List of top Mathematics Questions

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 \(\ldots\)

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 \(\frac{dy}{dx} = \ldots\)

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 \(\ldots\)

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 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.

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

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

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 \(\ldots\)

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 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 \(f_6(x)-f_4(x) = \ldots\)

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 \(\ldots\)

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 \(\ldots\)

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

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.

Let \(F(x)\) be the cumulative distribution function (c.d.f.) of a continuous random variable \(X\). If \(F(b) = 0.7\) and \(P(X > a) = 0.4\), then the value of \(P(a < X < b)\) is ...

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...

A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

The maximum value of \(Z = 4x+5y\), subject to the constraints \(3x+y\leq 15,3x+4y\leq 24,x\geq 0,y\geq 0\) is

The acute angle \(θ\) between the \(xy\)-plane and the plane passing through the point \((1,2,4)\) and parallel to the vectors with direction ratios \(3,2,-1\) and \(1,-2,-2\) is...