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If the area of parallelogram $ABCD=70$ sq. units, then the area of $△ABE=$ ___ sq. units.

Find the area of an equlataral triangle having side 12xm

5. Simplify:

(i) 3√2–2√3 + √12 3√2+2√3 + √3–√2

the polynomial P of x is equal to 4 x³-2 X² + px + 5 and q of x is equal to x³+ 6 X² + P leaves remainder A and B respectively when divided by X + 2 find the value of p if a + b is equal to 0

Each of the median of a triangle is divided by the centroid in the ratio ___ from the side of vertices.

What is the class mark of the class interval 11.5 - 16.5?

Look at the image below. Please tell me why angle ADC won't be equal to angle AOC ÷ 2. As the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle here arc ABC is subtending 100° (angle AOC)angle at centre and an angle ADC at a part of circle. Am I correct?

A flooring tile is in the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. The number of such tiles required to cover a floor of area 1080 $m^2$ is

Justify why 22/7 is rational but π is irrational

$LMNO$ is a trapezium with $LM\parallel NO$. If $P$ and $Q$ are the mid-points of $LO$ and $MN$ respectively and $LM=5cm$ and $ON=10cm$ then $PQ=$

The area of a triangle with sides 10 cm, 7 cm and 7 cm and semi-perimeter 12 cm is

Match the two columns Column-II give quadrant for points given in Column-II.
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) (4,4)}& \text{(p) I quadrant}\\ \text{(B) (-3,7)}& \text{(q) II quadrant}\\ \text{(C) (2,-3)}& \text{(r) III quadrant}\\ \text{(D) (-1,-3)}& \text{(s) IV quadrant}\end{array}$
Choose the correct option :

Factorise : 8a³ + b³ + 12a²b + 6a b²

In the given figure, $\angle C={90}^{\circ }$ and D is the mid point of AC. Then $\frac{cot\angle CAB}{cot\angle CDB}=$ ___

$\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosB.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

A hollow prism has a rectangular base with sides 20 cm and 10 cm. If a solid cube of side 8 cm is immersed in it, by how much would the water level rise?

ABC is an equilateral triangle, P is a point on BC such that BP : PC = 2 : 1. Then $\frac{A{P}^2}{A{B}^2}=$

Calculate the compound interest accrued on Rs. 6,000 in 3 years, compounded yearly, if the rates for the successive years are 5%, 8% and 10% respectively.

In the given figure find the value of $x^0$

In a trapezium ABCD side BC is parallel to AD.If $\angle ADC={100}^{\circ }$, then $\angle DCB=$___ ${}^{\circ }$

A die is thrown, find the probability of follwoing events:
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear
(iii) A numbher less than or equal to one will appar.
(iv) A number more than 6 will appear.
(v) A number less tahn 6 will appear.

The mean of 12 numbers is 40.1f each number is divided by 8, what will be the mean of the new numbers?

A solid cylinder has a total surface area of 231 $c{m}^2$. Its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. $(Use\pi =\frac{22}{7})$

Question 6
In $\Delta ABC$, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that $ar\left(\Delta LOB\right)=ar\left(\Delta MOC\right)$.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.

(a) If you live in Delhi, then you have winter clothes.

(i) If you do not have winter clothes, then you do not live in Delhi

(ii) If you have winter clothes, then you live in Delhi.

(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram

Factorise:

2x^2 -x +(1/8)

If the ratio of the sum of the interior angles to measure of each exterior angle of a n sided polygon is 3: 2. Find the value of n.

What is the slope of the chord of contact of the point (6, -4) to the circle $x^2+y^2-2x-2y+1=0$

If a triangle in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 2.92 cm is constructed then the side length of AC is:

In the given figure AD is the bisector of $\angle$A and AB = AC. Then, by which criterion $△$ACD and $△$ABD are congruent?

In the following diagrams, the universal set is represented by a triangle and set A and B are the set of points in the triangle.

Then in which of the given figures the shaded portion represents $A^{\prime }\cup B$?

The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is______

The area of four walls of a room of height 5 m is 144 m². If the total surface area of the room is 244 m² then its length is

Explain the difference between a frequency distribution and a cumulative frequency distribution.

If $x=6-\sqrt{35}$, then $x^2+\frac{1}{x^2}=$ ___

A steel box has dimensions of 2 m, 3 m and 0.5 m. It has to be gold plated using electrolysis. If each square metre of gold plating costs Rs.100 , then gold plating the outer surface of the box costs

Points A(1,0), B(5,0), C(7,6) and D(3,6) are joined to form a quadrilateral ABCD. Point B(5,0) is joined with E(5,6); and A(1,0) is joined with F(1,6). Quadrilateral ABEF is completed. BD and AE is joined to intersect at O. Which of the following is correct?

If in a class, 4 students obtained 25 marks and another 4 students obtained 35 marks, then their average score is _______.

Question 3(i)
Find the value of:

$(3^0+4^{-1})\times 2^2$