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ABC is a right angled triangle,right angled at B such that BC = 6 cm and AB = 8 cm. A circle with center O is inscribed in $△$ABC. Find the radius of the circle.

The graph of the linear equation 2x - y = 4 cuts x-axis at

Factorise:
$2x^2+3\sqrt{3}x+3$

How many square meters of the canvas is required for a conical tent whose height is $3.5m$ and the radius of the base is $12m$?

There is a solid wooden cuboidal block of length, breadth and height 10 m, 8 m and 5 m respectively. On the top face of the block is a hemispherical depression of radius 3 m. What is the surface area of the solid so obtained?

Among the following instruments, which of the following has no use in angle bisector construction?

Verify whether the following values indicated against them are zeroes of the polynomial.
$\left(i\right)p\left(x\right)=5x-\pi ,x=\frac{4}{5}$
$\left(ii\right)p\left(x\right)=x^2-1,x=1,-1$ [4 MARKS]

Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he gently dropped a spherical ball of radius 0.7cm. By how much should the height be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places.

Factorise $a^2-81(b-c{)}^2$ is _____.

The probability of an event occurring is 0.65. What is the probability of the event not occurring?

The value of (√32+√48)/(√8+√12) is
A) √2
B) 2
C) 4
D) 8

The adjoining figure shows a pentagon inscribed in a circle with centre O. Given AB = BC = CD and $\angle$ABC = ${130}^{\circ }$

Find (i) $\angle$AEB (ii) $\angle$AED (iii) $\angle$COD

Which of these linear equations is written in slope-intercept form?

If the area of an equilateral triangle is $25\sqrt{3}c{m}^2$, then its perimeter = _____________________ cm.

Factorize: $x^3(2x-3y)-x^2(2x-3y{)}^2$

In the given figure, AB||CD, then the value of x is

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Write the equation of y -axis in term of x and y

Which of the following should be the FIRST sentence after rearrangement?

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?

__

If V and C stand respectively for the volume and curved surface area of a cylinder with radius r of base then

Which of the following is the value of $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$?

(a) -4

(b) 4

(c) $\sqrt{11}$

(d) $\sqrt{7}$

Draw a histogram and the frequency polygon from the following data:
$\begin{array}{ccccccc}\text{Class interval}& 20-25& 25-30& 30-35& 35-40& 40-45& 45-50\\ \text{Frequency}& 30& 24& 52& 28& 46& 100\end{array}$

$In\Delta ABC,\angle B={35}^{\circ },\angle C={65}^{\circ }\text{and the bisector of}\angle BAC\text{meets BC in X. Arrange AX, BX and CX in descending order.}$

What special name can be given to a quadrilateral $PQRS$ if $\angle P+\angle S={180}^{\circ }$?

The abscissa of any point on y-axis is

Write two solutions of the form $x=0,y=1andx=b,y=0$ for each of the following equations:

(i) 5x - 2y = 10 (ii) - 4x + 3y = 12 (iii) 2x + 3y = 24

The point of intersect of the co-ordinate axes is

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre is Rs 340.20 and the cost of matting the floor at 85 paise per square metre is Rs 91.80. Find the height of the room.

A kite is flying on a string of length 40$\sqrt{3}$m. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^{\circ }$. Find the height at which the kite is flying.

The sum of the three altitudes of a triangle is _________ than its perimeter.

For what value of x in the figure, points A, B, C and D are concyclic?

Question 3 (iii)
Construct the angles of the following measurements:
(iii) ${15}^{\circ }$

Find 4 rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ using d=$\frac{(y-x)}{n+1}$ [4 MARKS]

Thinking process

Firstly, use the property that sum of cointeritor angles is ${180}^{\circ }$.Secondly use the property that sum of all angles in a triangle Is ${180}^{\circ }$ and then prove the required result.

The sides of a triangle are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ and its perimeter is $104cm.$ The length of the longest side is ______.

The sum of the digits of a two-digit number is 9. Also, twice this number is nine times the number obtained by reversing the order of the digits. Find the number.

The total surface area of a rectangular box of dimensions a, 2a and 3a is

In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.

Things which coincide with one another are:

When 14 is added to a number, we obtain 72. The equation which shows this relationship is.

Find the coordinates of the point which lies both on x and y-axis.
[2 MARKS]

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of($△$BPC) equal to

In an equilateral triangle $ABC,$ if $AD\perp BC$, then

Question 4 (ii)
State whether the following statement is true or false. Give reasons for your answer.

Every integer is a whole number.

In $△$ABC, AC $>$ AB and AD bisects $\angle$A. Which of the following option is correct?