Explore topic-wise InterviewSolutions in Current Affairs.

The decimal expansion of $\sqrt{2}$ is

(a) finite decimal

(b) 1.4121

(c) non terminating recurring

(d) non terminating, non recurring

Simple interest on a sum of money for 2 years at 4% is Rs. 450. Find compound interest on the same sum and at the same rate for I year, if the interest is reckoned half-yearly.

A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16 cm, 12 cm and 20 cm. Find the cost of polishing the tiles at Rs 1 per sq cm.

If the letters of the word ‘LOGIC’ are arranged in dictionary order, what will be the position of the word ‘LOGIC’?

Draw triangle ΔABC with measurements as given below and draw the circum-circle of each:

(a) AB = 4 cm, AC = 5 cm, ∠A = 60°

(b) AB = 4 cm, AC = 5 cm, ∠A = 120°

(c) AB = 4 cm, AC = 5 cm, ∠A = 90°

Note the position of the circum-centre of each triangle. Draw more triangles and see whether any general conclusion can be formed.

Question 62

State whether the following statement is true or false:

The sum of first n odd natural numbers is $n^2$.

Question 129

Fill in the blank to make the statement true.

125 + (68+17) = (125+.........) +17

Question 3 (i)

Using divisibility test, determine whether the given number is divisible by 6:

639210

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$, and $\overrightarrow{d},$ are the unit vectors such that $(\overrightarrow{a}\times \overrightarrow{b}).(\overrightarrow{c}\times \overrightarrow{d})=1$ and $\overrightarrow{a}.\overrightarrow{c}=\frac{1}{2},$ then

100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{array}{cccccc}\text{Number of letters}& 1-4& 4-6& 6-8& 8-12& 12-20\\ \text{Number of surnames}& 6& 30& 44& 16& 4\end{array}$
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.

If DR's of a line are $(2,-a,3)$ and DC's are $(b,\frac{1}{2},c),$ then $\frac{a^2{c}^2-b^2}{a^2{b}^2-c^2}=$

Question 1 (viii)

Solve the following pairs of equations by reducing them to a pair of linear equations:

$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$

$\frac{1}{2(3x+y)}-\frac{1}{2(3x-y)}=\frac{-1}{8}$

Construct a triangle PQR in which QR = 6 cm, ∠Q = 60° and PR − PQ = 2 cm

If $\frac{a}{b}$ = $\frac{16}{3}$

then find the value of $\frac{a+b}{a-b}$

Find the ratio compounded of the subduplicate ratio of 36: 49, the reciprocal ratio of 15: 28 and the triplicate ratio of 5 : 4.

Ram appeared in his mid-term examination and his marks in different subjects were:-

$$\begin{array}{cc}\text{Subject}& \text{Marks}\\ \text{Science}& 75\\ \text{Maths}& 85\\ \text{Hindi}& 75\\ \text{English}& 75\\ \text{Social Science}& 65\end{array}$$

The mode of the above data is ___

1. 75

Which of the following is a Pythagorean triplet?

Expand each of the following, using suitable identities:

(i) (ii)

(iii) (iv)

(v) (vi)

Find the area of the shaded region in Fig, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Pick an option which gives the meaning of the word - Geometry.

Evaluate the following products without multiplying directly:
(i) $103\times 107$
(ii) $95\times 96$
(iii) $104\times 96$

(i) p(x) = x – 4

(ii) g(x) = 3 – 6x

(iii) q(x) = 2x – 7

(iv) h(y) = 2y

The perpendicular to a chord from the centre of the circle divides the chord in ratio of

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per m².

If the side of a rhombus is 6 cm and its one diagonal is 10 cm, then find the area of the rhombus.

The ratio of the base radii of two right circular cylinders having the same height is 4 : 5. The ratio of their volumes will be :