Q. If $A=\{3,6,9,12,15,18,21\};B=\{4,8,12,16,20\}$
$C=\{2,4,6,8,10,12,14,16\};D=\{5,10,15,20\}$; find
(i) $A-B$ (ii) $B-A$ (iii) $C-A$ (iv) $D-A$
(v) $B-C$ (vi) $B-D$ (vii) $C-B$ (viii) $D-B$

Q. Expand $\log 15$.

Q. If $p\left(t\right)=t^3-1$, find the values of $p\left(1\right),p(-2).$

Q. For what value of $k$, the pair of equations $3x+4y+2=0$ and $9x+12y+k=0$ represent co-incident lines.

Q. If $P\left(E\right)=0.05$, what is the probability of "not $E$"?

Q. Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{1}{4},-1$ respectively

Q. Write roster and set builder form of "The set of all natural numbers, which divide $42$".

Q. Length of the shadow of a $15$ meter high pole is $5\sqrt{3}$ meters at 7'o clock in the morning. Then what is the angle of elevation of the Sun rays with the ground at that time?

Q. Formulate a pair of linear equations in two variables "$5$ pencils and $7$ pens together cost Rs. $50$, whereas $7$ pencils and $5$ pens together cost Rs. $46$".

Q. Find L.C.M. and H.C.F. of $72$ and $108$ by the prime factorization method.

Q. Find the roots of equation $2x^2-x-4=0$ by the method of completing the square.

Q. If $\cos 7A=\sin (A-6^o)$, where $7A$ is an acute angle. Find the value of $A$.

Q. Find the mean of the following data:
$5,6,9,10,6,12,3,6,11,10$.

Q. Find two numbers, whose sum is $27$ and product is $182$.

Q. Verify that $1,-1$ and $-3$ are the zeroes of the cubic polynomial $x^3+3x^2-x-3$ and check the relationship between zeroes and co-efficients.

Q. Find the co-ordinates of a point $A$, where $AB$ is the diameter of a circle, whose centre is $(2,-3)$ and $B$ is $(1,4)$.

Q. A box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
(i) red, (ii) white, (iii) not green?

Q. Calculate the length of tangent from a point $15cm$ away from the centre of a circle of radius $9cm$.

Q. A fraction becomes $\frac{4}{5}$ if $1$ is added to both numerator and denominator. If, however, $5$ is subtracted from both numerator and denominator, the fraction becomes $\frac{1}{2}$. What is the fraction?

Q. Prove that $\sqrt{5}$ is irrational by the method of Contradiction.

Q. Find the total surface area of a hemisphere of radius $3.5cm$.

Q. Solve the equations
$\frac{5}{x-1}+\frac{1}{y-2}=2$ and $\frac{6}{x-1}-\frac{3}{y-2}=1$

Q. If $b^2-4ac\ge 0$, then write the nature of roots of a quadratic equation $a{x}^2+bx+c=0$.

Q. Prove that "The lengths of tangents drawn from an external point to a Circle are equal".

Q. Find the area of the triangle, whose vertices are $(-5,-1),(3,-5),(5,2).$

Q. Write the formula for the sum of first $n$ positive integers.

Q. The curved surface area of a cone is $4070{cm}^2$ and its diameter is $70cm$. What is its slant height (in $cm$)?

Q. In a flower bed, there are $23$ rose plants in the first row, $21$ in the second row, $19$ in the third row, and so on. There are $5$ rose plants in the last row. How many rows are there in the flower bed?

Q. Prove that the points $(-7,-3),(5,10),(15,8)$ and $(3,-5)$ taken in order are the vertices of a parallelogram.

Q. If $V=\{a,e,i,o,u\}$ and $B=\{a,i,k,u\}$, then find $V-B$ and $B-V$. Are they equal?