Explore topic-wise InterviewSolutions in Current Affairs.

A car is travelled between two villages A and B. Speed of the car while travelling to village B is 100 km/hr and while returning from the village B is 50 km/hr. Find the average speed during the whole journey.

If $a_1$,$a_2$, $a_3$($a_1>0)$ are three successive terms of a G.P. with common ratio r, the value of r for which $a_3>4a_2-3a_1$ is

In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If $\angle ABC$ = $\angle ADC={90}^{\circ }$, then AD =____________cm

One side of a right-angled triangle exceeds the other side by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter side of the triangle.

If $(x-1)$ divides $m{x}^3-2x^2+25x-26$ without remainder, find the value of $m$.

An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is $3\frac{1}{2}$ cm and height 8 cm. Find the volume of water required to fill the vessel. If this cone is replaced by another cone, whose height is $1\frac{3}{4}$ cm and the radius of whose base is 2 cm, find the drop in the water level.

If the radius of a cylinder is reduced by 50 $\%$, then volume of the cylinder gets reduced by ___.

$\sqrt{2}x+\sqrt{3}y=0$

$\sqrt{3}x-\sqrt{8}y=0$

Solve the following pair of linear equations by the substitution method.

Probability to have a holiday on 15${}^{th}$ August in India is ___.

In a right triangle ABC, $\angle$ B = ${90}^{\circ }$ and sec A = $\frac{5}{3}$. Find sin A.

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting diagonal AC in L and AD produced in E. Prove that : EL = 2 BL.

Solve:
$\frac{1}{x}-\frac{2}{y}+4=0$

$\frac{1}{y}-\frac{1}{z}+1=0$

$\frac{2}{z}+\frac{3}{x}=14$

1. 41

X/a+y/b=2;ax-by=a^{​​​​​​2}​-b^​​​2

What is the value of cot B in terms of a,b,c?

In the given frequency distribution, which is the median term?
$\begin{array}{cc}\text{Age in years}& \text{Number of people}\\ 15& 3\\ 16& 8\\ 17& 10\\ 18& 10\\ 19& 5\\ 20& 4\end{array}$

AB is a chord of a circle with centre O. If $\angle AOB={70}^{\circ }$ and AB=16 cm, the diameter of the circle will be $[sin{35}^{\circ }=0.57]$

In $\Delta ABC$, DE || BC. Then which of the following is stated by Basic Proportionality Theorem?

When a polynomial denoted by $p\left(x\right)$, is divided by $(x-a)$, then the remainder is:

Find the ${30}^{th}$ term of the sequence :

$\frac{1}{2},1,\frac{3}{2}$,............ .

Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see Fig.). If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of 300 $m^3$, and there are 20 workers, each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed (in $m^3$)? (Take $\pi =\frac{22}{7}$)

Sheela went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. After transaction Sheela got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received. [4 MARKS]

A box contains 19 balls bearing numbers 1, 2, 3…… 19. A ball is drawn at random from the box. What is the probability that the number on the ball is

a) a prime number

b) divisible by 3 or 5

If $x=a\text{sec A}\text{cos B}$, $y=b\text{sec A}\text{sin B}$ and $z=c\text{tan A}$, then $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=$

From two points A & B on the same side of a building, the angles of elevation of the top of the building are 30^o & 60^o respectively. If the height of the building is 10 m, find distance AB correct to 2 places of decimal.

If the sum of the $3^3+7^3+{11}^3+{15}^3...................20$ terms is $S_{20}$. Find the value of $\frac{S_{20}}{100}$ .

The diameter of the base of a cylinder is 4 cm and its heighht is 14 cm. The volume of the cylinder is

(a) 176 $c{m}^3$ (b) 196 $c{m}^3$ (c) 276 $c{m}^3$ (d) 352 $c{m}^3$

If the roots of the equation $x^3-12x^2+39x-28=0$ are in A.P., then find the common difference.

Number of common factors of 360 and 18144 are

Express 360 as product of its prime factors.

Question 2 (ii)
For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k -1)x + (k -1)y = 2k + 1

what is the HCF of the smallest composit number and smallest prime number

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of ${30}^{\circ }$ to the ground. What should be the length of the slide (in m)?

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.

$3\tan \theta$ + $\cot \theta$ = 5cosec$\theta$. Solve for $\theta$, $0\le \theta \le 90$.

Taylor purchased a rectangular plot of area 634$m^2$. The length of the plot is 2m more than thrice its breadth. Find the length and breadth (approximate values).

If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

In the equation $ax+by+c=0$, in how many different ways can you express $y$ in terms of $x?$

The sum of n terms of three arithmetical progression are $S_1$, $S_2$ and $S_3$. The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that $S_1$ + $S_3$ = 2$S_2$.

Find the sum of the series : 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + .... to 3n terms.