PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Rewrite of the  statement in the form "p if and only if q".

 p : If you watch television, then your mind is free and if your mind is free, then you watch television.

Rewrite of the  statement in the form "p if and only if q".

 q : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Rewrite of the  statement in the form "p if and only if q".

r : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

If a, b, c are in G.P., prove that the following is also in G.P.:

a² + b², ab + bc, b² + c²

Rewrite of the  statement in the form "p if and only if q".

 s : If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.

If a, b, c, d are in G.P., prove that:

(a² + b²), (b² + c²), (c² + d²) are in G.P.

If a, b, c, d are in G.P., prove that:

(a² − b²), (b² − c²), (c² − d²) are in G.P.

If a, b, c, d are in G.P., prove that:

\[\frac{1}{a^2 + b^2}, \frac{1}{b^2 - c^2}, \frac{1}{c^2 + d^2} \text { are in G . P } .\]

If a, b, c, d are in G.P., prove that:

(a² + b² + c²), (ab + bc + cd), (b² + c² + d²) are in G.P.

Determine the contrapositive of the statement:

 If Mohan is a poet, then he is poor.

If a, b, c are in G.P., then prove that:

Determine the contrapositive of the statement:

 Only if Max studies will he pass the test.

Determine the contrapositive of the statement:

If she works, she will earn money.

Determine the contrapositive of the statement:

If it snows, then they do not drive the car.

Determine the contrapositive of the statement:

 It never rains when it is cold.

If the 4^th, 10^th and 16^th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.

Determine the contrapositive of the statement:

 If Ravish skis, then it snowed.

Determine the contrapositive of the statement:

If x is less than zero, then x is not positive.