Explore topic-wise InterviewSolutions in Current Affairs.

A cylindrical can whose base is horizontal and of radius 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can,

Calculate:
(i) the total surface area of the can in contact with water when the sphere is in it.
(ii) the depth of water in the can before the sphere was put into the can.

Take π as ²²/₇ and give your answers as proper fractions.

If (2 θ + 45 θ) and (30⁰ - θ) are acute angles, the degree measure of θ satisfying
sin(2 θ + 45⁰) = cos (30⁰ - θ) is

In the given figure, $DB\perp BC,DE\perp ABandAC\perp BC.$

Prove that $\frac{BE}{DE}=\frac{AC}{BC}$.

If sin[90 - (A+B)] = cosx = cosy

find the value of x and y; if y is the angle C of triangle ABC. (In triangle ABC, $A+B={90}^{\circ }$)

In $\Delta$ ABC, if D is a point on the side AB such that $\frac{AB}{AD}=3$. Find $\frac{AD}{DB}$.

To divide a line segment PQ in a certain ratio, we draw a ray PM. Why don’t we draw it with an obtuse angle?

A company manufactures cassettes and its cost revenue functions for a week are $C=300+\frac{3}{2}andR=2x$ respectively, where x is the number of cassettes produced and sold in a week.How many cassettes must be sold for the company to realize a profit ?

17 cards numbered 1, 2, 3,……,16,17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is
(i) Odd

(ii) Prime

(iii) Divisible by 3

(iv) Divisible by 3 and 2 both

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

The graph of the polynomial f(x) = 2x - 5 crosses the X-axis at the point

1. 16

Write the condition for a rational number which can have a terminating decimal expansion.

The height of two buildings is 50 cm and 40 cm respectively. If the distance between their base is 24 cm, then the distance between their top is equal to

Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.

In the given figure, 3 secants are drawn from point P, intersects the circle at Q, M, and R respectively. What is the value of $\angle QXR$?

Find the degree of the polynomial $x^3+3x-2$ .

If $\frac{8x+13y}{8x-13y}=\frac{9}{7}$, find x : y

If the number$(2n-1),(3n+2)$ and $(6n-1)$are in AP, find the value of $n$ and the numbers.

Which of the following statements is not true ?

(a) A line which intersects a circle in two points, is called a secant of the circle.

(b) A line intersecting a circle at one point only, is called a tangent to the circle.

(c) The point at which a line touches the circle, is called the point of contact.

(d) A tangent to the circle can be drawn from a point inside the circle.

Assertion-and-Reason Type

Each quation consists of two statements, namely Asserction (A) and Reason (R). For selecting the correct answer, use the following code;

(a) Both Assertion (A) and Reasson (R) are true and Reason (R)

is a correct explanation of Assertion (A).

(b) Bothe Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 $c{m}^3$ and its diameter is 7 cm, find the height of the toy.

In a rectangular park of dimensions $50\times 40m$,a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 $m^2$.Find the length an breadth of the pond.

What is the coefficient of $y^2$ in $-6ax{y}^2$?

AB is line segment of length 24 cm. C is its midpoint. On AB, AC and BC semicircles are described. Find the radius of the circle which touches all the three semicircles.

A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 84 kg ?

What number should be added to $x^2+6x$ to make it a perfect square?

In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games?

In the given figure , a balloon is descending at a constant speed of 10m/s as shown in the dotted lines.A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground.(in seconds)

If given a dart board of radius 50 cm. What is the probability that you hit the bull's eye of radius 5 cm?

A couple has 6 children, of which 5 are girls and 1 is a boy. The probability (in percentage) of having a girl next, is

The sum of roots of the equation 2 $x^2$ - 3+ $\sqrt{2}$ = 0

State 'T' for true and 'F' for false.
I. If one angle of a cyclic trapezium is four times the other, then the greater one measures ${144}^{\circ }$.
II. The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is $\sqrt{d^2-(R-r{)}^2}$

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

(i) $-\frac{8}{3},\frac{4}{3}$ (ii) $\frac{21}{8},\frac{5}{16}$ (iii) $-2\sqrt{3},-9$ (iv) $\frac{-3}{2\sqrt{5}},-\frac{1}{2}$

Solve the following systems of equations:

$\frac{1}{2x}+\frac{1}{3y}=2$

$\frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}$

Question 2(e)

Find the product by suitable arrangement:

$285\times 5\times 60$

How many multiples of 4 lie between 10 and 250 ?

What is The locus of the door-handle, as the door opens?

In a given AP if pth term is q and qth term is p then show that it's nth term is (p+q-n)

Which of the following is a correct statement?

The top of a $15m$ high tower makes an angle of depression of ${60}^{\circ }$ with the bottom of an electric pole and angle of depression of ${30}^{\circ }$ with the top of the pole. What is the height of the electric pole?

Find the value of $si{n}^2\theta +co{s}^2\theta at\theta ={30}^{\circ }$ and ${60}^{\circ }$.

In the given figure, $OB$ bisects $DE$. Then, which of the following is true?

If alpha and beta are zeroes of polynomial x^2-6x+a. Find the values of k and m.

Question 12

A vessel has 4 litres and 500 ml of curd. In how many glasses each of 25 ml capacity, can it be filled?

The sum of two numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers

Four numbers are in AP whose sum is 50 and the greatest number is four times the smallest number. Find the greatest number among the four.