Explore topic-wise InterviewSolutions in Current Affairs.

The total surface area of a cube is 864 $c{m}^2.$ Its volume is

(a) 3456 $c{m}^3$ (b) 432 $c{m}^3$ (c) 1728 $c{m}^3$ (d) 3456 $c{m}^3$

Using the distance formula, show that the given points are collinear:

(i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

(iii) (-1, -1), (2, 3) and (8, 11) (iv) (-2, 5), (0, 1) and (2, 3).

Find the sum of all multiples of $9$ lying between $300$ and $700.$

The sum of a number and its reciprocal is $2\frac{1}{30}$. Find the number.

A letter of English alphabet is chosen at radnom. Determine probability that the chosen letter is a consonant.

Solve each of the following quadratic equations:
$4^{(x+1)}+4^{(1-x)}=10$

Find the mean, mode and median of the following frequency distribution:
$\begin{array}{cccccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Frequency}& 5& 10& 18& 30& 20& 12& 5\end{array}$

If two of the zeros of the cubic polynomial $a{x}^3+b{x}^2+cx+d$ are 0 then the third zero is

(a) $\frac{-b}{a}$ (b) $\frac{b}{a}$ (c) $\frac{c}{a}$ (d) $\frac{-d}{a}$

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be ${30}^{\circ }$ and ${60}^{\circ }$ respectively. Find
(i) the horizontal distance between AB and CD.
(ii) the height of the lamp post.
(iii) the difference between the heights of the building and the lamp post.

A telephone company charges Rs. 0.05 per minute for local calls and Rs. 0.12 per minute for long distance calls. Which expression gives the total cost in rupees for "$x$" minutes of local calls and "$y$" minutes for long distance calls?

If the sum of a pair of opposite angles of a quadrilateral is ${180}^{\circ }$, then the quadrilateral is

The solution for the equations $c_1$x + $b_1$y + $a_1$ = 0 and $c_2$x + $b_2$y + $a_2$ = 0 is

$S_1$ : x = $\frac{(b_1{a}_2–b_2{a}_1)}{(c_1{b}_2-c_2{b}_1)}$

$S_2$ : y = $\frac{(c_1{a}_2–c_2{a}_1)}{(a_1{b}_2-a_2{b}_1)}$

The marks obtained by the students of a class , in a exam which was out of 50 mark given below

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$

(i) Find the mean for the ungrouped data.

(ii) Represent the same data as grouped data, with class interval of width = 10 [4 MARKS]

From the given figure, find :

(i) the co-ordinates of A, B and C.

(ii) the equation of the line through A and parallel to BC.

The median of the observations 5, 8 , 12 , (x+2) , (x + 4) , 24 , 26 , 30 arranged in ascending order is 18.

Find the Value of x .

Which of the following relations between two sets are functions?

ABC is a triangle, D is the mid-point on side BC.



Given, AB=2 cm, AC=4 cm and BD=3 cm
Find the value of AD.

Question 7
Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?
(A) $\frac{1}{8}$
(B) $\frac{1}{64}$
(C) $\frac{1}{4}$
(D) $\frac{9}{64}$

Question 26

Fill in the blanks to make each statement true:

When a number is divided by 8, the result is -3. The number is .....................

Question 41

State whether the following statement is true (T) or false (F).

In the equation 2x=4-x, transposing -x to LHS, we get x=4.

Find a matrix X such that A-X=B, given

$A=\left(\begin{array}{ccc}3& 7& 2\\ -4& -3& 0\\ 5& 1& -2\end{array}\right)andB=\left(\begin{array}{ccc}8& -6& 1\\ 2& 0& -3\\ 3& 4& -1\end{array}\right)$

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R and S respectively. If $AB=11cm,BC=xcm,CR=4cm$ and $AS=6cm,$ the value of $x$ is ___ $cm.$

Graph of f(x) is given. Draw the graph of f${}^{-1}$(x)

Mr Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is 8% per annum and Mr Britto gets ₹ 8088 from the bank after 3 years, find the value of his monthly installment.

Which of the following functions are into functions if they are all defined from $R$ to $R$?

Which is the correct graph of y < x + 2?

Read the following information carefully to answer the given questions:

V, U and T are sitting around a circle. A, B and C are sitting around the same circle but two of them are not facing centre (they are facing the direction opposite to centre). V is second to the left of C. U is second to the right of A. B is third to the left of T. C is second to the right of T. A and C are not sitting together.

Which of the following is the position of T in respect of B?

We know that Probability of an event E, written as P(E) $=\frac{NumberofoutcomesfavourabletoE\left(m\right)}{Numberofallpossibleoutcomesoftheexperiment\left(n\right)}$.
Which of the following options correctly explains the relationship between m and n?

Therefore is ROOT of sin2theta + ROOT of cos2theta must be equal to ROOT of one ?

Basically is sin ROOT theta +cos ROOT theta = 1

What must be subtracted from or added to 6x⁴+7x³-26x²-25x+25 so that it may be exactly divisible by 3x²-x+4?

For $\sqrt{3}{x}^2$ to be irrational, x should be

In the laboratory, a student measures the thickness of a metal sheet using a screw gauge as shown in the given figure. What is the thickness of the sheet?

form a quadratic polynomial one of whose zeroes is 2+ root 5 and the sum of the zeroes is 4

A cylindrical can, whose base is horizontal and of radius 3.5 cm, contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate :
(i) the total surface area of the can in contact with water when the sphere is in it;
(ii) the depth of water in the can before the sphere was put into the can.

According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a>b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

If ln(a+c) , ln(a-c) , ln(a-2b+c) are in A.P, then

The sum of n terms of an AP is 3n² + 5n and then which term of AP is 164.

One sees the top of a tree on a bank of a river at an elevation of ${70}^{\circ }$ from the other bank. Stepping 20 m back, he sees the top of the tree at an elevation of ${55}^{\circ }$. If height of the person is $1.4m$ then the width of river is $[tan{70}^{\circ }=2.75,tan{55}^{\circ }=1.43]$

If 2y –$a^2$x = 3 and 2y – (4ax +1) = 0 are parallel, find the value of a, where a is a natural number.

There is a boat with speed 17 $\frac{km}{hr}$. The stream has a speed of x $\frac{km}{hr}$. What are the upstream and downstream speeds respectively?

100 surnames were randomly picked up from a local telephone directory & the frequency distribution of the number of letters in the English alphabets in the surname was obtained as follows.

$\begin{array}{ccccccc}\text{Number of letters}& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ \text{Number of surnames}& 6& 30& 40& 16& 4& 4\end{array}$
Determine the median number of letters in the surnames.

1. 8.05

State, Whether the following statements are true of false.

(i) If $a<b,thena-c<b-c$

(ii) If $a>b,thena+c>b+c$

(iii) If $a<b,thenac>bc$

(iv) If $a>b,then\frac{a}{c}<\frac{b}{c}$

(v) If $a-c>b-d;thena+d>b+c$

(vi) If $a<b,andc>0,thena-c>b-c\text{where a, b, c and are real numbers and}c\ne 0.$

The points A (2, 3), B(3, 5) and C (–1, –1) are the vertices of the triangle ABC. Find the equation of the altitude of the triangle through A.

The longest chord of a circle is the ____ of the circle.