Explore topic-wise InterviewSolutions in Current Affairs.

The circumferences of two circles are in the ratio 2 : 3. What is the ratio between their areas?

If ABC is an equilateral triangle of side a, prove that its altitude = $\frac{\sqrt{3}}{2}$a

What is ${\varphi }^{\prime }s$ position with respect to$\psi$ ?

$\text{In the figure, PQ || AB. CQ = 4.8 cm,}\text{QB = 3.6 cm and AB = 6.3 cm. If AP = x,}\text{then what is the length of AC in terms of x ?}$

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{13}{3125}$ [1 MARK]

Which of the following figures has/have more than one line of symmetry?

(i) Square
(ii) Rectangle
(iii) Regular pentagon
(iv) Isosceles triangle

For the AP ($\frac{3}{2}$ ),($\frac{1}{2}$ ),(-$\frac{1}{2}$ ),(-$\frac{3}{2}$ ),… write the first term a and the common difference d. Also write the next two terms after the given last term -$\frac{3}{2}$

If $tan(A+B)=\sqrt{3}$, $tan(A-B)=\frac{1}{\sqrt{3}}$ and $B<A<{90}^{\circ }$, then B=

Question 71

State whether the statement is True or False.

Two figures can have the same area but different perimeters.

Find duplicate ratio of :

(i) 3 : 4 (ii) $3\sqrt{3}:2\sqrt{5}$

Question 116

In a park of dimensions $20m\times 15m$, there is an L shaped 1m wide flower bed as shown in the figure. Find the total cost of manuring for the flower bed at the rate of ₹ 45 per $m^2$.

Question 124

The table shows the cost of sunscreen of two brands with and without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate of each brand ?$\begin{array}{ccc}\text{Quantity}& \text{Cost(in Rs.)}& \text{Cost+Tax(in Rs)}\\ X\left(100g\right)& 70& 75\\ Y\left(100g\right)& 62& 65\end{array}$

Find the value of ${sin}^6$$\alpha$ + ${cos}^6$$\alpha$ if sin$\alpha$ + cos$\alpha$ = m

In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Question 4
The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

Write the sum of first n odd natural numbers.

Two circles of radii 18 cm and 8 cm touch externally. Find the length of a direct common tangent to the two circles.

How to prove any irrational number as irrational

Question 10
Which of the following equations has no real roots?
(A) $x^2-4x+3\sqrt{2}=0$
(B) $x^2+4x-3\sqrt{2}=0$
(C) $x^2-4x-3\sqrt{2}=0$​​​​​​​
(D) $3x^2-4\sqrt{3}x+4=0$​​​​​​​

$\overleftrightarrow{CX}$ is a tangent to a circle with centre A, at a point X. $\overline{AX}$ = 5 cm, CX = 12 cm, AC = ?

Find the missing number in the series 2, 10, 26, ___, 242

How many real numbers satisfy the condition 0 $\le$ $\frac{2}{3}\left[x\right]\le$ 1 ?

Cards marked with numbers 40 , 41 , 42..........60 are well shuffled and a card is drawn at random. What is the probability that the number of the cards is

(i) a prime number

(ii) divisible by 3

(iii) a perfect square

What are the possible outcomes when three unbiased coins are tossed simultaneously? Please explain it in detail how to calculate it mentally when some other number is used as in this case,3.

Rohan deposited Rs. 150 per month in his bank for eight months under the Recurring Deposit Scheme. What will be the maturity value of his deposit, if the rate of interest is 8% per annum and the interest is calculated at the end of every month?

Which is the first negative term of the arithmetic progression 112, 107,102?

The area of a rectangle is $A=25a^2-35a+12$. Its length is ($5a-3$). Find its width.

If $\cot A=\frac{12}{5}$, then find the value of $(\sin A+\cos A)\times cosecA$.

Which of the following are Pythagorean triplets?

Draw a circle of radius $5cm.$ Take a point $P$ on it. Without using the centre of the circle construct a tangent at the point $P$. [3 MARKS]

Maurice applied for a job and got selected. She has been offered a job with a starting monthly salary Rs.10000. If annual increment in her salary is Rs.400, form a series for her monthly salary for first six years. Is this series an AP?

Use a graph paper for this question. Take 1 cm = 1 unit on both the axes.

Plot the points A(2,2), B(6,4) and C(3,8). Construct the locus of points equidistant from A and B. Also, construct the locus of points equidistant from AB and AC. Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length of PA in cm is

Each of the letters in the word RIVAL is on a separate card, face down on the table. If you pick a card at random, what is the probability that its letter will be R?

A two digit number is such that the product of its digits is 38. When 152 is subtracted from the number, the digits interchange their places. Find the second degree equation in x from which we can find tens digit.

See the figures made with matchsticks:

The numbers of sticks needed for the next figure is

Under which condition can a secant to a circle be called a tangent?

Find the ratio in which A (-2, 6) & B (3, -4) is divided by the y – axis. Also find the equation of line with slope ³/₂ passing through this point.

$\text{Find the value for x, y for :}\frac{5}{x+y}+\frac{3}{x-y}=4,\frac{2}{x+y}+\frac{5}{x-y}=5\frac{2}{5}$

If two angles of two triangles are congruent to each other, then the third angles will be congruent to each other.

Using the above statement, choose which two congruency criteria eventually becomes same.