Q. The value of $\sum _{a,b,c}^{}a(b-c)$ is

1. $0$
2. $ab+bc+ca$
3. $2(ab+bc+ca)$
4. $a+b+c$

Q. The quadratic equation having the roots $(2+\sqrt{3})$ and $(2-\sqrt{3})$ is

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

Q. The simplified form of $10\sqrt[3]{3x}-8\sqrt[3]{3x}$ is:

1. $18\sqrt[3]{3x}$
2. $2\sqrt{x}$
3. $2\sqrt[3]{3x}$
4. $18\sqrt{x}$

Q. If $3\oplus y\equiv 2\left(\mathrm{mod}6\right)$, then the value of $y$ is

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

Q. In $△ABC$, $D$ and $E$ are the mid-points of $AB$ and $AC$ respectively, then the area of $△ADE$ is:

1. $4\times$ Area of $△ABC$
2. $\frac{1}{2}$ Area of $△ABC$
3. $2\times$ Area of $△ABC$
4. $\frac{1}{4}$ Area of $△ABC$

Q. Shape of each face of Dodecahedron is ______

Q. If $A+B=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$ and $A=\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$, then matrix $B$ is

1. $\left[\begin{array}{cc}1& 1\\ 4& 2\end{array}\right]$
2. $\left[\begin{array}{cc}2& 4\\ 1& 1\end{array}\right]$
3. $\left[\begin{array}{cc}1& 4\\ 1& 2\end{array}\right]$
4. $\left[\begin{array}{cc}4& 2\\ 1& 1\end{array}\right]$

Q. In the given figure $AC,CE$ and $EH$ are tangents drawn to the circle at $B,D$ and $F$ respectively. If $CB=5cm$ and $EF=3cm$, then length of $CE$ is

1. $2cm$
2. $5cm$
3. $3cm$
4. $8cm$

Q. Find the sum of the series $1+2+4+...$ upto $9$ terms. (Using the formula)

Q. In the given figure, $XY\parallel BC$, then $\frac{AX}{BX}=$

Q. If one factor of $a^3+b^3$ is $(a+b)$, then the other factor is:

1. $a-b+ab$
2. $a^3+b^3+ab$
3. $a^2+b^2-ab$
4. $a^2+b^2+ab$

Q. If $A,B$ and $C$ are non-empty sets then the 'Intersection of sets is distributive over union of sets' is represented as

1. $(A\cup B)\cup C=(A\cap C)\cup (B\cup C)$
2. $(A\cap B)\cup C=(A\cup C)\cap (B\cup C)$
3. $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$
4. $A\cap (B\cap C)=(A\cap B)\cap (A\cap C)$

Q. The formula to find volume of a right circular cylinder is _____

Q. In $△ABC,\angle ABC={90}^o$. If $AC=(x+y)$ and $BC=(x-y)$, then the length of $AB$ is:

1. $2xy$
2. $2\sqrt{xy}$
3. $x^2-y^2$
4. $x^2+y^2$

Q.

If $4x=\frac{81}{x}$, then the value of $x$ is

1. $\pm 4.5$
2. $-4.5$
3. $4.5$
4. $\pm 0.45$

Q. If ${{}^{n}C}_8={{}^{n}C}_5$, then the value of $n$ is

1. $2$
2. $1$
3. $13$
4. $3$

Q. If the circumference of the base of a cylinder is $44cm$ and height $20cm$, then its lateral surface area is

1. $440sq.cm$
2. $880sq.cm$
3. $44sq.cm$
4. $88sq.cm$

Q. If $A$ and $B$ are the subsets of the universal set $U$ then $(A\cup B{)}^{\prime }=$ ____

Q. Which term of the Geometric progression $2,2\sqrt{2},4,...$ is $64$?

Q. The expansion of $\sum _{p,q,r}^{}{p}^2$ is

1. $p^2+q^2+r^2$
2. $p^2{q}^2{r}^2$
3. $pqr$
4. $p^2$

Q. If $A$ is a matrix of order $(m\times n)$ and $B$ is a matrix of order $(n\times p)$ then order of $AB$ is ................

Q. If the square on one side of a triangle is equal to the sum of the squares on the other two sides, then those two sides contain ____

Q. If $4\sqrt{y}=\sqrt{80}$, the value of $y$ is

1. $5$
2. $16$
3. $4$
4. $20$

Q. Rationalising factor of $\left(\sqrt{x+y}\right)$ is ____

Q. If $5$ and $2$ are the Arithmetic Mean and Harmonic Mean of two distinct numbers, then their Geometric Mean is

1. $7$
2. $3$
3. $\sqrt{10}$
4. $10$

Q. The standard form of the quadratic equation is ____

Q. Out of the following sets, $Z_4$ is

1. $\{0,1,2\}$
2. $\{0,1,2,3\}$
3. $\{1,2,3,4\}$
4. $\{0,1,2,3,4\}$

Q. The H.C.F of $5x^2{y}^3$ and $10x^3{y}^2$ is

1. $10x^3{y}^3$
2. $5x^2{y}^2$
3. $5xy$
4. $5x^3{y}^3$

Q. If the value of the discriminant of the quadratic equation $a{x}^2+bx+c=0$ is less than $0$, then the nature of the roots is ____

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