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Form the differential equation of the family of hyperbolas having foci on the x-axis and centre at the origin.

The equation of hyperbola required is... View Article

What is the degree of the given monomial 3mn?

The degree of the monomial 3mn is 2.... View Article

Suresh’s age is double Kiran’s age. The sum of their ages is 24 years. How old is Suresh?

Let Kiran's age be x years. So, the age of Suresh = 2x years x + 2x = 24 ⇒ 3x = 24 ⇒ x = 24 / 3 ⇒x = 8 ∴ Suresh's age = (2... View Article

Two numbers are respectively 30 per cent and 40 per cent less than a third number. What per cent is the second of the first?

Let the third number be x.... View Article

Find the value of tan^-1 [tan (5π / 6)] + cos^-1 [cos (13π / 6)].

Consider... View Article

Express tan theta in terms of sin theta.

tan theta can be expressed as... View Article

If 7 8 = 49, 4 4 = 12, 6 * 4 = 18 then, 9 * 6 = ?

7 * 8 = 56 - 7 = 49. 4 * 4 = 16 - 4 = 12. 6 * 4 = 24 - 6 = 18. 9 *6 = 54 - 9 = 45.... View Article

In which quadrant or on which axis do each of the points (- 2, 4), (3, – 1), (- 1, 0), (1, 2) and (- 3, – 5) lie?

Point (1, 2) lies in the first quadrant. Point (- 2, 4) lies in the second quadrant. Point (- 3, - 5) lies in the third quadrant. Point (3, - 1)... View Article

A right circular cone is 5.4cm high and the radius of its base is 2cm. It is melted and recast into another right circular one with a radius of base as 1.5 cm. find the height of the new cone formed.

Volume of the old cone = volume of the new cone... View Article

The natural number which is a multiple of every number is

The natural number which is a multiple of every number is 1.... View Article

Which term of 37, 32, 27, … is – 103?

The nth term of the given sequence is... View Article

A man earns Rs. 25440 per month. He spends 1 / 4 of it on house rent, 3 / 8 on food and clothes, 1 / 10 on insurance and 1 / 5 on other items. The rest he saves. How much does he save each month?

He earns Rs. 25440 per month.... View Article

ⁿP_r and ⁿC_r are equal when

They are equal when... View Article

The equation of plane passing through a point A (2, – 1, 3) and parallel to the vectors a = (3, 0, – 1) and b = (- 3, 2, 2) is:

Let the direction ratios of the normal of the required plane be a, b, c. The plane is parallel to (3,0,-1), hence, the normal must be... View Article

64000 is obviously not a perfect square. Give reason.

64000 is not a perfect square as the number of zeroes are odd.... View Article

An average daily wage of 10 workers in a factory ‘A’ is Rs. 30 and an average daily wage of 20 workers in a factory ‘B’ is Rs. 15. Find the average daily wages of all workers of both the factories.

From the question,... View Article

State whether the following statement is true or false: All real numbers are irrational.

The statement, all real numbers are irrational is false.... View Article

Gist of EPW August Week 2, 2021

The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment. In this... View Article

Who said dams are temples of modern India?

Jawaharlal Nehru proclaimed the dams as the ‘temples of modern India’; because the dams would integrate the agricultural development... View Article

How is a Tanka built?

Tanka is a technique to collect rainwater by making tanks (tanka). A pit is dug in the courtyard and it is made pucca. The tanka is kept covered... View Article