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In $\Delta ABC$, $\angle ACB={90}^{\circ }$, AB = C units, BC = a units, AC = b units, CD is perpendicular to AB and CD = p units. Then $\frac{1}{p^2}=$

Factorize:

$x^4+x^2{y}^2+y^4$

Construct a $\Delta ABC$ in such a way that $\angle ABC={45}^{\circ }$, $\angle CAB={45}^{\circ }$ and AB = 7 cm. Construct a rectangle, the area of which is equal to the area of $\Delta ABC$. What are the dimensions of the rectangle?

Factorise:

$a^2+4b^2-4ab-4c^2$

Which of the following graphs may correspond to the equation y = k where k is a negative rational number.

In Fig, AB and CD are two diameters of a circle (with center O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

The diameter of a cylinder jar is increased by 25%. By what percent must the height of the jar be decreased so that there is no change in its volume?

If f: $[1,\infty )\to [2,\infty )$ is given by $f\left(x\right)=x+\frac{1}{x}$ , then $f^{-1}\left(x\right)$ is equal to

1. 10

Define whole numbers. [1 MARK]

Figure shows that AD is the median of ∆ABC and E is the mid point of AD. Also, BE produced meets AC in F and DP is parallel to EF. Then AF is equal to

Which of the following is not a property of a rational number?

The base of a prism is a rectangle with sides 4 cm and 6 cm respectively. If the height of the prism is 12 cm, the volume of the prism is :

The angles of a triangle are in the ratio 2 : 3 : 4. The angles, in order, are :

In the adjoining figure, BDEF and AFDE are parallelograms. Is AF = FB? Why or why not?

Data-Sufficiency-Based MCQ

In each of such questions, one question is followed by two statements I and II. The answer is

(a) if the question can be answered by one of the given statements alone and not by the other;

(b) if the question can be answered by either statement alone;

(c) if the question can be answered by both the statements together but not by any one of the two;

(d) if the question cannot be answered by using both the statements together.

Find the median of the following data: 41,43,127,99,61,92,71,58,57.If 58 is replaced by 85, what will be the new median?

Three cubes of metal with edges 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is

$\left(a\right)72c{m}^2\left(b\right)144c{m}^2\left(c\right)128c{m}^2\left(d\right)256c{m}^2$

In the given figure, O is centre of a circle in which $\angle AOC={100}^{\circ }$. Side AB of quad. OABC has been produced to D. Then, $\angle$CBD = ?

(a) ${50}^{\circ }$

(b) ${40}^{\circ }$

(c) ${25}^{\circ }$

(d) ${80}^{\circ }$

Factorise:
$a^2+2ab+b^2-9c^2$

In the given figure, three lines AB, CD and EF intersect at a point O such that $\angle AOE={35}^{\circ }$ and $\angle BOD={40}^{\circ }$. Find the measure of $\angle AOC,\angle BOF,\angle COF$ and $\angle DOE$.

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hand to talk each other. Find the length of the string of each phone.

There are two identical circles with same inside design as shown in the figure. The identical triangular leaves are to be painted red and the remaining area green. Find the total area to be painted red.

Insert two rational numbers between:

(i) $\frac{3}{8}$ and $\frac{7}{12}$

(ii) $\frac{1}{3}$ and $\frac{1}{4}$

If ${10}^x=64,whatisthevalueof{10}^{\frac{x}{2}+1}?$

A momento is made as shown in the figure. Its base PBCR is silver plated from the front side. Find the area which is silver plated, where AP = AR = 7 $cm$ and PB = RC = 3 $cm$. $(Use\pi =\frac{22}{7})$

The monthly pocket money of six friends is given below:
Rs 45, Rs 30, Rs 40, Rs 50 , Rs 25, Rs. 45
(i) What is the highest pocket money?
(ii) What is the lowest pocket moneY?
(iii) What is the range?
(iv) Arrange the amounts of pocket money in ascending order.

Factorize $(a-2b{)}^3-512b^3$

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is

Represent 0.35 in a rational form.

There is a regular octagonal park. The surface area of the park $=$___ $m^2$

Factorise

(a^2 - b^2) (c^2 - d^2) - 4abcd

If $(3x-1{)}^7=a_7{x}^7+a_6{x}^6+...............a_1+a_0$, then find the value of $a_7+a_6+..a_0$

Factorise:
$(5-20x^2)$

The $\frac{p}{q}$ form of $0.\overline{18}$ is (where p and q are integers and $q\ne 0$) .

In the given figure, O is the centre of a circle. If $\angle AOB={100}^{\circ }and\angle AOC={90}^{\circ }then\angle BAC=?$

(a) ${85}^{\circ }$

(b) ${80}^{\circ }$

(c) ${95}^{\circ }$

(d) ${75}^{\circ }$

If each side of a cube is doubled then its volume

(a) is doubled

(b) becomes $4$ times

(c) becomes $6$ times

(d) becomes $8$ times

In the given figure, PQ is a diameter of a circle with centre O. If $\angle PQR={65}^{\circ },\angle SPR={40}^{\circ }and\angle PQM={50}^{\circ },\text{find}\angle QPR,\angle QPMand\angle PRS$

Find the arithmetic mean of the first 3 positive integers and first 3 negative integers ( do not include 0 )

Question 71(ii)

It is given that l varies directly as m.
Find the constant of proportion (k), when l is 6, then m is 18.