Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is :

The sum of the infinite series
$$1 + {2 \over 3} + {7 \over {{3^2}}} + {{12} \over {{3^3}}} + {{17} \over {{3^4}}} + {{22} \over {{3^5}}} + ......$$ is equal to :

The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\cos }^2}x} \over {1 + {3^x}}}} dx$$ is :

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :