Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Find the distance between the following pairs of points:

(–1, 3, –4) and (1, –3, 4)

Find the distance between the following pairs of points:

(2, –1, 3) and (–2, 1, 3)

Verify the following:

(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.

Verify the following:

(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.

Verify the following:

(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.

Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.

For each of the following compound statements first identify the connecting words and then break it into component statements.

All rational numbers are real and all real numbers are not complex.

For each of the following compound statements first identify the connecting words and then break it into component statements.

Square of an integer is positive or negative.

For each of the following compound statements first identify the connecting words and then break it into component statements.

The sand heats up quickly in the Sun and does not cool down fast at night.

For each of the following compound statements first identify the connecting words and then break it into component statements.

x = 2 and x = 3 are the roots of the equation 3x² – x – 10 = 0.

Identify the quantifier in the following statements and write the negation of the statements.

There exists a number which is equal to its square.

Identify the quantifier in the following statements and write the negation of the statements.

For every real number x, x is less than x + 1.

Identify the quantifier in the following statements and write the negation of the statements.

There exists a capital for every state in India.

Check whether the following pair of statements is negation of each other. Give reasons for the answer.

(i) x + y = y + x is true for every real numbers x and y.

(ii) There exists real number x and y for which x + y = y + x

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

Sun rises or Moon sets.

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

To apply for a driving licence, you should have a ration card or a passport.

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

All integers are positive or negative.

Find the mean deviation about the mean for the data.

4, 7, 8, 9, 10, 12, 13, 17