Explore topic-wise InterviewSolutions in Current Affairs.

In $△$ABC, if $\angle$A = ${45}^{\circ }$ and $\angle$B = ${70}^{\circ }$, then the shortest and the longest sides of the triangle, respectively, are:

In the figure, the value of x is

The length,breadth and height of a cuboid are 15 cm,12 cm and 4.5 cm respectively.Its volume is
$\left(a\right)243c{m}^3\left(b\right)405c{m}^3\left(c\right)810c{m}^3\left(d\right)603c{m}^3$

Three statements are given below:

I. In a ||gm, the angle bisectors of two adjacent angles enclose a right angle.

II. The angle bisectors of a ||gm form a rectangle.

III. The triangle formed by joining the midpoints of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III

Write the sum of the angles of an obtuse triangle.

In the figure, if $l_1||l_2$, what is the value of y?

Factorize $\frac{1}{27}{x}^3-y^3+125z^3+5xyz$

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

The point (–3, 2) belongs to which quadrant?

If any two sides of a triangle are unequal, then the larger side has the __angle opposite to it

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The area of the curved surface in $c{m}^2$ is

Simplify: $39x–[23x–\{29x–(17x–3x)\left\}\right]$

Which of the following is not a linear equation in one variable? (Consider a, b and c as constants and x as variable)

In the given figure, E is the midpoint of side AC and D is the midpoint of side AB, then

S1 : DE = $\frac{1}{2}$BC and DE || BC

S2 : Midpoint theorem : A line segment joining midpoints of 2 sides of a triangle is parallel to the third side and is half of it.

Juice is filled upto 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at Rs. 3, how much money can be earned by selling the juice?

The diameter of wheel is 0.70 m. Find the distance covered by it in 500 revolutions. If the wheel takes 5 minutes to make 500 revolutions; find its speed in:

(i) m/s

(ii) km/hr

In the given figure, $AD$ is a median of $△ABC$ and $E$ is the mid-point of $AD.$ Also, $BE$ produced meets $AC$ in $F.$ Then $AF=$

If $\alpha$ and $\beta$ are the zeros of a polynomial
$f\left(x\right)=6x^2+x-2$, find the values of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$.

Question 14
In the figure, O is the centre of the circle BD = OD and CD $\perp$ AB. Find $\angle CAB$.

3x÷2-5y÷2=0

2x-3y+10=0

Which of the following numbers can form sides of a right angled triangle?

A) 4
B) 5
C) 6
D) 7

What will you substitute to make the following equation a linear equation?

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

Form the equation the cost of 4 books and 5 pens is rupees 105

In $△$ABC, $\angle$A and $\angle$B measure ${50}^{\circ }$ and ${30}^{\circ }$, respectively. Find the longest side of the triangle.

Two relatively prime need not be prime numbers. What does this mean?

Which among the following is sufficient to prove that a quadrilateral is a parallelogram?

The adjoining figure shows a trapezium ABCD in which side AB is parallel to side DC. P and Q are mid - points of diagonals AC and BD respectively. CQ joined and produced meets AB at point R.
Which of the following options are correct?

Factorise :

2√2a³ + 16√2b³ + c³ - 12abc

In a $\Delta ABC$, the internal bisector of $\angle A$ meets opposite side BC at D. Through vertex C, line CE is drawn parallel to DA which meets BA produced at point E. Which of the following is true?

Which of the following is surely a regular polygon?

In $△$ABC, $\angle B={90}^{\circ }$.

If $tanA=\frac{1}{\sqrt{3}}$, then

$sinA.cosC+cosA.sinC=$ ___
and, $cosA.cosC-sinA.sinC=$ ___

If one of the angles of a triangle is 130° then find the angle between the bisectors of the other two angles .

AX and BX are two adjacent sides of a regular polygon.If angle ABX=1/3 OF angle AXB then the number of sides in the polygon are

Solve the following pair of equations:

7x - 15y = 2 ; x + 2y = 3.

Hence find 'm' in y = mx - 30/29

In the adjoining figure, PQ || BC, the what could be the values of AQ & QC respectively

Find the length of the diagonal AC of the parallelogram ABCD when AE = 4x + 5 and EC = 3x + 7

In the given figure, if parallelogram ABCD and rectangle ABEF are of equal area then:

A circle of radius 26 cm has a chord of length 20 cm, then the distance of the chord from the centre is

If x+y+z=9 and xy+yz+zx = 23, the value of $(x^3+y^3+z^3-3xyz)=?$

(a) 108

(b) 207

(c) 669

(d) 729

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=${90}^{\circ }$)

If $p\left(x\right)=x+4$ then $p\left(x\right)+p(-x)=?$
(a) 0
(b) 4
(c) 2x
(d) 8

Simplify the following:

$\left(i\right)3(a^4{b}^3{)}^{10}\times 5(a^2{b}^2{)}^3\left(ii\right)\left(2x^{-2}{y}^3{)}^3\right(iii\left)\frac{(4\times {10}^7)(6\times {10}^{-5})}{8\times {10}^4}\right(iv\left)\frac{4a{b}^2(-5a{b}^3)}{10a^2{b}^2}\right(v\left){\left(\frac{x^2{y}^2}{a^2{b}^3}\right)}^n\right(vi)\frac{(a^{3n-9}{)}^6}{a^{2n-4}}$

Diameter of a circular park is $14m.$ Find its circumference. (Take $\pi =\frac{22}{7}$)

What is the area of the parallelogram whose base is 6 cm and height is 4 cm long?

The difference between simple interest and compound interest on a certain sum is Rs. 54.40 for 2 years at 8 percent per annum. Find the sum.

The mean of the following data $1^2,2^2,3^2,4^2,........n^2$ is ______.