List of top Mathematics Questions

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

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 \(f(x) = \ldots\)

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

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

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

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 \(\ldots\)

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

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 \(\ldots\)

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

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 \(\ldots\)

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 \(\ldots\)

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

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

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 \(\ldots\)

If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are \(0.6\), \(0.5\) and \(0.4\) respectively, while the probability of succeeding in both A and B is \(0.3\), in both B and C is \(0.2\), in both A and C is \(0.2\), and in all three is \(0.1\), then the probability that the student succeeds in exactly one of these tests is......

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

If the plane \(\overset{̄}{r} = (λ+μ)\hat{i}+(2+μ)\hat{j}+(3λ+2μ)\hat{k}\), where \(λ\) and \(μ\) are parameters, intersects coordinate axes at points \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\) then \(a+b+c =\)...

The coordinates of the point of intersection of the lines \(\frac{x-3}{1} = \frac{y-5}{2} = \frac{z-1}{-1}\) and \(\frac{x-4}{2} = \frac{y-2}{-1} = \frac{z-4}{2}\) are...