List of top Mathematics Questions

If \(e^x+e^{f(x)} = e\), then the domain of \(f(x)\) is

If the function f is continuous at \(x = π\), where \(f(x) = \frac{1-cos[7(x-π)]}{5(x-π)^2}\), for \(x\neq π\), then \(f(π) =\)

If \((tan^{-1}x)^2+(cot^{-1}x)^2 = \frac{5π^2}{8}\), then the value of \(x\) is equal to...

If \(f(\frac{x-1}{x+1}) = x+1\), then \(\int f(x)\,dx = \cdots\)

If \(cot[f(x)] = \frac{3x-x^3}{1-3x^2}\) and \(sin[g(x)] = \frac{1-x^2}{1+x^2}\), then \(\underset{x\rightarrow t}{lim}\frac{f(x)-f(t)}{g(x)-g(t)} = \ldots\)

Let f(x) be a twice differentiable function such that \(f^{''}(x) = -f(x)\), \(f^'(x) = g(x)\) and \(h(x) = \{f(x)\}^2+\{g(x)\}^2\). If \(h(5) = 11\), then \(h(10)\) is equal to ...

The value of \(cot^{-1}[\frac{\sqrt{1-sinx}+\sqrt{1+sinx}}{\sqrt{1-sinx}-\sqrt{1+sinx}}]\), where \(x\in (0,\frac{π}{2})\) is...

If \(A = [a_{ij}]_{3\times 3}\) is a matrix such that \(a_{ij} = |2i-5j|\), where \(|.|\) denotes the modulus function, then the element in the \(2^{\text{nd}}\) row and \(3^{\text{rd}}\) column of \(A^{-1}\) is ...

If \(A = [\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}]\) and \(A^2+xA+yI_2 = O_2\), where \(I_2\) and \(O_2\) are the identity matrix and null matrix of order 2 respectively, then:

If \(A = [\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}]\), \(B^{-1} = \left[ \begin{array}{cc}\frac{1}{5} & \frac{2}{5} \\ \frac{2}{5} & -\frac{1}{5}\end{array} \right]\), then \((AB)^{-1} =\)

In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...

If \(\underset{x\rightarrow 0}{lim}\frac{45^x-9^x-5^x+1}{(k^x-1)(3^x-1)} = 2\), then the value of \(k\) is ...

The combined equation of the pair of lines passing through the origin and making an angle \(\frac{π}{4}\) with the line \(3x+y-6 = 0\) is...

The negation of the contrapositive of the statement \((p∨\sim q)\rightarrow (p∧\sim q)\) is

If the truth value of the compound statement \([(p\leftrightarrow q)∧(q\rightarrow r)∧\sim r]\rightarrow (p∧\sim q)\) is false, then the truth values of the statement patterns \((p\rightarrow q)\leftrightarrow (q\rightarrow r)\) and \(\sim (p∨r)\rightarrow (q∧p)\) are, respectively ...

Line \(l:x+y = 4\) intersects the circle \(x^2+y^2-2x-2y = 2\) at points \(A\) and \(B\). If C is the center of the circle, then the area of \(△ABC\) is...

If \(θ\) is the acute angle between the lines \(2x^2+7xy+3y^2 = 0\), then the value of \(\frac{2cosθ-3sinθ}{4sinθ+5cosθ} = \ldots\)

The number of 4-letter words formed from the English alphabet such that there are exactly 2 vowels and 2 consonants and no vowel is repeated, but consonants may be repeated is:

The value of \(cos(60^{\circ}-A)\cdot cosA\cdot cos(60^{\circ}+A)\) is

The general solution of the equation \(cotθ\cdot cot2θ = 1\) is...

The line \((2+k)x+(1+k)y = 5+7k\) passes through the fixed point for different values of k. If 'd' is the distance of a fixed point from the origin, then \(d^2 = \ldots\)

If \(n\) is a positive integer, then \((1+i\sqrt{3})^{2n}+(1-i\sqrt{3})^{2n}\) is equal to .........

Two dice are thrown successively 4 times and getting a doublet is called a success. The probability of getting at least 1 success is

Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is

A random variable X has the probability distribution

\(X = x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)
\(P(X = x)\)	\(0.23\)	\(0.15\)	\(0.12\)	\(0.10\)	\(0.20\)	\(0.07\)	\(0.08\)	\(0.05\)

for the events E = {X is a prime number} and F = {X \(\leq\) 3}, then P (E\(\cup\)F)=