Explore topic-wise InterviewSolutions in Current Affairs.

Matrix A is such that $A^2=2A-I,$ where I is the Identity matrix. Then for $n\ge 2,A^n$ is equal to

For what value of 'K' will the system of equations 3x + y = 1,
(2K - 1)x + (K - 1)y = 2K + 1 have no solution

The capacity of a tub, which is of the shape of the frustum of a cone, is 16720000 cm³. The respective radii of the upper and lower bases of the tub are 90 cm and 40 cm. (Use π = ²²/_⁷)

What is the slant height of the tub?

Find the point of y-axis which is equidistant from the points (-5, -2) and (3, 2).

Probability of an event E + Probability of an event “not E” is equal to = ___.

The below distribution shows the number of wickets taken by bowlers in one-day cricket match. Find the mean of the wickets.

$\begin{array}{ccccccc}\text{NUMBER OF WICKETS}& 20-60& 60-100& 100-150& 150-250& 250-350& 350-450\\ \text{NUMBER OF BOWLERS}& 7& 5& 16& 12& 2& 3\end{array}$

A student noted the number of cars passing throught a spot on a road for 100 periods each of 3 minutes and summarized it in the table gives below.

The mode, median and mean of the data is

Match the following:

$\begin{array}{cc}1.\text{sin}({90}^{\circ }-A)& a)\text{cosec}A\\ 2.\text{tan}({90}^{\circ }-A)& b)\text{cot}A\\ 3.\text{sec}({90}^{\circ }-A)& c)\text{cos}A\end{array}$

If $bcos\theta =a$, then prove that

$cosec\theta +cot\theta =\sqrt{\frac{b+a}{b-a}}$ [4 MARKS]

The number of solutions of equations represented by this graph is

In the figure, TF is a tower. The elevation of T from A is ^o, where tan = ²/₅ and AF = 200m. The elevation of T from B where AB = 80m is y^o. Calculate /y correct to nearest degree.

Find the value of 'a' if the point (a, 2a-1) lies on the line 9x -10y + 1 = 0.

A man of height y is standing between two buildings with heights x and z respectively as shown in the figure. Then, which of the following statements is true about the relation of the heights?

Question 6
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

If a curve $y=a\sqrt{x}+bx$ passes through the point (1, 2) and the area bounded by the curve, line x=4 and x-axis is 8 sq. unit, then

Which of the following options are equal to $\sqrt{\frac{1+cosA}{1-cosA}}?$

The areas of two similar triangles are $9c{m}^{2}and16c{m}^2$ respectively . The ratio of their corresponding sides is ____.

If the equation $x^2+2(k+2)x+9k=0$ has equal roots, then values of k are __________.

A square pyramid covers an area of $400m^2$ on the ground and height of the pyramid is 10 m. Then find its total surface area of the pyramid

The roots of the equation $x^2+2x–15=0$ are

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: $\frac{23}{8}$

$△PQR$, right-angled at Q, if PR=24cm, QR=12cm, then find the value of $\angle QRP$.

In Fig. 7.136, $\Delta ACB\sim \Delta APQ$. If BC = 8 ~cm, [Q = 4 ~cm, BA = 6.5 cm and P= 2.8 cm, find CA and AQ.

Which of the following is an inference that could be drawn from central tendency.

Prove the following trigonometric identities:

$\frac{1+cos\theta -si{n}^2\theta }{sin\theta (1+cos\theta )}=cot\theta$

250 lottery tickets were sold and there are 5 prizes on these tickets. If kunal has purchased one lottery ticket, what is the probability that he wins a prize?

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$3a^2{x}^2+8abx+4b^2=0,a\ne 0$

$\frac{cos{38}^{o}cosec{52}^o}{tan{18}^{o}tan{35}^{o}tan{60}^{o}tan{72}^{o}tan{55}^o}$ = ?

(a) $\sqrt{3}$ (b) $\frac{1}{3}$ (c) $\frac{1}{\sqrt{3}}$ (d) $\frac{2}{\sqrt{3}}$

If centroid of a triangle having two of its vertices $A(1,3),B(2,4)$ is $(0,0)$. Then the third vertex is _______ .

Find the total surface area of hemisphere of radius 7 cm.(Take $\pi$ = $\frac{22}{7}$).

Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying instalments every month. If the instalment for the first month is Rs. 1,000 and it increases by Rs. 100 every month, what amount will she pay as the ${30}^{th}$ instalment of loan ? What amount of loan she still has to pay after the ${30}^{th}$ instalment ?

The factorisation of $2y^3+10y^2-48y$ is ____.

The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.

Solve the following quadratic equation by factorization.
$(a+b{)}^2{x}^2-4abx(a-b{)}^2=0$

The perimeter of one face of a cube is 20 cm. Its volume will be:

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 8 units then the other two vertices of the triangle are___

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is $\frac{1}{27}$ of the volume of the given cone, at what height above the base is the section made?

Question 71

Solve the following:

$\frac{9-3y}{1-9y}=\frac{8}{5}$

Draw, in the same diagram , a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:

$\begin{array}{ccccccccc}\text{Cost of living index}& 440-460& 460-480& 480-500& 500-520& 520-540& 540-560& 560-580& 580-600\\ \text{No. of months}& 2& 4& 3& 5& 3& 2& 1& 4\end{array}$

What is the condition for the equation $x^2+bx-c=0$ to have real roots?

If two lines are perpendicular, then the product of their slope is _____.

Using the method of completion of squares find one of the roots of the equation $2x^2-7x+3=0$. Also, find the equation obtained after completion of the square.

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