Explore topic-wise InterviewSolutions in Current Affairs.

Given:
$sin(B+C)=\frac{\sqrt{3}}{2}$
$sin(A+C)=sinB$ and
$sinA=\frac{1}{2}.$

Find $sin(A+B-C)$.

What is the quadratic polynomial whose sum of zeros is -3/2 and the product of zeros is -1

Show that if x is real , the expression (x^2-bc)/(2x-b-c) has no real value between b and c.

In the following figure, $\angle$ AXY = $\angle$ AYX. If $\frac{BX}{AX}=\frac{CY}{AY}$, show that triangle ABC is isosceles.

If sum and the product of the zeroes of the polynomial f(x)=4x^2-27x+3k^2 are equal, find the value of k

Simplify the rational expression $\frac{a^2-1}{a^4-1}$ into lowest terms

Find the value of the unknown in the following figures.

If p is a positive prime integer . Then √P_________

The probability that a randomly chosen number from one to twelve is a divisor of twelve is

Factorise :

$1-2a-2b-3(a+b{)}^2$

In an experiment with 15 observations, the results are as follows:$\sum x^2=2830,\sum x=170$. One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c{m}^2$).

The value of $si{n}^2{5}^{\circ }+si{n}^2{10}^{\circ }+si{n}^2{15}^{\circ }$ + ..............+

$si{n}^2{85}^{\circ }+si{n}^2{90}^{\circ }$ is equal to

The sum and product of zeros of a quadratic polynomial are $2$ and $-15$ respectively. The quadratic polynomial is

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 $c{m}^2$. $[Use\pi =\mathrm{3.14.}]$

Solve for x and y:

$px+qy=p-q,qx-py=p+q.$

Find the coordinates of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5).

If the radii of the circular ends of a bucket 24 cm high are 5 cm and 15 cm respectively, find the surface area of the bucket.

Find a point on the x-axis which is equidistant from the points $(7,6)$ and $(-3,4)$.

Find the sum of n terms of an A.P. whose nth terms is given by $a_n=5-6n$.

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of ${60}^{\circ }$. After 10 seconds, its elevation is observed to be ${30}^{\circ }$. Find the speed of the aeroplane in km/hr.

If PT is a tangent to a circle with centre O and PQ is a chord of the circle such that $\angle$ QPT = ${70}^o$, then find the measure of $\angle$ POQ.

A contractor plans to install two slides for the children to play in a park. For elder children he wants to make a steep slide at a height of 6 m and inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide (in m)?

There are 1000 labourers in a factory. The factory supervisor wants to find out the typical productivity of a worker. Which measure of central tendency should he use?

Which of the following series forms an AP?

(i) a – 2d, a – d, a, a + d, a + 2d

(ii)a, a + d, a + 2d, a + 3d, a + 4d

(iii) a – 3d, a – d, , a + d, a + 3d

Find the equations representing the given graph.

Question 112 (iv)

Use the following figure, showing the layout of a farmhouse.

Each banana tree required $1.25m^2$ of ground space. How many banana trees can there be in the orchard?

A tangent PT is drawn parallel to a chord AB as shown in figure. Prove that APB is an isosceles triangle.

The sum to n terms of the AP 5, 2, -1, -4, -7, ... is

The digits of a positive integer ,having three digits are in AP and their sum is 15 .The number obtaining by reversing the digit is 594 less than the original number .find the number

If the digits of the number 12345 are randomly rearranged, what is the probability that the new number is divisible by
(i) 3 (ii) 9
[4 MARKS]

For four numbers a, b, c, d if a : b = c : d, then a : c = b : d. Which property of proportion is this?

If y = f : A $\to$ B, then which of the following is true if f(x) is a function in x.

(i) x must be able to take each and every value of A

(ii) one value of x must be related to one and only one value of y in set B.

Which of the following is a rational number and explain why :

1.Root 2

2. 0(zero)

3. Root 4

4. Root of -16

Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

Find the relation between p and q if n=3 ,y=1 is a solution of a pair of lines x-4y+p=0 and 2x+y-q-2=0

State the type of the conditional clause in the sentence.
We are going out this afternoon if the weather is good.

If $A=\left[\begin{array}{cc}9& 2\\ 6& 12\end{array}\right],B=\left[\begin{array}{cc}3& 4\\ 1& 3\end{array}\right]andC=\left[\begin{array}{cc}6& 3\\ 1& 3\end{array}\right]$, find X such that A+B-C=3X

Which of the following is an example of direct taxes?

On which of the following products the government imposes heavy taxes by adopting differential commodity taxation?

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. $\angle SPT$ is ${50}^{\circ }$, the value of $\angle SQT$ is:

The sum of first 14 terms of an A. P. is 1050 and its ${14}^{th}$ term is 140. Find the ${20}^{th}$ term.

I am three times as old as my son's age . Five years later ,I shall be two and half times as old as my son. How old am I and my son?

In the given figure, AC is a diameter, AB = BC & ∠AED = 118⁰.

Calculate ∠DAB

The points $(a,a)$, $(-a,-a)$ and $(–\sqrt{3}a,\sqrt{3}a)$ form the vertices of an