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The expression $V={\int }_0^H\pi R^2(1-h/H{)}^{2}dh$ for the volume of a cone is equal to

Which among the following institutions reserves seat for women?

The distance between points $(a+b,b+c)$ and $(a–b,c–b)$ is :

Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___?

The equation of a line AB is 2x - 2y + 3 = 0, its slope is ______ .

ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle with centre O through A, B, C, D. If $\angle ADC={130}^{\circ }$, Calculate $\angle$BAC.

In the figure given below CD is the median and DB = 3 cm , CD = 4 cm. The find the length of BC.

Question 2 (vi)

Write whether the given statement is true or false. Justify your answer.

If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

There are lottery tickets labelled numbers from 1 to 500. I want to find the number which is most common in the lottery tickets. What quantity do I need to use?

Factorise $x^2-16$

Find the coordinates of the points B, C, D in the picture below:

Write the lengths AB, BC, CD in the order of their magnitudes.

Write the coefficient of $x^2$ in each of the following?
(1) $2+x^2+x$
(2) $2-x^2+x^3$
(3) $\frac{\pi }{2}{x}^2+x$
(4) $\sqrt{2}x-1$

A solid metallic cuboid of dimensions $9m\times 8m\times 2$ m is melted and recast into solid cubes of edge 2m. Find the number of cubes so formed.

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If $\angle$ PRQ = ${120}^o$, then prove that OR = PR + RQ.

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If $\angle Aand\angle B$ are acute angles such that sin A = sin B then prove that $\angle A=\angle B$.

What is the perimeter of a triangle whose vertices are (0,4), (0,0) and (3,0)?

Find the coordinates of the points of trisection of the line segment joining (4, − 1) and (− 2, − 3).

If $tan\theta =1$, then find the value of $\theta$.

The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is. Find his present age.

AB and CD are common tangents to two circles of equal radii. Prove that AB=CD.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angles of elevation of his eyes to the top of the building increase from ${30}^{\circ }$ to ${60}^{\circ }$ as he walks towards the building. Find the distance he walked towards the building.

In the given figure, $\angle ACB={90}^{o}andCD\perp AB$.

Prove that $\frac{B{C}^2}{A{C}^2}=\frac{BD}{AD}$.

Which of the following securities comes under the provisions of the Banking Regulation Act, 1949?

Identify the non-finite verbs in the sentence.
The teacher walked into the class and instructed the students to study in silence.

A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm .The metal everywhere is 0.4 cm thick. The volume of the metal used is

1. 90

$27$ spherical iron balls of radius $5cm$ each are melted and recasted into a big sphere.The radius of the single sphere is______.

If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

If tan $\theta$ = $\frac{a}{b}then\frac{(cos\theta +sin\theta )}{(cos\theta -sin\theta )}$ = ?

(a) $\frac{a+b}{a-b}$ (b) $\frac{a-b}{a+b}$ (c) $\frac{b+a}{b-a}$ (d) $\frac{b-a}{b+a}$