List of top Mathematics Questions

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

A cylindrical tank without a top lid is being manufactured to hold a fixed volume of \(125π\) cubic cm. The minimum surface area required to construct this tank is ............square cm

If \(f(x) = cosx\), then the value of \(\int \frac{e^{f(x)}(xsin^3x+f(x))}{1-(f(x))^2}dx =\)

If \(y = cos^{-1}(\frac{1-4^x}{1+4^x})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

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 \(f(\frac{x-1}{x+1}) = x+1\), 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 ...

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

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

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

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:

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

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:

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

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 \(d^2 = \ldots\)