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A metal rod is $64.522cm$ long at $12{}^{\circ }C$ and $64.576cm$ at $90{}^{\circ }C$. Find the coefficient of linear expansion of its material.

The base of a triangular field is three times its altitude. If the cost of sowing the field at $Rs.58$ per hectare is $Rs.783,$ find its base and height.

If the mean of the data is 60, find the value of p

$\begin{array}{cc}Classmark& frequency\\ 25-35& 12\\ 35-45& 16\\ 45-55& p\\ 55-65& 15\\ 65-75& 8\\ 75-85& 19\\ 85-95& 13\end{array}$

The reason for the equations $x+2y=5$ and $4x+8y=20$ to have infinite solutions is

If 2 is a zero of the polynomial $p\left(x\right)=x^3-a{x}^2+bx+c,$ then which of the following equations is true?

What is the degree of the expression $(3x+4)(2x+3)$?

Number of circles drawn through two points is

The average age of 29 boys of a class is 17 years . When the age of the class teacher is included , the average age becomes 18 years . Find the age of the class teacher.

If AB || DE, ∠AOD = ${50}^{\circ }$ and ∠DPC = ${160}^{\circ }$, find the value of ∠DBE?

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

(a) $2\pi h^2$ (b) $\frac{3}{2}\pi h^2$

(c) $\frac{4}{3}\pi h^2$ (d) $\pi h^2$

The area of triangle with vertices $A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)$ is:

The cross section of a piece of metal of length 4 m is shown. Find the volume of the cross section.

If x is an acute angle of a right triangle and sin x = 3 / 7, find the exact value of the trigonometric function cos x.

If ∪ = {2, 4, 6, 8, 10, 12, 14, 17}, where ∪ is Universal set

and some set A = {1, 4, 6, 9, 11, 12}

The set A^C is

In the given figure, $\angle ABD={54}^{\circ }\text{and}\angle BCD={43}^{\circ },$, calculate

(i) $\angle ACD$

(ii) $\angle BAD$

(iii) $\angle BDA$.

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in the figure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Find the volume of a sphere whose surface area is $154c{m}^2$

If ₹70 is distributed equally among 40 poor children, how much will each child get?

Find the area of the shaded region in Fig, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

Rational numbers can be added or multiplied in any ____

Q15. Which of the following statements about Alternate Investment Funds (AIF) is not correct?

Which statement is not true about the sentence?

Three hours are enough for you to complete your exam.

In quadrilateral ABCD, side AB is parallel to side DC and ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5.

Measure of angles of quadrilateral ABCD are

In ΔABC and PQR, AB=QR, BC=RP, AC=QP. So,

The areas of three adjacent faces of a cuboid are $x,y$ and $z.$ If the volume is $V,$ then $V^2$ is equal to :

The figure formed by joining the midpoints of the adjacent sides of a square is a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

How many pairs of adjacent angles are formed when two lines intersect in a point?

If $4^x-4^{x-1}=24,then(2x{)}^x$ equals

If the diameter of a cylinder is 28 cm and its height is 20 cm then its curved surface area is

$\left(a\right)880c{m}^2\left(b\right)1760c{m}^2\left(c\right)3520c{m}^2\left(d\right)2640c{m}^2$

The polynomial equations $P_1\left(x\right)$ = $x^3+x^2+x+1$ and $P_2\left(x\right)$ = $x^2-1$ have how many factors in common?

Let $a_1,a_2,a_3\cdots$ be terms of A.P.
$If\frac{a_1+a_2+\cdots a_p}{a_1+a_2+\cdots +a_q}=\frac{p^2}{q^2},p\ne q,$then $\frac{a_6}{a_{21}}$ equal

The marks obtained by 40 students of a class in an examination are given below.
3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20,3,10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 24, 6, 23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 10-15 (15 not included).

The sides of a triangle are 7cm, 9cm, 14cm. Its area is

Question 177(v)

Find x.
$2^{3x}=8^{2x+1}$

In the adjoining figure, two circles with centres at A and B, and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

In the figure, ABCD is a trapezium in which AB || DC. Prove that $ar(△AOD=ar(△BOC)$

Sum of a rational and an irrational number is a/an

For what value of k, the system of equations $x+2y=5,3x+ky+15=0$ has a unique solution?

___

Which of the following CANNOT be the length of BC required to construct the triangle ABC such that AC = 7.4 cm and AB = 5 cm?

Prove that:

x² + y² + z² - xy - yz - zx is always positive.

The midpoints of the adjacent sides of a quadrilateral will form a__________.​

Factorise $100-x^2$

Multiply $(7x^{2}y+2x+3)$ by $(2x+3y).$ ​​​​​​

The mean weight of 8 students is 45.5 kilogram 2 more students having weight of 41.7 kg and 53.3 kg join the group what is the new mean weight

If $x^2+\frac{1}{x^2}=7$ then find the value of $x^3+\frac{1}{x^3}$ using only the positive value of $x+\frac{1}{x}$.