Explore topic-wise InterviewSolutions in Current Affairs.

For an A.P. the third and the fifth terms are given as 10 and 16 .What is the fourth term and the common difference?

It takes one and a half hour less to cover a journey of 450 km if the speed of a bus is increased by 10 km/hr. The original speed of the bus is ___ km/hr.

Find the values of p, q, r and s in the given cumulative frequency distribution.
$\begin{array}{ccc}x& frequency& Cumulativefrequency\\ 10& 3& p=----\\ 15& 10& q=----\\ 20& 25& r=----\\ 25& 7& s=----\\ 30& 5& 50\end{array}$

To draw a pair of tangents to a circle which are inclined to each other at an angle of 45^oit is required to draw tangents at the end point of those two radii of the circle, the angle between which is :

In triangle ABC, right angled at B, if $\angle A$ is made smaller and smaller till it becomes zero, find the value of Sin A and Cos A.

The areas of two similar triangles are 169 $c{m}^2$ and 121 $c{m}^2$ respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.

There is a circle with inner radius of 4 cm and outer radius of 6 cm. A coin is tossed onto this circle. What is the probability of the coin falling outside the smaller circle but inside the bigger circle?

If 10 times the tenth term of an A.P is equal to 30 times the thirtieth term, then find its 40th term.

Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.

The angle of elevation of the top of a building from the foot of a tower is ${30}^{\circ }$. The angle of elevation of the top of the tower from the foot of the building is ${60}^{\circ }$. If the tower is 60 m high, find the height of the building.

The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, what is the othe number ?

(a) 36 (b) 45 (e) 9 (f) 81

Find the area of a right-angled triangle, the radius of whose circumcircle measures 8 cm and the altitude drawn to the hypotenuse measures 6 cm.

If sin (A + B) = 1 and cos (A - B) = 1, $0^{\circ }\le (A+B)\le {90}^{\circ }$ and A > B then find A and B.

A passenger train takes one hour less for a journey of 150km if its speed is increased by 5km/hr from its usual speed. Find the usual speed of the train.

Match the following solid objects with the expressions of their volume.

If ($x^5-9x^2+12x-14)$ is divided by $(x–3)$, then the remainder is:

A marksman is equally likely to hit or miss his target. How many times must he fire to have a $90\%$ chance to hit the target at least once? [4 MARKS]

Question 105

Solve the following:

An employee works in a company on a contract of 30 days on the condition that he will receive Rs. 120 for each day he works and he will be fined Rs. 10 for each day he is absent. If he receieves Rs. 2300 in all, for how many days did he remain absent?

The ___ of a class interval is the sum of frequencies of all the classes up to this class interval.

Find the roots of quadratic equation x² - 4x + 4 = 0 using the quadratic formula.

The vector$\overrightarrow{V}$ directed along the internal bisector of the angle between the vectors
$\overrightarrow{A}=3\hat{i}-4\hat{j},\overrightarrow{B}=4\hat{i}+2\hat{j}-4\hat{k}$ and $\left(\overrightarrow{V}\right|=2$ is

Draw a map of your class room using proper scale and symbols. There are 20 tables in the class room arranged in two columns and two windows are located at the center of two side of rectangular class. Dimension of a class room is $8m\times 4m$, Dimension of a table $1.5m\times 1m$. Dimension of window $3m\times 2m$. [4 MARKS]

If two vertices of an equilateral triangle be $(0,0),(3,\sqrt{3})$, find the third vertex. [4 MARKS]

Find the value of $\theta$ in each of the following

(1) 2 sin 2$\theta$ = $\sqrt{3}$

(2) 2 cos 3$\theta$ = 1

(3) $\sqrt{3}$tan 2$\theta$ - 3 = 0

Factorise :

$1-2a-3a^2$

In a ΔABC, obtuse angled at B, if AD is perpendicular to CB produced, prove that AC = ${AB}^2$ + ${BC}^2$ + 2BC $\times$ BD [4 MARKS]

Prepare Single Column Cash Book of Vinod from the following transactions:

Aug.1 Business started with cash Rs.10,000.

Aug.2 Purchased goods for cash Rs.6,000.

Aug.5 Purchased furniture for office use Rs.1,000.

Aug.7 Goods sold for cash Rs.4,000.

Aug.9 Goods purchases from Ram on credit Rs.4,000.

Aug.10 Commission received Rs.500.

Aug.15 Paid to Ram Rs.2,000.

Aug.18 Goods sold to Hari on credit Rs.5,000.

Aug.24 Received from Hari Rs.4,000.

Aug.28 Stationery purchased Rs.300.

Aug.31 Rent paid Rs.700 and withdrew for personal use Rs.2,800.

Find the LCM and HCF of 12, 15 and 21 by applying the prime factorization method. [2 MARKS]

The mid-point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Then the values of a and b are _________ .

How many of the following are functions ?

(i) f(x) = $x^5;\{-1,0,1\}\to \{0,1,2\}$

(ii) f(x) = $\pm \sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iii) f(x) = $\sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iv) f(x) = $x^2;\{0,1,2\}\to \{0,1,2,3,4\}$

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

Find the area of a quadrant of a circle whose circumference is 88 cm.

An incomplete distribution is given as follows:
Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Solve the following quadratic equation by factorization.
$3x^2=-11x-10$

The area of a right triangle is 600 $c{m}^2$. If the base of the triangle exceed the altitude by 10 cm, find the dimensions of the triangle.

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be ${45}^{\circ }$ and ${30}^{\circ }$ respectively. Find the height of the hill.

If a,b,c are the sides of a triangle ABC such that $x^2-2(a+b+c)x+3\lambda (ab+bc+ca)=0$ has real roots, then

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
$\begin{array}{cccc}\text{Expenditure}& \text{Frequency}& \text{Expenditure}& \text{Frequency}\\ \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)& \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)\\ 100-150& 24& 300-350& 30\\ 150-200& 40& 350-400& 22\\ 200-250& 33& 400-450& 16\\ 250-300& 28& 450-500& 7\end{array}$
Find the average expenditure (in rupees) per household.

On decreasing the radius of a circle by 30 %, its area is decreased by

(a) 30 % (b) 60 % (c) 45% (d) none of these

Find four numbers in AP whose sum is $28$ and the sum of whose squares is $216$.

The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circles is

(a) 320 $c{m}^2$ (b) 330 $c{m}^2$
(c) 332 $c{m}^2$ (d) 340 $c{m}^2$

$△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ABC. If EF = 4 cm, then the perimeter of $△$DEF is -