Explore topic-wise InterviewSolutions in Current Affairs.

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If $\angle ADC={130}^{\circ }$, find $\angle BAC.$

Factorize $6t^2+13t+7$ and verify the relationships between the zeroes and the coefficients.

Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. If JF = $8x+4$ and EG = $24x–8$, find the value of $x$.

Prove that if a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic. [4 MARKS]

Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is

Perform the following arithmetic operations. [4 MARKS]

1) $62.5-4.13+7.48-1.2$ = ?
2) $(2.7\times 4.1)-(3.5\times 1.7)$ = ?
3) $(0.07\times 100)+(21.5\times 2)$ = ?
4) $5.07+1.53-4.014$ = ?

The cost of painting outer curved surface of a hollow hemispherical iron ball at rate of Rs. 2 per cm square is Rs. 1256. If thickness of the iron is 1 cm, find the cost of painting the inner curved surface of the ball.(Take $\pi$ = 3.14).

The area of a rectangle gets reduced by 9 square units. if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Let the length of the rectangle = x units and its breadth = y units

According to first condition :
$(x-5)(y+3)=xy-9$ and

According to second condition:
$(x+3)(y+2)=xy+67$

Find the sum of first 22 terms of an AP in which d = 7 and the 22${}^{nd}$ term is 149.

The equation 4x² + 3x + 5 = 0

Five different objects 1, 2, 3, 4, 5 are distributed randomly in 5 places marked 1, 2, 3, 4, 5. One arrangement is picked at random. The probability that in the selected arrangement, none of the object occupies the place corresponding to its number is:

Choose the limits of the inverse cosine function

Find the value of expression

sin (-$\theta$) + cos (-$\theta$) + sec (-$\theta$) + sin($\pi$-$\theta$) + cos($\pi$-$\theta$)+ sec($\pi$-$\theta$)

An equilateral triangle ABC is inscribed in a circle with centre O. Then, $\angle BOC$ is equal to:

During the summer months, one ice cream truck visits Dipanshu's neighbourhood every 4 days and another ice cream truck visits his neighbourhood every 5 days. If both trucks visited today, when is the next time both trucks will visit on the same day?

if α and β are the zeroes of x²+5x+8 then find the value of α + β

In a class of 75 students, 40 follow cricket, 38 follow hockey and 10 follow basketball. Five students follow all the three games. Then the number of students who follow exactly two of these three games are ___.

If $\frac{1}{3}$ and -$\frac{1}{3}$ are the roots of equation $a{x}^2+bx+c=0$, then value of (a+b+c) is

Find all other zeros of the polynomial p(x) = 2x^4-7x^3+19x^2-14x+13 if 2 of its zeros are √2 & -√2

Given $A=\left[\begin{array}{cc}-3& 3\\ 2& -2\end{array}\right]\text{and}B=\left[\begin{array}{cc}4& 6\\ 4& 6\end{array}\right]$ Find AB

A cone is $8.4cm$ high and the radius of its base is $2.1cm.$ It is melted and recast into a sphere. The radius of the sphere is

A) $4.2cm$

B) $2.1cm$

C) $2.4cm$

D) $1.6cm$

ax^2 +bx +c=k(x-alpha)(x-beta)

What does this equation mean why k has been taken as a constant and for more details alpha and beta are the zeroes of the polynomial p(x)=ax^2 +bx+c

Find three numbers are A. P. whose sum is 24 and whose product is 440.

A security guard standing on the top of a 100 m high lighthouse sees an enemy ship coming towards it. It was initially at an angle of depression of ${35}^{\circ }$ but after 10 minutes the angle of depression changes to ${55}^{\circ }$. The speed of enemy ship is equal to $[tan{55}^{\circ }=1.42,tan{35}^{\circ }=0.7]$

If m times the m^th term of an AP is equal to n times its n^th term, find the (m+n)^th term of that AP?

For the following distribution the difference in the upper limit of median and modal class is

If 3 cos θ = 1, then the value of cosec θ is :

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. The common difference of the AP is

Nikita invests Rs 1680 in buying 62.5 shares each of nominal value Rs 24 selling at % premium.

i) Calculate the value of

ii) Calculate the percentage return on the investment, if 14% dividend is declared.

If sin(A – B) = sin A cos B – cos A sin B, then value of sin 15^ois:

If A = $\left[\begin{array}{cc}2& 10\\ 21& 1\end{array}\right]$, B =$\left[\begin{array}{cc}-2& 0\\ 4& 5\end{array}\right]$ then find 2A + B.

Two numbers are in the ratio $4:7$. If thrice the larger be added to twice the smaller, the sum is $59$. Find the numbers.

The discriminant of x square - 3 x - k = 0 is 1.the value of X is

Given below is the pulse count of 40 patients.

66, 79, 89, 67, 72, 82, 85, 80, 82, 81, 67, 87, 71, 68, 63, 74, 73, 86, 84, 75, 85, 80, 85, 61, 75, 85, 80, 85, 61, 75, 68, 69, 64, 75, 73, 72, 82, 76, 74, 77.
Group the data first in discontinuous class intervals such that one of the class intervals is 70-74.
Next, group the data in continuous class intervals such that one of the class intervals is 85-90.
Find the second class interval and the corresponding frequency of the class for both the groupings of the data.

If f: X$\to$Y is a function defined by f(x) = $2x^2-x$, check whether the function is an odd function or even function.

The degree of the polynomial 8x³- 3x²+ 5x -9 is

The corresponding sides of two similar triangles ABC and DEF are BC = 9.1 cm and EF = 6.5 cm. If the perimeter of $\Delta DEF$ is 25 cm, find the perimeter of $\Delta ABC$.

Deep purchases a computer for Rs 37,206 which includes 10% rebate on the marked price and then 6% sales tax on the net price. Find the marked price of the computer.

Which of the following is an example of non-tax revenue?

If D, E and F are the mid points of sides BC, CA and AB respectively of a $\Delta ABC$, then using coordinate geometry, prove that

Area of $\Delta DEF=\frac{1}{4}\left(Areaof\Delta ABC\right)$

The sum of a natural number and its positive square root is 132. Find the number.

The largest cone is curved out from one face of solid cube of side 21 cm.Find the volume of the remaining solid.