If \(\sin(\alpha)\) and \(\cos(\alpha)\) are the roots of the equation \(ax^2 + bx + c = 0\), then \(b^2\) is

[Figure: four circles, each of radius r, placed at the four corners of a square so that adjacent circles touch each other; a small circle in the middle touches all four outer circles.] If radius of each of four outer circles is r, then radius of innermost circle is

Match List I with List II List I | List II A. Mean of first five prime numbers is | I. 12 B. Mean of all factors of 24 is | II. 7.5 C. Mean of first six multiples of 4 is | III. 5.6 D. If the mean of x-5y, x-3y, x-y, x+y, x+3y and x+5y is 12, then x is | IV. 14 Choose the correct…

Three years ago, ratio of ages of Amisha and Namisha was 8:9. 3 years from now the ratio will become 11:12 . What is the present age of Amisha?

\(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{8-2\sqrt{15}}} + \frac{\sqrt{11+2\sqrt{30}}}{\sqrt{6}-\sqrt{5}} =\)

The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present age (in years) of the son and the father are, respectively

If \(a \times b = 2a - 3b + ab\), then \(3 \times 5 + 5 \times 3\) is equal to

If LCM of two numbers is 12 times HCF and the sum of LCM and HCF is 403, if one number is 93, find the other number

The value of \(\frac{325 \times 325 \times 325 + 175 \times 175 \times 175}{325 \times 325 - 325 \times 175 + 175 \times 175}\) is