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If numbers n -2, 4n -1 and 5n +2 are in A.P., find the value of n and its next two terms.

The surface area of a cube is 384 cm². What is its volume?

What will be the simple interest on a sum of ₹ 1820 from March 12, 2003 to May 23, 2003 at 7.5% rate?

The condition for the equation $x^2+bx-c=0$ to have real roots is .

If (x + b)(x+a) is a factor of the polynomial $x^2-2x-15$. Then value of ab is

A ray of light is incident on a glass slab of width $3\text{cm}$ at point $\text{A}$. The lower portion of the glass slab is silvered. The lights get reflected from it and emerges out of the slab at point $\text{B}$. Then, the distance $\text{AB}$ is

What is the probability of getting a sum of 7 on two rolls of a die?

A solid toy in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2 cm and the diameter of the base is 4 cm.if a right circular cylinder circumstances the toy,find how much more space it will cover

If $\overrightarrow{a}=(2,1,-1),\overrightarrow{b}=(1,-1,0),\overrightarrow{c}=(5,-1,1),$ then the unit vector parallel to $\overrightarrow{a}+\overrightarrow{b}-\overrightarrow{c}$ in the opposite direction is

In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?

The system x-2y=3 and 3x+ky=1 has a unique solution only when

(a) k=-6 (b)$k\ne -6$ (c) k=0 (d) $k\ne 0$

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows:
The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also, he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the $2^{nd}$ digit, given that ‘b’ is the second digit?

Find the curved surface area of a cone whose circumference of the base is 66 cm and slant height is 12 cm.

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is:

The value of $\frac{co{s}^2\theta }{sin\theta }-cosec\theta +sin\theta$ is

An 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs.40 per $m^2$.

In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE||BC.

Find the first term of an arithmetic progression, if its $7^{th}$ term is 4 and common difference is -4.

The total surface area of a hollow metal cylinder, open at both ends, of external radius $8cm$ and height $10cm$ is $338\pi c{m}^2.$ Taking $r$ to be inner radius, write down an equation in $r$ and use it to state the thickness of the metal.

A tent is in the form of a cylinder of diameter 4.2 m and height 4m, surmounted by a cone of equal base and height 2.8 m. Find the volume of tent .

The graphs of the equations 2x+3y-2=0 and x-2y-8=0 are two lines which are

(a) coincident

(b) parallel

(c) intersecting exactly at one point

(d) perpendicular to each other

$(-3)\times (-2)\times \left(5\right)\times (-6)\times (-1)\times 1=$

The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA.

Find the point that divides the line joining $A(2,4)$ and $B(6,8)$ in the ratio $a:1$.

The expression $x^4$ + 8$x^2$ + 16 can be factorized as

From a well-shuffled pack of 52 cards, a card is drawn at random, find the probability that it is a spade.

The diagonal of a square $2\sqrt{2}$ cm.Find the length of the sides of the square