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The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Show that

ar (ABCD) = ar (PBQR).

[Hint: Join AC and PQ. Now compare area (ACQ) and area (APQ)]

Write three polynomials with variable y

The shaded portion in the figure given below shows a circular path enclosed by two concentric circles. If the inner circumference of the path is 176 m and the uniform width of the circular path is 3.5 m. Find the area of the path.

A rectangular sheet of paper is made to cover a cylinder such that the width of the rectangular sheet is equal to the height of the cylinder and length is just enough to go round the cylinder. Which of the following option correctly represents the curved surface area of the cylinder?

The total surface area of a right circular cylinder of radius 49 cm and height 10 cm is

Solve the following inequalities graphically $3x+2y\le 12,x+y\ge 4,5x\le 10$ and $x\ge ,y\ge 0$

Or

How many litres of water will have to be added to 1125 L of the 45$\%$ solution of acid, so that the resulting mixture will contain more than 25$\&$ but less than 30$\%$ acid content ?

Which shape has 12 triangles? Tap on the correct option.

What will be the product of $p^2-3pq$ and $q^2+4pq$?

Choose the correct answer in each of the following questions:
Let L be the lower class boundary of a class in a frequency distribution and m be the midpoint of the class. Which one of the following is the upper class boundary of the class?
(a) $m+\frac{(m+L)}{2}$
(b) $L+\frac{(m+L)}{2}$
(c) $2m-L$
(d) $m-2L$

Find 'x' if:

log (x-1) + log (x+1) = log_​2​​​1.

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 $c{m}^2$ and ar(ABFE) = 18 $c{m}^2$, then ar (EFCD) [in $c{m}^2$] is

For the given triangle ABC, identify the side opposite to angle $x$.

$\text{in the given figure,}AB||CDandEF\perp AB.ifEG\text{is a transversal, such that}\angle GED={130}^{\circ },find\angle EGF.$

In geometry, is the fundamental unit which exists by itself.

In the figure, state which lines are parallel and why.

The absolute difference of the two positive numbers whose arithmetic mean is $34$ and the geometric mean is $16,$ is

In the figure, ABCD is a parallelogram in which P is the mid -point of DC and Q is a point on Ac such that $CQ=\frac{1}{4}AC$ If PQ produced meets BC at R, prove that R is a mid -point of BC.

A coin was tossed 1500 times and out of these, 100 times, the coin stuck somewhere so the result was not counted. The frequency of occurrence of a head was 700. Find the probability of occurrence of a tail.

From the choices given below, choose the equation whose graph is given in the figure.



(i) y= x + 2



(ii) y = x −2



(iii) y = x + 2



(iv) x + 2y = 6

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$\left(i\right)\frac{11}{(2^3\times 3)}\left(ii\right)\frac{73}{(2^2\times 3^3\times 5)}$

The HCF of two numbers is 13 and LCM is 1001. Find the larger number.

The rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is .

Question 4
If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

If twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178 and thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177, then the difference between the sum of 5 consecutive odd numbers and 4 consecutive even numbers is