PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Determine the contrapositive of the statement:

 If he has courage he will win.

If pth, qth, rth and sth terms of an A.P. be in G.P., then prove that p − q, q − r, r − s are in G.P.

Determine the contrapositive of the statement:

 It is necessary to be strong in order to be a sailor.

Determine the contrapositive of the statement:

Only if he does not tire will he win.

Determine the contrapositive of the statement:

If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.

If x^a = x^b/2 z^b/2 = z^c, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.

If a, b, c are in A.P., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.

If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.

If p^th, q^th and r^th terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]

Check whether the statement are true or not: 

p : If x and y are odd integers, then x + y is an even integer.

Check whether the statement are true or not: 

 q : If x, y are integers such that xy is even, then at least one of x and y is an even integer.

Insert 6 geometric means between 27 and  \[\frac{1}{81}\] .

Insert 5 geometric means between 16 and \[\frac{1}{4}\] .

Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .

Find the geometric means of the following pairs of number:

2 and 8

Find the geometric means of the following pairs of number:

a³b and ab³

Find the geometric means of the following pairs of number:

−8 and −2