Explore topic-wise InterviewSolutions in Current Affairs.

If one A.M., A and two geometric means $G_1$ and $G_2$ inserted between any two positive numbers, show that $\frac{G_1^2}{G_2}+\frac{G_2^2}{G_1}=2A$.

Which average is affected most by the presence of extreme items?

(a) median

(b) mode

(c) arithmetic mean

(d) geometric mean



(e) harmonic mean

If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

A, B, C and D are four points on the same straight line. The distances between successive points are equal such that AB = BC = CD. If A is (1,-3), C is (4, a) and D is (b, 5), then the values of a and b are :

What quantity must be added to each term of the ratio 7:13 so as to make it equal to 9:11

Find F, V and E for the following solids and verify Euler’s formula (i) Pentagonal based prism (ii) Hexagonal based prism (iii) Octagonal Pyramid.

In throwing a die, let $A$ be the event 'an odd number turns up', $B$ be the event 'a number divisible by $3$ turns up' and $C$ be the event 'a number $\le 4$ turns up', then the probability that exactly one of events $A,B,C$ occur is :

A fully filled hemispherical tank of radius R has an orifice of the small area a at its bottom. Find the time required to completely empty the tank, (Assuming that the top surface area of the liquid is always much greater than the orifice area)

Find the distance between the centers of the circles in the figure.

Let the tangent to the circle $x^2+y^2=25$ at the point $R(3,4)$ meet $x-$axis and $y-$axis at points $P$ and $Q,$ respectively. If $r$ is the radius of the circle passing through the origin $O$ and having centre at the incentre of the triangle $OPQ,$ then $r^2$ is equal to :

Decide whether the real number with decimal expansion as $125.\overline{987654321}$ is rational or not. If rational, and of the form $\frac{p}{q}$, what can you say about the prime factors of q? :

Black Stone Ltd. issued 10,000 Equity Shares of ₹ 10 each at a premium of ₹ 3 per share payable ₹ 5 on application, ₹ 5 (including premium) on allotment and the balance on first call. All the shares offered were applied for and allotted. All the money due on allotment was received except on 200 shares. Call was made. All the amount due thereon was received except on 300 shares. Directors forfeited 200 shares on which both allotment and call money were not received.

Q36. The 10 households on a certain street have household incomes that range from Rs. 34,000 to Rs. 150,000 and an average (arithmetic mean) household income of Rs. 60,000. If the household with the highest income and the one with the lowest income are excluded, what is the average household income for the remaining 8 households?

An aeroplane when $900m$ high, passes vertically above another aeroplane at an instant when their angles of elevation from the same observation point are ${60}^{\circ }$ and ${45}^{\circ }$ respectively. Approximately, by how many meters is the aeroplane higher than the other?

(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

A bag contains 3 red and some Blue Balls. If the probability of drawing a blue ball is 4 times that of drawing a red ball .Find the number of blue balls in the bag.

Find the value of x for which the numbers (5x+2), (4x-1) and (x + 2) are in AP.

Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

Factorise $x^2-3x+2$ by using the Factor Theorem.

A shopkeeper purchases an audio system for $Rs.3,000$ and sells it off at a again of $15\%$. He also charges a sales of tax of $10\%$ on the selling price. Calculate the amount that the buyer will pay to the shopkeeper.

$\frac{cose{c}^{2}A}{1+co{t}^{2}A}$ = __________

Question 86

Altitudes MN and MO of parallelogram MGHK are 8 cm and 4 cm long respectively in the below figure. One side GH is 6 cm long. Find the perimeter of MGHK.

If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.

The number ${(1+\sqrt{3})}^2$ is a/an

Consider the following information and answer the questions that follow.

There is a solid cuboid with dimensions 16 cm×16 cm×12 cm, which is painted with red colour on all its six faces. It is then cut into identical cubes of maximum possible size such that no part of cuboid is wasted.

Q66. In how many ways can a cuboid of the dimensions 16×16×12 be cut into identical cubes such that no part of it is wasted and the length of each side of the cuboid is an integer number?

नीचे दी गई जानकारी पर विचार कीजिए और इसके आगे आने वाले प्रश्न का उत्तर दीजिए।

16 से.मी. × 16 से.मी. × 12 से.मी. के आयामों वाला एक ठेस घनाभ है, जिसकी सभी छह फलकों को लाल रंग से रंगा गया है।

अब इसे अधिकतम संभव आकार के समान घनों में इस तरह काटा जाता है कि घनाभ का कोई भी भाग व्यर्थ नहीं जाता है।

Q66. 16 × 16 ×12 के आयाम वाले घनाभ को कितने तरीकों से समान घनों में से इस तरह काटा जा सकता है कि उसका कोई भी भाग व्यर्थ न जाए और घन की प्रत्येक भुजा की लंबाई एक पूर्णांक हो?

Prove that sin2A is equal to 2sinAcosA

The value of

$5\frac{4}{7}÷1\frac{3}{10}=$

What should be added to each of the numbers 1, 21 and 121 so that the resulting numbers are in continued proportion?

What is the sum of first 30 multiples of 4?