Explore topic-wise InterviewSolutions in Current Affairs.

If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius R then

(a) $R_1+R_2=R$

(b) $R_1+R_2>R$

(c) $R_1^2+R_2^2<R^2$

(d) $R_1^2+R_2^2=R^2$

If we multiply all the digits of 78549542, what will be the last two digits of the resultant number?

In the following Fig. AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

In the given figure, $RQ$ is a tangents to the circle with centre $O.$ If $SQ=6cm$ and $QR=4cm,$ then $OR$ is equal to

(a) $2.5cm$ (b) $3cm$ (c) $5cm$ (d) $8cm$

A game of chance consists of spinning an arrow, which comes to rest pointing at one of the numbers 1,2,3,4,5,6,7,8 and these are equally likely outcomes. Find the probability that the arrow will point at any factor of 8.

If tan $\theta$ = $\frac{4}{3}$ then (sin $\theta$ + cos $\theta$) = ?

(a) $\frac{7}{3}$ (b) $\frac{7}{4}$ (c) $\frac{7}{5}$ (d) $\frac{5}{7}$

The surface area of a solid metallic sphere is 616 $c{m}^2$. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed. (Use ~\pi = \frac{22}{7}).

23 spoons and 17 forks together cost Rs.1770,while 17 spoons and 23 forks together cost Rs.1830.Find the cost of a spoon and that of a fork.

Find the equation of the line whose slope is $-\frac{5}{6}$ and x-intercept is 6.

Cards marked with numbers 1,2,3,4,.....20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is :

(i) a prime number ? (ii) divisible by 3 ? (iii) a perfect square ?

In the given triangle DE II BC, which of the following statements is true?

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is king.

If the sum of the zeros of the quadratic polynomial $k{x}^2+2x+3k$ is equal to the product of its zeros then k = ?

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

Question 127

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.

A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

If the average of n natural numbers is (n+10)/4 then what is the value of n?

a.8 b.9 c.10 d.11

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

Prove that the following is irrational : $\frac{1}{\sqrt{2}}$

which of the following is true, if A is an invertible square matrix :-

The radius and height of a right circular cone are in the ratio $3:4$. If its slant height is $25\text{cm}$, its total surface area is:

Question 22

Fill in the blanks to make each statement true:

The share of A when Rs. 25 are divided between A and B, so that A gets Rs. 8 more than B, is ...................

Without solving, the following quadratic equation find the value of p ; for which the root are real and equal

Xsquare+(p-3)x+p =0

At each stage the black dot moves 3 corners clockwise and the white dot moves 3 corners anticlockwise. After how many stages will both dots be together in the same corner?

$\text{If}f\left(x\right)=\sqrt{1+x^2}\text{, then}$ ____

BL and CM are medians of a triangle ABC right angled at A. Prove that
$4({BL}^2+{CM}^2)=5{BC}^2$. [3 MARKS]

The value of $\tan$ ${30}^{\circ }$ is

Rubik's cube has total surface area of 54 ${cm}^2$. The area occupied by a single red tile on rubik's cube is

The ${10}^{th}$ term of an AP is 52 and ${16}^{th}$ term is 82. Find the ${32}^{nd}$ term and the general term.

In the given figure, O is the centre of the circle, the value of x is

Find the value of p if the lines, whose equations are 2x - y + 5 = 0 and px + 3y = 4 are perpendicular to each other.

What is the largest four digit number which is exactly divisible by 88 what are the steps to find it

Forrest got a box of chocolate from Jenny. It had n different chocolates. Forrest asked Jenny how many chocolates the box has. Jenny, who is an aspiring data scientist replied, the probability of you getting a KitKat is $\frac{1}{19}$. How many chocolates are there in the box, if each chocolate brand is equally - likely and there is only one chocolate of each brand?

Question 2
Draw a right $\Delta$ABC in which BC = 12 cm AB = 5 cm and $\angle B={90}^{\circ }$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$. Is the new triangle also a right triangle?
Thinking process
Here scale factor $\frac{m}{n}=\frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

The side AC of triangle ABC is produced to D so that CD=AC/2. If E is the mid point of BC and DE is produced to meet AB at F and EQ||AB, prove that EF=1/3DF

What is the least number that is divisible by all the natural numbers from 1 to 10 (both inclusive) ?

(a) 100 (b) 1260 (c) 2520 (d) 5040

In a triangle PQR right angled at Q if QS = SR then prove that PR² = 4PS² - PQ²

Pavan asked Preeti to draw a triangle. He gave following data

1.the base BC

2.a base angle, say $\angle$B

3.The difference of other two sides AB - AC or AC - AB, Assume, AB $>$ AC

She was unable to draw the triangle ABC. So as a hint he gave steps of construction but it was not in correct order. He gave following steps

1.Draw the base BC and at point B make an angle say XBC equal to the given angle.

2.Join DC and draw the perpendicular bisector, say PQ of DC.

3.Cut the line segment BD equal to AB - AC from ray BX.

4.Let it intersect BX at a point A. Join AC

​Arrange the steps in correct order.

A man saved Rs.32 during the first year, Rs. 36 in the second year and in this way he increases his savings by Rs. 4 every year. Find in what time his saving will be Rs. 200.

Let p be a prime number. If p divides $a^2$ then p divides a, where a is a positive integer. Which theorem is this statement previously based on?

The areas of two concentric circles are 1386 $c{m}^2$. The width of the ring is

(a) 2.8 cm (b) 3.5 cm (c) 4.2 cm (d) 3.8 cm

Comment upon the nature of the roots without solving

1.). X^{​​​​​​2} - as - b^{​​​​​​2} = 0

When I solved the equation I got the roots as

A^{​​​​​​2} + 4b²

But the answer is given as the roots are positive so it is real and unequal how is it? And why is it?

A's value can be a negative no also like a= -3

So how can this be possible?

The ratio of base radius to slant height of a right circular cone is 4:3. Calculate the ratio of the total surface of the cone to the curved surface of the cone.(Take pi=$\frac{22}{7}$)

Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centres if :

(i) they touch each other externally,

(ii) they touch each other internally.

Two circles touch each other externally.If the sum of their areas is $130\pi c{m}^2$ and the distance between their centres is $14cm$. Find the sum of their radii.

Let triangle ABC~DEF, area of triangle ABC = 169cm^2 and area of triangle DEF = 121cm^2 . If AB = 26cm , then find DE .

Question 4 (ii)
The heights of 50 students, measured to the nearest centimeters, have been found to be as follows:
$\begin{array}{cccccccccc}161& 150& 154& 165& 168& 161& 154& 162& 150& 151\\ 162& 164& 171& 165& 158& 154& 156& 172& 160& 170\\ 153& 159& 161& 170& 162& 165& 166& 168& 165& 164\\ 154& 152& 153& 156& 158& 162& 160& 161& 173& 166\\ 161& 159& 162& 167& 168& 159& 158& 153& 154& 159\end{array}$
$\begin{array}{cc}\text{Height (in cm)}& \text{Number of studentss(frequency)}\\ 150-155& 12\\ 155-160& 9\\ 160-165& 14\\ 165-170& 10\\ 170-175& 5\\ \text{Total}& 50\end{array}$
(ii) What can you conclude about their heights from the table?