Explore topic-wise InterviewSolutions in Current Affairs.

The coordinates of a point on the x-axis is ________

The age wise participation of students in the Annual Function of a school is shown in the following distribution.
$\begin{array}{cccccccc}\text{Age (in years)}& 5-7& 7-9& 9-11& 11-13& 13-15& 15-17& 17-19\\ \text{Number of}& & & & & & & \\ \text{students}& x& 15& 18& 30& 50& 48& x\end{array}$

Find the missing frequencies when the sum of frequencies is $181$. Also, find the mode of the data.

Find $sin(A+B-C)$ if
$sin(B+C)=\frac{\sqrt{3}}{2}$
$sin(A+C)=sinB$ and
$sinA=\frac{1}{2}.$

The area enclosed between the concentric circles is $770c{m}^2$. If the radius of the outer circle is 21 cm, find the radius of the inner circle.

In a flower bed, there are 43 rose plants in the first row, 41 in the second, 39, in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?

Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are

In Fig. the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find

(i) The length of the boundary

(ii) The area of the shaded region.

Show that the following points are collinear :

(i) A (2, -2), B(-3, 8) and C(-1, 4)

(ii) A(-5, 1), B(5,5) and C(10, 7)

(iii) A(5, 1), B(1, -1) and C(11, 4)

(iv) A(8, 1), B(3, -4) and C(2, -5)

The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.

Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

An insect is moving on a rectangular plane from one vertex point to other along the diagonal, How many minimum number of independent informations required to completely specify its position.

The Curved surface area and Total surface area of a cone having slant height ${}^{\prime }{l}^{\prime }$ and base radius ${}^{\prime }{r}^{\prime }$ respectively are
&
.

Find value of $x$ in the given pair of equations.

$\frac{1}{x}+\frac{1}{y}=4$

$\frac{1}{x}-\frac{1}{y}=2$

In the given right-angled triangle, if $AB=3cm,BC=4cm,$ then the value of $AC$ is ___ $cm$

A wall of thickness 10cm and height 5m has to be built across a play ground of length 15m. How many bricks are needed to construct the wall, if each brick has dimensions of 20cm x 10cm x 5cm?

For the given linear equation:
y - 3x + 1 = 0,
what are the values of y for x = [3, -4, 2]?

A vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the fower.

The sides of certain triangles are given below. Determine which of them are right triangles.

(i) 9 cm, 16 cm, 18 cm

(ii) 7 cm, 24 cm, 25 cm

(iii) 1.4 cm, 4.8 cm, 5 cm

(iv) 1.6 cm, 3.8 cm, 4 cm

(v) (a-1) cm, $2\sqrt{a}cm,(a+1)cm$

A man is standing on the fourth step of a staircase. Each step is 40 cm wide as shown in the figure. Find the distance between the man and the ground if the inclination of the staircase from the ground is ${50}^{\circ }[tan{50}^{\circ }=1.19]$

Write the first three terms in each of the sequences defined by the following -
(i) $a_n$ = 3n + 2
(ii)$a_n$ = $n^2$ + 1

If the range of n observations $x_1,x_n$ is zero , then the mean of these observations is

Find the area of $△ABC$ whose vertices are :

(i) A(1, 2), B (-2, 3) and C(-3, -4)

(ii) A (-5,7),B(-4, -5) and C(4,5)

(iii) A(3, 8), B(-4, 2) and C(5, -1)

(iv) A (10, -6),B (2,5) and C(-1, 3)

One says, "Give me a hundred,friend! I shall then become twice as rich as you." The other replies, "If you give me ten, I shall be six times as rich as you. "Tell me what is the amount of their respective capital?

Explanation of substitution method through an example .

After Six years, a man's age will be three times the age of his son and three years ago he was nine times of his son's age. The present age of the man is

The total surface area of a right circular cone of slant height 13 cm is 90$\pi$ $c{m}^2$. Calculate :
(i) its radius in cm,
(ii) its volume in $c{m}^3$, in terms of $\pi$.

In a right $△$ ABC, if $\angle$ A is acute and tanA = 3/4, find the remaining trigonometric ratios of $\angle$ A.

Find the mean, median and mode of the following data:
$\begin{array}{cccccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120& 120-140\\ \text{Frequency}& 6& 8& 10& 12& 6& 5& 3\end{array}$

In a $△$ABC, right anged at B, if tan A = $\frac{1}{\sqrt{3}}$ , find the value of

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Question 110 (iii)

A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50.
Which method do you think stores actually use? Why?

From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $\alpha$ and $\beta$. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, find the distance between the ships is metres.

The volume of a right circular cylinder with its height equal to the radius is $25\frac{1}{7}c{m}^3.$ Find the height of the cylinder.

A hollow sphere of external and internal diameters 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.

The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two trains differ by 20 km/hr.

The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be ${45}^{\circ }$ and ${30}^{\circ }$ respectively. If the ships are $200m$ apart, find the height of the lighthouse.

(i) In Fig. 7.70, if AB ||CD, find the value of x.
(ii) In Fig. 7.71, if AB || CD, find the values of x.

(iii) In Fig. 7.72 AB||CD, If OA =3x-19, OB=x-4, OC=x-3 and OD= 4, find x.

The volume of a sphere is 4851 $c{m}^3$. Find its curved surface area.

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Question 11
Show that ${12}^n$ cannot end with the digit 0 or 5 for any natural number n.

Which is the following is true about addition of matrices.

In the given figure, ABCD is a quadrilateral with $\angle 1=\angle 2$ and $\angle 3=\angle ABC$ and $\angle 4=\angle BAD$. Also, AP and BQ are produced to points E and F, respectively. Then, we can say that

If $[A{]}_{m\times n}$ and $[B{]}_{n\times p}$ are two matrices, then the order of AB will be .

The age of 30 workers in a factory are as follows

$\begin{array}{cc}\text{Age}& \text{No. of workers}\\ 24& 5\\ 25& 7\\ 26& 8\\ 27& 4\\ 28& 6\end{array}$

(i) Find the mean,median and mode for the above ungrouped data. [4 MARKS]