Class 11 Mathematics - Chapter Conic Secrtions NCERT Solutions | Find the equation of the circle with cen

Find the equation of the circle with centre (0, 2) and radius 2

Solve 24x < 100, when
   (i)   x is a natural number.         (ii)   x is an integer.

Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

A point is on the x-axis. What are its y-coordinates and z-coordinates?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

Describe the sample space for the indicated experiment: A coin is tossed three times.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

A point is in the XZ-plane. What can you say about its y-coordinate?

If f is a function satisfying f(x +y) = f(x) f(y) for all x,y N  such that f(1) = 3

 and  , find the value of n.

If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P² = (ab)ⁿ.

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio 

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

 Find the sum to n terms in the geometric progression 

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Given a G.P. with a = 729 and 7th term 64, determine S₇.

The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.