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In $\Delta PQR$, $\angle PQR={30}^{\circ }\angle PRQ={60}^{\circ }$, QR = 5 cm. Which of the following figures accurately represents the triangle.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?

Question 80

State whether the statement is True or False.

When we change the order of integers, their difference remains the same.

Rationalise $\sqrt{2}+\sqrt{3}$

Which of the following is a pair of linear equation in two variables?

Find X if $2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}7& -2\\ -1& 5\end{array}\right]$

If the surface area of a sphere is 616 cm² its diameter is

The line x = 3 is

In the following figure, $\angle ABC={60}^{\circ },AC=CD$ and $\angle ADE={150}^{\circ }.$ Find the value of the $\angle BAC.$

$132300=2^2{.3}^3{.5}^2.a^b$

Which of the following is always true ?

$\frac{lo{g}_{x}3-3}{lo{g}_{x}3-5}<0$.If a, b are integers which satisfy this inequation, find the maximum possible value of a - b.

The supplement of 65 degrees is

Factorize: $a^3+a-3a^2-3$

Factorise $32a^4-8a^4$

Which of the following is a linear inequality with two variables?

Three angles of a quadrilateral are ${100}^{\circ }$ ,${90}^{\circ }$ and ${85}^{\circ }$ .The fourth angle is ___

Find the principal which gives an amount of Rs 6,174 at 5% p.a. in 2 years, interest being compounded annually.

If the angles of a quadrilateral are in A.P. whose common difference is ${10}^{\circ }$, then find the angles of the quadrilateral.

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 cm. Find the area of the shaded region in cm².

Factorise: $7\sqrt{2}{k}^2-10k-4\sqrt{2}$.

Two measuring cylinders A and B are partly filled with water as shown in the figure below. The initial level of water was 60 ml in both the cylinders. When a stone is dropped in the cylinder B, the stone immerses and the level of water rises to 90 ml. Find the volume of the stone in S.I unit.

How to find rational numbers between two fractions

a+b+c=15 and a square + b square + c square =83

Find the value of a cube + b cube + c cubeb - 3abc

The area of a parallelogram is 338 m square if its altitude is twice the corresponding base determine the base and altitude

Question:- If 25 ^x-1 = 5 ^2x-1 - 100, then the value of x is_____________.

A) 3

B) 2

C) 4

D) 1

Construct a $\angle$ABC = 60${}^{\circ }$ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle which touches AB at B and also pass through D.

What are the possible outcomes when a coin is tossed?

Question 3
If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={60}^{\circ }$, then $\angle CAO$ is equal to__.

In parallelogram ABCD given below:If $\angle B=40°$, then find the value of
$\angle A,\angle Cand\angle D.$

A tank with length,breadth and height of 5, 6 and 3 units respectively is open at the top. Find the cost of anti-microbial coating inside the tank at the rate of ₹10 per sq. units.

By using factor theorem show that x+2 is a factor of polynomial 3x³-x²-20x-12 hence factorise the given polynomial

Factorize: $27p^3+8q^3$

If $A=\{1,2,3\},B=\{2,4,5\}$ and $C=\{4,1,9\},$ then $A\cup (B\cap C)$= ___.

The quadrilateral formed by joining the mid points of the sides of a quadrilateral, in order, is a __.

If 2 is added to the numerator and denominator the fraction becomes $\frac{9}{10}$ and if 3 is subtracted from the numerator and denominator it become $\frac{4}{5}$. Find the fraction.

Question 1
In which quadrant or on which axis do each of the points (-2,4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie?
Verify your answer by locating them on the Cartesian plane.

Question 6
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

In a right ∆, the ratio between the lengths of the the opposite side to the hypotenuse is known as

When the sun's altitude changes from ${30}^{\circ }$ to ${60}^{\circ }$, the length of the shadow of a tower decreases by $70m$. What is the height of the tower?

A fire burns steadily for 3 hours with 6 logs of wood. How many hours will it burn if 12 logs are used?