Q. Find the area of the triangle formed by joining the mid points of the sides of the triangle, whose vertices are $(0,1);(2,1)$ and $(0,3)$. Find the ratio of this area to the area of the given triangle

Q. Exponential form of ${\log }_{4}8=x$ is _____

1. $x^8=4$
2. $x^4=8$
3. $4^x=8$
4. $8^x=4$

Q. Find the number of terms in the following $A.P.7,13,19,....,205$

Q. If $\log 625=k\log 5$, then the value of $k$ is ____

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

Q. Find the area of the triangle, whose vertices are $(2,0),(1,2),(-1,6)$. What do you observe?

Q. Draw the Venn diagrams of the sets $(A-B),(B-A)$

Q. A chord of a circle of radius $10cm$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $\pi =3.14$)

Q. $\frac{p}{q}$ form of $0.0875$ is _______

1. $\frac{7}{2^4\times 5}$
2. $\frac{7}{2\times 5^4}$
3. $\frac{5^3\times 7}{2^3\times 5^4}$
4. $\frac{7}{2^4\times 5^4}$

Q. Find a quadratic polynomial, if the zeroes of it are $2$ and $-1$ respectively.

Q. Find the roots of the equation $2x^2+x-6=0$ by factorisation.

Q. Solve the pair of equations by Elimination method.
$2x+y-5=0,3x-2y-4=0$

Q. Solve the equations
$\frac{10}{x+y}+\frac{2}{x-y}=4,\frac{15}{x+y}-\frac{5}{x-y}=-2$

Q.

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

$\begin{array}{cccccccc}\text{Weight(in Kgs)}& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ \text{Number of students}& 2& 3& 8& 6& 6& 3& 2\end{array}$

Q. Expand $\log \frac{343}{125}$

Q. Solve the following equations graphically.
$3x-y=7$,
$2x+3y=1$

Q. Find the common ratio of G.P.
$2,2\sqrt{2},4,....$

Q. $10$ students of class $X$ took part in a mathematics quiz. If the number of girls is four more than the number of boys, then find the number of boys and the number of girls who took part in the quiz

Q. If $p\left(x\right)=x^2-5x-6$; find the value of $p\left(3\right)$

Q. Find the mid point of the line segment joining the points $(2,7)$ and $(12,-7)$

Q. If $A=\{1,2,3,4\},B=\{1,2,3,5,6\}$, then find

Q. If the sum of the first $7$ terms of an A.P. is $49$ and that of $17$ terms is $289$; find the sum of the first $n$ terms

Q. If $p$ is prime, then $\sqrt{p}$ is:

1. Composite number
2. Rational number
3. Positive integer
4. Irrational number

Q. Show that $(5-\sqrt{3})$ is irrational.

Q. Solve the quadratic equation $2x^2+x-4=0$ by completing the square

Q. Find the zeroes of the polynomial $p\left(x\right)=x^2-4x+3$ and verify the relationship between zeroes and coefficients

Q. Write the following set $\{x:x=2n+1andn\in N\}$ in roster form

Q. List all the subsets of the following set $B=\{p,q\}$

Q. Find the value of ${\log }_{81}3$

Q. Draw the graph of $p\left(x\right)=x^2+3x-4$ and find zeroes.
Verify the zeroes of the polynomials

Q. Find the coordinates of the point, which divides the join of $(-1,7)$ and $(4,-3)$ in the ratio $2:3$