),(a-b)$ and $(a^2-2ab+b^2)$ is

1. $(a^2-b^2)(a-b)$
2. $(a-b)$
3. $(a^2-b^2)$
4. $(a^2-b^2)(a+b)$

Q. The value of $\sum 18+\sum 19$ is

1. $703$
2. $324$
3. $361$
4. $743$

Q. $a^3+b^3+c^3$ can be written using $\sum$ notation as _____ .

Q. The pure quadratic equation in the following is

1. $x+\frac{1}{x}=4$
2. $x+\frac{1}{x}=0$
3. $x-\frac{3}{4}=2x$
4. $3x(x-1)=0$

Q. In a sequence if $T_n=4n^2-1$ and $T_n=35$, then the value of $n$ is

1. $9$
2. $3$
3. $5$
4. $6$

Q. In the given figure, $XY\parallel BC$ and $XZ\parallel AC$, then $\frac{AX}{AB}=$

1. $\frac{XZ}{AB}$
2. $\frac{XY}{AC}$
3. $\frac{BZ}{BC}$
4. $\frac{CZ}{BC}$

Q. The formula to find $n^{th}$ term of Harmonic progression is

1. $\frac{1}{a+(n+1)d}$
2. $\frac{1}{a-(n-1)d}$
3. $\frac{1}{a+(n-1)d}$
4. $\frac{1}{a-(n+1)d}$

Q. The value of ${{}^{n}C}_1$ is _______

Q. In the given figure, $AB,BC$ and $AC$ touch the circle at $L.M$ and $N$ respectively. If $\angle B={70}^o$ and $\angle C={60}^o$, then the measure of $\angle LON$ is

1. ${110}^o$
2. ${120}^o$
3. ${50}^o$
4. ${130}^o$

Q. If $a+b+c=2s$ then the value of ${(b+c)}^2-a^2$ is

1. $4s(s-a)$
2. $4(s-a)$
3. $2s(s-a)$
4. $2(s-a)$

Q. The roots of the quadratic equation $a{x}^2+bx=0$ are

1. $0,-\frac{b}{a}$
2. $0,+\frac{b}{a}$
3. $-\frac{b}{a},-\frac{b}{a}$
4. $+\frac{b}{a},-\frac{b}{a}$

Q. The formula to find the volume of sphere is _______

Q. The value of $\left(4{\oplus }_{5}2\right){\oplus }_{5}3$ is

1. $4$
2. $2$
3. $1$
4. $0$

Q. Maximum number of tangents that can be drawn from an external point to a circle is ______ .

Q. If $A=\{0,1,2,3\}$ and $B=\{2,3,4,5,6\}$, then verify that $A-(A-B)=A\cap B$

Q. The quadratic equation having the roots $(1+\sqrt{2})$ and $(1-\sqrt{2})$ is

1. $x^2+2x+1=0$
2. $x^2+2x-1=0$
3. $x^2-2x-1=0$
4. $x^2-2x+1=0$

Q. In the given figure, $AB\parallel PQ$. If $PQ=1.5cm,QC=2cm$ and $BQ=8cm$, then the measure of $AB$ is:

1. $10cm$
2. $7.5cm$
3. $9.5cm$
4. $3.5cm$

Q. If $3p=\left[\begin{array}{cc}6& 0\\ -9& 12\end{array}\right]$, then the matrix $2p$ is

1. $\left[\begin{array}{cc}4& -6\\ 0& 8\end{array}\right]$
2. $\left[\begin{array}{cc}12& 0\\ -18& 24\end{array}\right]$
3. $\left[\begin{array}{cc}12& -18\\ 0& 24\end{array}\right]$
4. $\left[\begin{array}{cc}4& 0\\ -6& 8\end{array}\right]$

Q. If $A$ is any square matrix then $(A-A^{\prime })$ is always ______

Q. If $2y\otimes y\equiv 3\mathrm{mod}5$ then the value of $y$ is

1. $1$
2. $0$
3. $4$
4. $2$

Q. The value of ${{}^{n}P}_0$ is _______.

Q. The product of two consecutive natural numbers is $12$. The equation form of this statement is

1. $x^2+2x-12=0$
2. $x^2+1x-12=0$
3. $x^2+1x+12=0$
4. $x^2+2x+12$

Q. The sum of roots of a quadratic equation $a{x}^2+bx+c=0$ is ______

Q. If $\sum _{a,b,c}^{}a=0$ then the value of $\sum _{a,b,c}^{}{a}^3-abc$ is

1. $0$
2. $abc$
3. $2abc$
4. $3abc$

Q. The standard form of quadratic equation $x^2=2x-3$ is _____ .

Q. The biggest chord of a circle is called _______

Q. The product of $\sqrt[3]{32}$ and $\sqrt{2}$ is:

1. $\sqrt[6]{632}$
2. $\sqrt[6]{624}$
3. $\sqrt[6]{616}$
4. $\sqrt[6]{64}$

Q. In the given figure, $APB$ is tangent at $P$ to the circle with the centre $O$. If $\angle QPB={60}^o$ then measure of $\angle POQ=$

1. ${30}^o$
2. ${120}^o$
3. ${60}^o$
4. ${90}^o$