Explore topic-wise InterviewSolutions in Current Affairs.

In the given triangle ABC, D is mid-point of AB. P is on AC such that $PC=\frac{1}{2}AP$ and $DE||BP$. If $AE=xAC$, then find the value of $x$.

Fill in the blank with a modal auxiliary indicating necessity.

Rahul _____ submit a letter authorising him to collect Samir’s mark sheet.

The mean of the numbers $a,b,8,5,10$ is $6$ and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$?

The shaded region consists of a chord and the arcs of the circle. The region in the yellow has the major arc so it is the major segment and the purple region consists of the minor arc so it is the minor segment.

Raj was very late for the morning assembly. The principal asked him to run 0.616 km as a punishment. The shape of the ground is in a form of semi-circle mounted on the rectangle as shown. How many times will raj have to pass the starting point in order to complete the punishment?

In a right angled triangle, the longest side is the ___

In triangle ABC, right angled at B, if $\angle A$ is ${45}^{\circ }$, find the value of cot A and tan C.

A line segment joining the vertex of a triangle to the mid point of the opposite side is called the

The radius of a cone of height 21 cm and volume 352 cm³ is

x+1 is a factor of p(x)= x³+3x²+3x+1 , so what is the value of p(-1)

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases :

(i) f(x) = 3x + 1, x = - $\frac{1}{3}$

(ii) f(x) = $x^2$ - 1, x = 1, -1

(iii) g(x) = $3x^2$ - 2, x = $\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}}$

(vi) p(x) = $x^3-6x^2$ + 11x - 6, x = 1,2,3

(v) f(x) = 5x -$\pi ,x=\frac{4}{5}$

(vi) f(x) = $x^2$,x = 0

(vii) f(x) = lx + m, = - $\frac{m}{l}$

(viii) f(x) = 2x + 1, x = $\frac{1}{2}$

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Solve for x

$x^2-3x-10=0$

In the given figure, AB||CD. Find the value of x.

In the figure, PQRS is a square and SRT is an equilateral triangle. Prove that

(i) PT = QT (ii) $\angle TQR={15}^{\circ }$

The following picture is a miniature version of a drawing that Ram did.

If the height of the actual drawing is 56 cm, what is the length of Ram’s actual drawing?

The price of 1kg of potato is Rs.60. 1 kg of onions costs 10% less than 1 kg potato. If I pay Rs.180 for potatoes, what will be the cost of onions of the weight same as the weight of the potatoes?

The mean of a set of observation is $\overline{x}$ .If each observation is divided by $\alpha \alpha \ne 0$, and then is increased by 10,
then the mean of the new set is

Which of the following are not the sides of a right angled triangle?
A. 5, 12, 13
B. 6, 8, 10
C. 10, 24, 25
D. 7, 24, 25

ABCD is a quadrilateral such that $\angle ABC$+$\angle ADC$ =${180}^{\circ }$. Inside the quadrilateral :

Statement 1: the circumcircle of $\Delta ABC$ intersects diagonal BD at D.

Statement 2: the circumcircle of $\Delta ABC$ intersects BD at $D^{{}^{\prime }}$inside the quadrilateral.

Statement 3: the circumcircle of $\Delta ABC$ intersects BD at $D^{{}^{\prime }}$ outside the quadrilateral.

Statement 4: the circumcircle of $\Delta ABC$does not intersect BD at all.

Statement 5: ABCD is called cyclic quadrilateral.

A rectangular prism has a base perimeter of 28 m and height 12 m. What is its lateral surface area?

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

A point with both of its coordinates positive lies in which quadrant?

Find the value of x?

When the degree measure of the angle at the center is 1, what is the area of the sector with radius r = 1?

ABCD is a parallleogram and E is the mid-point of BC. DE and AB when produced meet at F. Then , AF =

The numbers which have a non-terminating and non-repeating decimal expansion and cannot be represented in the form of $\frac{p}{q}$ ( q is not equal to '0') are known as

numbers.

Question 16

State whether the given statements are true (T) or false (F).

$\frac{3}{8}=\frac{15}{40}$

Which of the following numbers is not irrational?

A solid cylindrical party popper having radius 7 cm and length 20 cm needs to be gift wrapped by a paper sheet. What is the area of sheet required to cover it completely ?

What is the length of AD in the given figure ABCD? ( Take $\sqrt{2}$ = 1.4 and $\sqrt{5}$ = 2.2

In Fig. X and Y are two points on equal sides AB and AC of a ΔABC such that AX = AY. Prove that XC = YB. [2 MARKS]

If the value of $tan\alpha =\frac{5}{2}$, then find the value of $cot\theta$.
Given : $\alpha +\theta ={90}^{\circ }.$

Mid point theorem is a special case of which of the following theorems?

Question 7
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1:2:3.

What are the factors of $({101}^2-{99}^2)$?

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

The number of dimensions of a surface is

(a) 1

(b) 2

(c) 3

(d) 0

On the basis of graph, the pair of linear equation gives _______________solution(s).

The number $\frac{665}{625}$ will terminate after how many decimal places?