Explore topic-wise InterviewSolutions in Current Affairs.

A chord 16 cm long is 6 cm away from the centre of the circle. Then the chord of length 8 cm is ___ cm away from the centre.

An object lying at the distance of $5\text{cm}$ from a spherical interface as shown in the figure, is moving with the velocity of $5\text{cm/s}$. If the interface is moving with a velocity of $3\text{cm/s}$, then calculate the velocity of the image formed by the spherical surface.

(Assume that spherical interface always seperates air and medium of refractive index $1.5$)

In the question above, instead of assuming ∠OAB = ∠OCD, assume that AB = CD and then prove that ∠OAB = ∠OCD.

In a right angle triangle ABC (right angled at B), find the value of $\tan A\times \tan C$.

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are unit vectors, then the value of $|\overrightarrow{a}-\overrightarrow{b}{|}^2+|\overrightarrow{b}-\overrightarrow{c}{|}^2+|\overrightarrow{c}-\overrightarrow{a}{|}^2$ does not exceed

Let $A$ and $B$ be two square matrices of order $3$ such that $det\left(A\right)=5$ and $det\left(B\right)=2.$ Then the value of $det(det(B)\cdot A)$ is

If x + y + z = 0, show that $x^3$ + $y^3$ + $z^3$ = 3xyz.

Let $x=\frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^m{5}^n$, where $n,m$ are non-negative integers. Then, $x$ has a decimal expansion which is

Question 145

There are 86400 sec in a day. How many days long is a second? Express your answer in scientific notation.

The curved surface area of a right circular cylinder is $4.4m^2$. If the radius of the base of the cylinder is $0.7m.$ find its height.

The edges of 3 cubes of metal are 3cm, 4cm & 5 cm. they are melted and recasted into a single cube.Find the edges of the new cube.

Question 85

Solve the following:

The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

In a triangle ABC, right angled at A, AB = AC. Find the value of angle B and angle C.

If one angle of a linear pair is acute, then its other angle will be ___________.

Question 1

Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?
(a) 2 and 3
(b) 8 and 12
(c) 15 and 20
(d) 25 and 37.5

In quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS using constructions.

In the figure, it is given that O is the centre of the circle and $\angle AOC={150}^{\circ }$. Find $\angle ABC$.

Question 1 (i)

State whether the following statement is true or false. Justify your answer.

Every irrational number is a real number.

Question 9

Without actually performing long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

Let $S=\{1,2,3,\dots \dots ,m\},m>3$. Let $X_1,X_2,\dots \dots X_n$ be subsets of $S$ each of size $3$. Define a function $f$ from $S$ to the set of natural numbers as $f\left(i\right)$ is the number of sets $X_j$ that contains the element $i$. That is $f\left(i\right)=|\left\{j|iϵX_j\right\}|$. Then $\sum _{i=1}^{m}f\left(i\right)$ is

Tap on the shapes that form a square.

For a cylinder of radius r and height h and a cuboid of length l, breadth b and height h, match the following.

See the given figure, and write the following:

(i) The coordinates of B.

(ii) The coordinates of C.

(iii) The point identified by the coordinates.

(iv) The point identified by the coordinates

(v) The abscissa of the point D.

(vi) The ordinate of the point H.

(vii) The coordinates of the point L.

(viii) The coordinates of the point M

$\text{If}{\left(\sqrt{1024}\right)}^3=8^x\text{, then}x\text{is}$ ________.

A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

The product of two linear polynomials is x² – 7x + 12 .So, they are

Kaju barfi was cut exactly in the middle as shown such that both the parts of the barfi were exactly equal. The area of one part of the barfi is ___

A rectangular block has 20,25 and 30 as length, width and height respectively. If the sides of the block are extended by the same length x, what is the equation for the new volume?

The area of a trapezium whose parallel sides are 57 cm and 39 cm and the distance between them is 28 cm is

What is the value of $2\sqrt[3]{33}\times 3\sqrt[3]{34}\times 4\sqrt[3]{35}$

Which word/phrase has been omitted in the sentence?

The customer insisted getting complimentary drinks at the fancy restaurant.