Explore topic-wise InterviewSolutions in Current Affairs.

ABC is an isosceles triangle, right-angled at B. Similar triangles, $△ACD$ and $△ABE$ are constructed on sides AC and AB. Find the ratio of the areas of $\Delta ABE$ and $\Delta ACD$.

Define HCF of two positive integers and find the HCF of the following pairs of numbers.
(i) 32 and 54 (ii) 18 and 24 (iii) 70 and 30
(iv) 56 and 88 (v) 475 and 495 (vi) 75 and 243
(vii) 240 and 6552 (viii) 155 and 1385 (ix) 100 and 190
(x) 105 and 120

Find the value of P for the following equation:
P $\times$ 1000 mL = 7.65 L

O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A $<$ ${360}^{\circ }$ then the path taken by P is called __.

Prove the following trigonometric identities:

$\frac{1}{1+sinA}+\frac{1}{1-sinA}=2se{c}^{2}A$

Prove that X² -X is divisible by 2for all positive integer X

Secant intersects the circle at ___ distinct points.

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.

How many numbers of two digit are divisible by 3?

Is 184 a term of the AP 3, 7, 11, 15, ..?

In an A.P., the first term is 22, nth term is -11 and the sum to first n term is 66. Find n and d, the common difference.

Find n if the given value of x is the nth term of the given A.P.
(i) 25,50,75,100,...,x=1000
(ii)-1,-3,-5,-7,...,x=-151
(iii)$5\frac{1}{2},11,16\frac{1}{2},22,...,x=550$
(iv)$1,\frac{21}{11},\frac{31}{11},\frac{41}{11},...,x=\frac{171}{11}$

The sum of the first 9 terms of an AP is 81 and that of its firsts 20 terms is 400. Find the first term and the common difference of the AP.

Find the distance between the points $(\frac{-8}{5},2)and\left(\frac{2}{5}2\right)$

In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options.

At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all.
Which of the following words will be most appropriate for blank (7)?

The breadth of a rectangle whose area is 600 square metres and perimeter is 100 metres, is ___ metres.

One card is drawn from a pack of 52 cards , each of the 52 cards being equally likely to be drawn. Find the probablity of

the card drawn is either a heart , a queen or king

1)17/52 2)21/52 )19/52 4)9/26

1. 1

In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If angle BOD = 160°, find the measure of angle BAD.

If the angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of its reflection in the lake be 60 .find the height of the cloud from the surface of the lake.

2x-3y+4=0 cuts the y axis at which point

A company with 10000 shares of Rs 100 each, declares an annual dividend of 5%. If he received 4% of his investment, find the price he paid for each share.

Given
A = {$x:11x-5>7x+3,xϵR$}
B = {$x:18x-9\ge 15+12x,xϵR$}
Find the range of set $A\cap B.$

In the figure below, is any side of ΔABC parallel to X-axis? If so, the side is:

Identify the number of triangles similar to $△$ABC if B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC.

A ladder of length 26m rests against a wall. If it reaches a height of 24 m from the ground, then the distance of the foot of the ladder from the wall is _________ m

The total cost price of a certain number of identical aricles is Rs.4,800. By selling the articles at Rs. 100 each. a profit equal to the cost price of 15 articles is made. Find the number of articles bought.

When the polynomial f(x) = 4x³ + 8x² + 8x + 7 is divided by the polynomial g(x) = 2x² - x + 1, the quotient and the remainder are

Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais.

(a) Name the image of P on reflection in the origin.

(b) Write the coordinates of the point to which M is mapped on reflection in - axis

In the following diagram, Calculate the value of I₁ and I₂ if I=9 A R₁ = 6 Ω and R₂ is 3 Ω.

The co-ordinates of the point which divides the line joining the points (–1, 7) and (4, –3) in the ratio 2:3 is ___.

The 5th term of an A.P. is 18, the common difference is 2. What is the first term ?

In the ∆ ABC, AD is ⊥ to BC, tan B = ³/₄ and tan C = ⁵/₁₂, BC = 56 cm. Calculate the length of AD.

The following chart shows the sales of cars in thousands. [3 MARKS]

a) What is the number of cars sold in 2002-2003?

b) What is the total sale of Maruti cars?

c) What is the difference in the sales of Maruti & GM?

The pair of linear equations: x + 2y = 5 and 4x + 4y - 6 = 0 intersect at points (-2, 3.5) when represented graphically.
What can you say about the pair of equations?

Which of the following fractions is a terminating decimal?

Which of the following is a trigonometric identity?

Three terms x, y and z are in A.P.. So they are related by the equation:

The y-coordinate of the mid-point of the line passing through the points (1,4) and (5,6) is

If 7sin²x + 3cos²x = 4 then , secx + cosecx =

In a question

Blue -18,Yellow-3,Green-9,Red-6

Total=36

Blue=18/36×360

=180

Are those steps right?

IF $x^3+a{x}^2+bx+6$ has $x-2$ as a factor and leaves a remainder 3 when divided by x-3, fidn the value of a and b.

In figure, DEFG is a square and $\angle BAC={90}^o$, Prove that
(i)$△AGF\sim △DBG$
(ii)$△AGF\sim △EFC$
(iii)$△DBG\sim △EFC$
(iv)${DE}^2=BD\times EC$

Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is $800m^2$? If so, find its length and breadth.

Which term of thes AP 21, 42, 63, 84,... is 210 ?
(a) 9th (b) 10th (c) 11th (d) 12th

Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.

The angle of depression of a tower from a point on the ground which is 30m away from the foot of the tower is ${60}^{\circ }$.Find the height of the tower.

Write the value of k for which the system of equations $3x+ky=0,2x-y=0$ has a unique solution.

The factors of $(p-q{)}^3+(q-r{)}^3+(r-p{)}^3$ are: