List of top Mathematics Questions

If \(f(x) = cot^{-1}(\frac{3x-x^3}{1-3x^2})\) and \(g(x) = cos^{-1}(\frac{1-x^2}{1+x^2})\), then \(\underset{x\rightarrow a}{lim}\frac{f(x)-f(a)}{g(x)-g(a)}\), \((0 < a < \frac{1}{2})\) is

If \(f(x) = cosx\,cos2x\,cos4x\,cos8x\,cos16x\), then \(f^'(\frac{π}{4}) =\)

If \(y = \sqrt{cosx^2+\sqrt{cosx^2+\sqrt{cosx^2+\ldots \infty }}}\) and \(\frac{dy}{dx} = \frac{f(x)}{2y-1}\) then, \(\int f(x)\,dx = \ldots\)

The derivative of \(tan^{-1}(\frac{\sqrt{1+x^2}-1}{x})\) with respect to \(tan^{-1}(\frac{x}{\sqrt{1-x^2}})\) at \(x = \frac{1}{2}\) is

If \(f(x) = \frac{1-x}{1+x}\), then \(f(f(cosx)) =\)

If \(A = \left[ \begin{array}{ccc}3 & 0 & 0 \\ 0 & -5 & 0 \\ 0 & 0 & 7\end{array} \right]\); \(B = \left[ \begin{array}{ccc}-1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array} \right]\) then, \((2A+3B)^{-1} =\) _______

\(sin(3sin^{-1}(\frac{1}{5})) =\)

If \(sin^{-1}(x-2)+cos^{-1}(x)+tan^{-1}(x+2)+cot^{-1}(x+4) = sec^{-1}(\sqrt{k})-\frac{π}{2}\), then \(cos(2\,\text{cosec}^{-1}\sqrt{k-1}) = \ldots\)

\(cos^{-1}(cos\frac{4π}{3})+sin^{-1}(sin\frac{4π}{3}) = \ldots\)

The negation of \((p∧q)\rightarrow ((p∨r)\rightarrow \,\sim q)\) is equivalent to ...

In \(△ABC\), with usual notation, if cot A, cot B, cot C are in arithmetic progression, then

Which of the following statements is/are False?
\(S_1:\exists \,n\in N\), such that \(n^2+n+2\) is divisible by 4.
\(S_2:\exists \,x\in N\), such that \(x-17 < 20\).
\(S_3:\forall \,n\in N,\,x^2+3x-10 = 0\).
\(S_4:\forall \,n\in N,\,n^2\geq 1\).

The statement pattern \([(p∧q)\rightarrow (\sim p∨r)]∨[(\sim p∨r)\rightarrow (p∧q)]\) is

If \(A = \left[ \begin{array}{cc}1 & -tan\frac{θ}{2} \\ tan\frac{θ}{2} & 1\end{array} \right]\) and \(B = \left[ \begin{array}{cc}1 & tan\frac{θ}{2} \\ -tan\frac{θ}{2} & 1\end{array} \right]\) then \(A^{-1}B\) is equal to

\(\frac{(cos2θ+isin2θ)^7}{(cos4θ+isin4θ)^3} =\)

If the circles \(x^2+y^2 = 16\) and \(x^2+y^2+2ax+4y+4 = 0\) touch each other internally then \(a =\)

If the equation \(ax^2+4xy-2y^2+4x+8y+1 = 0\) represents a pair of straight lines, then the coordinates of their point of intersection are.........

The line \(y = 2x+c\) passes through a point that is equidistant from both the axes and lies in the first quadrant \((x > 0,y > 0)\). Then the value of c is...

If the line \(3x+4y+k = 0\) touches the ellipse \(9x^2+16y^2 = 144\), then the value of k is.

In a test, there are 5 questions of the 'true or false' type. No student has got all the answers correct and the sequence of answers for every student is unique. The maximum number of students who could have appeared for the test is....

If \(tanA\) and \(tanB\) are the roots of the equation \(5x^2-4x+1 = 0\), then the value of \(A+B\) is...

A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and \(E(X) = 1.2\), then \(N = \ldots\)

If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?

The region satisfying the inequalities \(y-x\geq 2, x+y\leq 5, x\geq 0\) and \(y\geq 0\) is

If the lines \(\overset{⃗}{r} = \hat{i}+\hat{j}-\hat{k}+λ(q\hat{i}-2\hat{j}+\hat{k})\) and \(\overset{⃗}{r} = p\hat{i}-3\hat{j}+2\hat{k}+μ(\hat{i}-2\hat{j}+2\hat{k})\) intersect each other and \(q\hat{i}-2\hat{j}+\hat{k}\) is collinear to \(4\hat{i}-4\hat{j}+2\hat{k}\), then the values of \(p\) and \(q\) are