Explore topic-wise InterviewSolutions in Current Affairs.

Use the factor theorem to determine whether g(x) is a factor of p(x) in the given expression p(x) = 2x³ + x^{​​​​​​2} - 2x - 1,g(x) = x + 1

If BCD and EFG are congruent by SAS congruence postulate and AB = MN, B =N, then which is the additional equality is right to complete the postulate?

Factorise $(1-x^2)(1-y^2)+4xy$ is _____

Common factor in quadratic polynomials $x{}^2+8x+15$ and $x^2+3x-10$ is

In the given figure, lines (i) and (ii) are parallel lines and $AC$ is the angle bisector of $\angle BAD$.

What type of triangle is $△ABC$?

In the given figure, ABCD is a parallelogram, then ∠CDB is:

The base of a parallelogram is thrice its height. If the area is $867$ sq. cm, find the base of the parallelogram.

Who reignited the question – “What is maturity?”

If a/b +b/a =1 find the value of a^3 +b^3

A man borrowed Rs. 16,000 for 3 years under the following terms :

20% simple interest for the first 2 years.

20% C.I. for the remaining one year on the amount due after 2 years, the interest being compounded half-yearly.

Find the total amount to be paid at the end of three years.

Assertion: The sides of a $\Delta ABC$ are in the ratio 2:3:4 and its perimeter is 36cm. Then, $ar\left(\Delta ABC\right)=12\sqrt{15}c{m}^2$

Reason: If $2s=(a+b+c)$, where a, b, c are the sides of a triangle, then its area $=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

If the angles subtended by the chords of a circle at the centre are equal, then the chords are

An ant struggling for food finds it at the north-east corner of the Cartesian plane. It moves 3 units east from the origin and then 3 units north. Find the location of the food.

In the figure $l||m,n||p$ and $\angle 1={85}^{\circ }$, then $\angle 2$ is equal to.

A cylinder of same height and radius is placed on the top of a hemisphere. Find the length of the shape be 7 cm.

In $\Delta$ ABC, D is a point on BC such that AB= AD = BD =DC. Show that : $\angle$ ADC : $\angle$ C = 4: 1.

A number '$x$' was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... .The value of $p-q$ is ___

In the figure ABCD is a ||^gm in which ∠DAB = 80^o and ∠DBC = 60^o, then ∠CDB and ∠ADB are equal to

Find the mean of:
(i) First eight natural numbers

(ii) First ten odd numbers

(iii) First five prime numbers

(iv) First six even numbers

(v) First seven multiples of 5.

(vi) Factors of 20

(vii) All prime numbers between 50 and 80

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

The zeros of the polynomial $p\left(x\right)=2x^2+5x-3$ are
(a) $\frac{1}{2},3$
(b) $\frac{1}{2},-3$
(c) $\frac{-1}{2},3$
(d) $1,\frac{-1}{2}$

The value of $\sqrt{3-2\sqrt{2}}$ is

Question 82

At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

The factors of $x^4+x^2+25$ are

On decreasing the temperature, the solubility of a solid solute in a liquid______.

A die is rolled 100 times and the outcomes are recorded as below. What is the probability of getting

(i) an odd number ?
(ii) an even number ?

$\begin{array}{ccccc}\text{Outcome}& 1& \text{Even number}<\text{6}& \text{Odd number}>\text{1}& 6\\ \text{Frequency}& 15& 33& 36& 16\end{array}$

[2 MARKS]

The size of a class interval is obtained by dividing the ________ of the data by the number of class intervals.

Find the intercepts of the line whose equation is x + y = 4

Match the two columns.
$\begin{array}{cc}Column-I& Column-II\\ \left(A\right)Abscissa& \left(p\right)x\\ \left(B\right)Ordinate& \left(q\right)y\\ \left(C\right)Co-ordinate& \left(r\right)x,y\\ \left(D\right)Origin& \left(s\right)0\end{array}$
Choose the correct option:

In given figure, ABCDE is any pentagon. BP is drawn parallel to AC and meets DC produced at P. EQ is drawn parallel to AD and meets CD produced at Q. Then, which of the following statements is true?

In the given figure, BA PARALLEL TO ED AND BC PARALLEL TO EF. SHOW THAT ANGLE ABC + ANGLE DEF =180 DEGREE

Find two irrational number between 0.5 and 0.55.

Given the area of a rectangle is, $A=3p^2+9p+6$. The length is given as ($3p+3$). Therefore, the width is:

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency:

(a) In $\Delta ABC$ and $\Delta DEF$, $AB=DE,BC=EF$ and $\angle B=$$\angle E$ .

(b) In $\Delta ABC$ and $\Delta DEF$, $\angle B=$$\angle E=$ ${90}^0$, $AC=DF$ and $BC=EF$.

(c) In $\Delta ABC$ and $\Delta QRP$ , $AB=QR$, $\angle B=$$\angle R$ and $\angle C=$$\angle P$ .

(d) In $\Delta ABC$ and $\Delta PQR$ , $AB=PQ,AC=PR$ and $BC=QR$.

(e) In $\Delta ABC$ and $\Delta PQR$ , $BC=QR$, $\angle A=$ ${90}^{\circ }$, $\angle C=$ $\angle R=$ ${40}^{\circ }$ and $\angle Q=$${50}^{\circ }$.

If √2 = 1.414 then find the value of

√{(√2-1)÷(√2+1)}.

The radius of a sphere is 'r' centimeters it is divided into two equal parts . Find the whole surface of two parts.

When we bisect an angle of ${90}^{\circ }$, we get two angles.

In $△$AJU, if $\angle$AUJ is a right angle, which of the following will always be true?

From a pack of 52 cards, I take out a King card and a Queen card. The total number of cards still left is ___.

The number of king cards still left is ___.
Fill both blanks respectively.

In the figure, A, B, and C are three points on a circle with centre O such that $\angle$BOC = ${30}^0$ and $\angle$AOB = ${60}^0$. If D is a point on the circle other than the arc ABC, find $\angle$ADC (in degrees).

The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is