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

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

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

Given below are two statements: Statement I: In \(\triangle ABC\), \(AB = 6\sqrt{3}\) cm, \(AC = 12\) cm and \(BC = 6\) cm, then angle \(B = 90^\circ\) Statement II: In \(\triangle ABC\), is an isosceles with \(AC = BC\). If \(AB^2 = 2AC^2\), Then angle \(C = 90^\circ\) In the li…

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

Given below are two statement: Statement I: If \(\sin(\theta) = \frac{5}{13}\), then the value of \(\tan(\theta) = \frac{5}{12}\) Statement II: if \(\cot(\theta) = \frac{12}{5}\), then the value of \(\sin(\theta) = \frac{5}{12}\) In the light of the above statements, choose the c…

[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

A two digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than original number. What is the number?