WB JEE 2010
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If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B.
Prov that the equation \(\cos 2x + a\sin x = 2a - 7\) possesses a solution if 2 \(\le\) a \(\le\) 6.
Use the formula \(\mathop {\lim }\limits_{x \to 0} {{{a^x} - 1} \over x} = {\log _e}a\), to compute \(\mathop {\lim }\limits_{x \to 0} {{{2^x} - 1} \over {\sqrt {1 + x} - 1}}\).
The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio
Let R be the set of real numbers and the mapping f : R \(\to\) R and g : R \(\to\) R be defined by f(x) = 5 \(-\) x2 and g(x) = 3x \(-\) 4, then the value of (fog)(\(-\)1) is
Find the values of x, (\(-\) \(\pi\), < x < \(\pi\), x \(\ne\) 0) satisfying the equation, \({8^{1 + |\cos x| + |{{\cos }^2}x| + ......\infty }} = {4^3}\).