Explore topic-wise InterviewSolutions in Current Affairs.

If P(x, y) is a point equidistant from the points A(6, -1) and B (2, 3) show that x - y = 3.

The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years): 5-15 15-25 25-35 35-45 45-55 55-65
No. of students: 6 11 21 23 14 5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

In a circus, a motorcyclist performs his stunts in a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is $14m,$ then find the area available for the motorcyclist to perform stunts. $(\text{Take}\pi =\frac{22}{7})$

A(6, 1),B(8, 2) and C(9,4) are the vertices of a parallelogram ABCD. If E is the midpoint of BD, find the area of $△ABE$.

In a particular family, each boy has as many brothers as the sisters, but each girl has twice as many brothers as that of sisters. How many boys and girls are there in the family?

The angle of elevation of the top of a vertical tower PQ from a point X on the ground is ${60}^{\circ }$. At a point Y, 40 m vertically above X, the angle of elevation of the top is ${45}^{\circ }$. Calculate the height of the tower.

2 Women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery, and that taken by 1 man alone.

In triangle ABC if BC is base, Angle B is 60° , AB-AC=0, what is the value of the angle opposite to side BC in degrees?

Factorise :

$\frac{1}{35}+\frac{12}{35}a+a^2$

What would be the perimeter of a triangle with sides (a - d), a and (a + d)?

Find the distance between the following pairs of points:

(i) (2, 3, 5) and (4, 3, 1)

(ii) (-3, 7, 2) and (2, 4, -1)

(iii) (-1, 3, -4) and (1, -3, 4)

(iv) (2, -1, 3) and (-2, 1, 3).

Find the value of $x$ in the following figure.

Mr. Parekh invested Rs 52,000 on Rs 100 shares at a discount of Rs 20 paying 8% dividend. At the end of year he sells the shares at a premium of Rs 20. Find :

(i) the annual dividend.

(ii) the profit earned including his dividend.

Look at the following table below.

$\begin{array}{cc}\text{Class interval}& \text{Class mark}\\ 0-10& A\\ 10-20& B\\ 20-30& 25\\ 30-40& 35\end{array}$

The value of A & B respectively are:

The square of a positive integer CANNOT be of the form ( k is an integer) : ( a ) 3k + 1. ( b ) 4K +2. ( c) 5k +1. ( d ) 5k + 4.

Construct a cyclic quadrilateral PQRS with PQ = 4 cm, QR = 6 cm, PR = 7.5 cm, QS = 7 cm

If we add 1 to the double of the numerator of a fraction, we get the denominator. If we add 4 to both the numerator and the denominator, the fraction becomes 3/5. Find the fraction.

The number of vehicles passing through the signal in a day is counted by a traffic police from Monday to Saturday is given below.

200, 156, 400, 350, 230, 120

The frequency table for this data is:

A vertical tower stands on horizontal plane and is surmounted by a vertical flagstaff of height h metre. At a point on the plane, the angle of elevation of the bottom of the flagstaff is $\alpha$ and that of the top of flagstaff is $\beta$. Prove that the height of the tower is $\frac{htan\alpha }{tan\beta -tan\alpha }$

Using trigonometric tables, find the value of $(sin{64}^{\circ }{42}^{\prime }+cos{42}^{\circ }{20}^{\prime })$

Select the set of numbers that forms an AP.

With respect to a screw gauge, how is zero correction different from zero error?

Additional amount which has to be returned along with the repayment of a loan is called the

AB & CD are two equal chord of circle with centre o. If AB and CD, on being produced, meet at a point P outside the circle, Prove that: (i) PA = PC (ii) PB = PD

Construct triangle with sides 5 cm, 4 cm, and 6 cm. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of triangle

Find the zeros of the quadratic polynomial √3x² - 8x + 4√3.

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. Find the height of the cone.

If (a, 2) is the mid-point of (7, b) and (3,6), find a + b.

In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?

Choose the correct options: the equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if -

Identify the quadratic polynomials among the following.

1. $3x^2+2x+1$

2.$x^2+2x+3$

3.$\sqrt{3}{x}^2+5$

4.$y+\sqrt{2}$

If A $\subset$ B and U is the universal set, then find A $\cap$ B and A\B using Venn diagram

The midpoint of line segment AB is $(2,-5)$. If the coordinates of point A are $(4,4)$, what are the coordinates of B?

If $\frac{3}{x+y}+\frac{2}{x-y}=2and\frac{9}{x+y}-\frac{4}{x-y}=1$ then

(a) x=$\frac{1}{2}$,y=$\frac{3}{2}$ (b) x=$\frac{5}{2}$,y=$\frac{1}{2}$ (c)x=$\frac{3}{2}$,y=$\frac{1}{2}$ (d) x=$\frac{1}{2}$,y=$\frac{5}{2}$

The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) form a ___

A box contains cards numbered 6 to 50. A card is drawn at random from the box. The proabbility that the drawn card has a number which is a perfect square is
(a) $\frac{1}{45}$ (b) $\frac{2}{15}$ (c) $\frac{4}{45}$ (d) $\frac{1}{9}$

In the figure, given below, AD = BC,

$\angle BAC={30}^{\circ }$ and $\angle CBD={70}^{\circ }$. Find: $\angle ADB$

The number of tangents that can be drawn from an external point to a circle is

(a) 1 (b) 2 (c) 3 (d) 4

Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at debt of 4 crore.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment. Find the height of the embankment.

Find the remainder when $x^{51}+51$ is divided by (x+1).

If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.

The sum of three terms of an A.P is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.

A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius 2.5 m and height 21 m and the cone has the slant height 8 m. Calculate the total surface area and the volume of the rocket.