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Suppose that there is a conical strainer as shown in the given figure. The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 ${cm}^2$ of strainer has an average of 8 tiny holes. Then the total number of holes in the entire strainer is:

Find the remainders when $x^4-3x^3+4x^2-x+4$ is divided by

1) $x+1$

2) $x-\frac{1}{4}$
[3 MARKS]

Write $x^2$ +8x+16 =0 in the form $x^2$ +px+qx+16 =0 such that p x q = 16

Divide 77 into two parts such that the sum of their reciprocals is $\frac{7}{12}$. From which of the following equations, we can get the required numbers? (Take one required number as x).

Solve each of the following quadratic equations:
$\frac{a}{(ax-1)}+\frac{b}{(bx-1)}=(a+b),x\ne \frac{1}{a},\frac{1}{b}$

Find the discriminant of each of the following equations :
(i) $2x^2-7x+6=0$ (ii) $3x^2-2x+8=0$
(iii) $2x^2-5\sqrt{2}x+4=0$ (iv) $\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0$
(v) $(x-1)(2x-1)=0$ (vi) $1-x=2x^2$

Solve each of the following quadratic equations:
$4x^2-2(a^2+b^2)x+a^2{b}^2=0$

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $10cm$ and its base is of radius $3.5cm$, find the volume of wood in the toy.

If $sin(B+C)=\frac{\sqrt{3}}{2}$ and$sinA=\frac{1}{2}$, find $B+C$and$A$.

Prove that the line segment joining the point of contact of two parallel tangles of a circle passes through its centre.

If the seventh term of an A.P. is $\frac{1}{9}$ and its ninth term is $\frac{1}{7}$, find its (63)rd term.

The sum of roots of the equation $x^2–8x+2=0$ is

A tangent from a point P outside the circle meets the circle at M. Then $\angle MOP=$ , if $\angle MPO={30}^{\circ }$.

The vertices of a triangle are (6. 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and circumcentre.

The x-coordinate of point C is ___.

The first three terms of an AP respectively are 3y - 1, 3y +5 and 5y +1. Then y equals

The probability of getting a red spade from a well-shuffled 52 pack card is___

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of ₹ 12.50 per $m^2.[Assume\pi =\frac{22}{7}]$

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

$\begin{array}{cc}ClassInterval& Frequency\\ 0-100& 2\\ 100-200& 5\\ 200-300& x\\ 300-400& 12\\ 400-500& 17\\ 500-600& 20\\ 600-700& y\\ 700-800& 9\\ 800-900& 7\\ 900-1000& 4\end{array}$ [4 MARKS]

When the cost of a used car was increased in the ratio 11:13, its cost became Rs 39,000. Find the original cost of the car.

A circular tent is a cylinder to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then the area of canvas required is

Question 10 (ii)
A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will not be a Rs. 5 coin?

Find the length of direct common tangent for circles $x^2+y^2-20x+64=0$and $x^2+y^2+30x+144=0$

The zeros of the polynomial $4x^2+5\sqrt{2}x-3$ are ____

In triangle ABC, right angled at B, if $\angle$A is made smaller and smaller till it becomes zero, and AB = 1 unit, what can you say about sides BC and AC ?

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 120° to each other. Refer the figure and select the option which would lead us to the required construction.

Four years ago, a mother was four times as old as her daughter. Six years later, the mother will be two and a half times as old as her daughter at that time. Find the present ages of mother and her daughter.

Which of the following graph represents a quadratic polynomial which has sum of its zeroes is zero?

Total surface area of a cone of radius 5 cm and slant height 10 cm is .
$(Take\pi =3.14)$

Solve the following quadratic equation: $x^2=15$

How many solutions are possible for the following pair of equations?

x - y = 1 and 3x - 4y = 4

What is the degree of the polynomial p(x):

$p\left(x\right)=a{x}^4+b{x}^3+c{x}^2+dx+e$, given $\frac{a}{b}$ = 0, b $\ne$ 0

If there are 5 people in the height range 170-175 cm in a class of 50 people, then what is the percentage of people in this height range ?

Solve

$\frac{5}{(x-1)}+\frac{1}{(y-2)}=2$

$\frac{6}{(x-1)}-\frac{3}{(y-2)}=1$ [4 MARKS]

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction. [3 MARKS]

An event, having only one favourable outcome, is called:

In the given figure, KL // AC // YZ. B and D are equidistant from AC. If 5KL = YZ, find the ratio of areas of $\Delta$ BKL and $\Delta$ DYZ.

Shooters are required to shoot at a target which is circular in shape. The target is fixed onto a rectangular board whose dimensions are $44cm\times 21cm$. Assuming that all the bullets hit the rectangular board, what is the probability that the bullets hit the circular target? (Given that: radius of the circle = 7 cms. )

A chord of a circle of radius 20 cm subtends an angle of ${90}^{\circ }$ at the centre. Find the area of the corresponding major segment of the circle. (Use $\pi =3.14$)

Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?