List of top Mathematics Questions

If the function \(f(x) = ax^2+bx+sinx\) satisfies all the conditions of Rolle's theorem on \([0,π]\) and the slope of the tangent to the curve \(y = f(x)\) at \(x = \frac{π}{4}\) is zero, then \(a-b =\)

Let \(y = \sqrt[p]{x^3y}\). If \(\frac{dy}{dx} = \frac{3}{2}\) when \(y = 1\), then the value of \(p\) is equal to \(\ldots\)

If \(f^'(x) = sin^2x\) and \(y = f(\frac{2x-1}{x^2+1})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

If \(f:R\rightarrow R\) is an even function then

\(sec^2(tan^{-1}3)-tan^2(sec^{-1}3) =\)

For \(x > 0\), if \(sin(cos^{-1}x+tan^{-1}x)-cos(sin^{-1}x+tan^{-1}x) = sin(cot^{-1}2)\) then \(x =\)

If \(tan^{-1}ax+tan^{-1}3x = \frac{π}{4}\), where \(3ax^2 < 1\), then value of \(a\) for \(x = \frac{1}{6}\) is \(\ldots\)

If \(f(x) = \frac{3^x+3^{-x}-2}{tanx\cdot log(1+x)}\) for \(x\neq 0\), is continuous at \(x = 0\), then the value of \(f(0)\) is equal to \(\ldots\)

If \(\int f^'(x)\cdot e^{x^2}\,dx = (x-1)\cdot e^{x^2}+k\), where \(k\) is constant of integration, then \(f(x) = \ldots\)

The domain of the function \(f(x) = \sqrt{\frac{x}{1+x}}\) is \(\ldots\)

Let \(A = [\begin{array}{cc}-3 & 2 \\ 1 & 4\end{array}]\) and if \(A^2-2A+I = [\begin{array}{cc}18 & p \\ q & 11\end{array}]\), then \(\ldots\)

If matrix A and its inverse \(A^{-1}\) are given by \(A = \left[ \begin{array}{ccc}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1\end{array} \right]\) and \(A^{-1} = \left[ \begin{array}{ccc}\frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & y \\ \frac{5}{2} & -\frac{3}{2} & \frac{1}{2}\end{array} \right]\), then the polar co-ordinates of the points whose Cartesian co-ordinates are \((x,y)\) are \(\ldots\)

In \(△ABC\), with usual notations, if \(\Delta\) denotes the area of triangle \(ABC\) then the value of \(2s(b+c-a)tan(\frac{A}{2})\) is equal to \(\ldots\)

For \(x > 0\) and \((xlogx) < 1\), if \(y = cot^{-1}(\frac{x-logx^{x^2}}{loge^{x^2}+logx^x})\), then \(\frac{dy}{dx} = \ldots\)

In a switching circuit, if the combination \((S_1∧S_2)\) is connected in parallel to the combination \((S_1^'∧S_2^')\), then the room is lit only when \(\ldots\)

The number of circles passing through the origin and touching the lines \(x+y = 1\) and \(x-y = 1\) is \(\ldots\)

The minimum number of switches in the simplified form of the following switching circuit is

If the truth value of the statement pattern \((\sim p∧q)∨(\sim p∧\sim q)∨(p∧\sim q)\) is \(F\), then the truth values of \((p∨\sim q)\) and \((p\rightarrow q)\) are \(\ldots\) respectively.

If \(\underset{x\rightarrow k}{lim}\frac{x^3-k^3}{x^2-k^2} = \underset{x\rightarrow 0}{lim}\frac{1-cos(2x)}{xsinx}\), then the value of \(k\) is \(\ldots\)

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If \(P(α,4)\) is a point on this parabola such that the tangent to the parabola at point P passes through the origin, then the distance of P from origin is

Let \(f_k(x) = \frac{1}{k}(cos^kx+sin^kx)\) where \(k\in N\), then \(f_6(x)-f_4(x) = \ldots\)

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by \(x^2-6xy+5y^2+10x-14y+9 = 0\) is \(\ldots\)

The difference between the roots of the equation \(x^2+2x+4 = 0\) is \(\ldots\) (where \(i = \sqrt{-1}\))

The coordinates of the orthocenter of the triangle whose sides are represented by the lines \(4x-7y+10 = 0\), \(x+y = 5\) and \(7x+4y = 15\) are \(\ldots\)

In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is \(\ldots\)