List of top Mathematics Questions

If \(0\leq x\leq 1\) and \((sin^{-1}x)^3+(cos^{-1}x)^3 = aπ^3\) then

If \(g(x) = (x^2+2x+1)\cdot f(x)\) such that \(f(0) = 5\) and \(\underset{x\rightarrow 0}{lim}\frac{f(x)-5}{x} = 4\) then \(g^'(0) =\)

Let \(f(x) = ax+b\) and \(g(x) = cx+d\). The condition \(f(g(x)) = g(f(x))\) holds for all \(x\) if and only if ...

If \(x\,e^{xy} = y+sin^2x\), then the value of \(\frac{dy}{dx}\) at \(x = 0\) is equal to

If \(\sum _{n = 1}^{2026}tan^{-1}(\frac{1}{n^2+n+1}) = tan^{-1}(1-\frac{1}{x})\), where \(x\neq 0\), then \(x =\)

The number of point / points where the function \(f(x) = \frac{1}{x^2-5|x|+6}\) is discontinuous is......

Let \(t\in (0,1)\) and \(α\in (0,\frac{π}{4})\). If \(x = \text{cosec}^{-1}(\frac{1+t^2}{2t})\), \(y = cot^{-1}(\frac{\sqrt{1-t^2}}{t})\) and \(\frac{dy}{dx} = f(t)\), then the value of \(f(tanα)\) is

If \(0\leq x\leq 1\), \(I_1 = \int sin^{-1}\sqrt{1-x^2}\,dx\) and \(I_2 = \int sin^{-1}x\,dx\), then which of the following is true?

Let \(A = \left[ \begin{array}{ccc}cosα & -sinα & 0 \\ sinα & cosα & 0 \\ 0 & 0 & 1\end{array} \right]\). If \(B = \text{adj}\,A\), then the matrix \(B^{-1}\) is equal to...

If \(y = tan^{-1}⎛⎝\frac{log(\frac{e}{x^3})}{logex^3}⎞⎠+tan^{-1}⎛⎝\frac{log(e^4x^3)}{log(\frac{e}{x^{12}})}⎞⎠\), \(x\in (e^{-\frac{1}{3}},e^{\frac{1}{12}})\) then \(\frac{dy}{dx}\) is equal to...

Let \(A = [\begin{array}{cc}3 & -4 \\ 1 & -1\end{array}]\) and \(B = [\begin{array}{cc}6 & -13 \\ 5 & -10\end{array}]\) be two matrices. If the variables \(x\) and \(y\) satisfy the matrix equation \(((A^{-1})^2+B)[\begin{array}{c}x \\ y\end{array}] = [\begin{array}{c}0 \\ 0\end{array}]\), then the ordered pair \((x,y) =\)

The negation of the converse of \(p∨q\) is

In \(△ABC\), with usual notation, if \(a = 13,b = 14,c = 15\), then the sum of the values of \(sin(\frac{A}{2})\) and \(sinA\) is....

In triangle ABC, with usual notations, if \((a+b+c)(a+b-c) = ab\), then the measure of angle C is...

The contrapositive of the statement pattern \([p∨(p\rightarrow q)]\rightarrow (p∧\sim q)\) is

If \(\underset{x\rightarrow \infty }{lim}[\frac{x^2+x+1}{x+1}-ax-b] = 3\), then \(a-b =\)...

The correct logical equivalence from the following is /are ___
(I) \(p\rightarrow (q\rightarrow r)\equiv (p∧q)\rightarrow r\)
(II) \((p\rightarrow q)\rightarrow r\equiv p\rightarrow (q∨r)\)
(III) \((p\rightarrow q)\rightarrow r\equiv (p\rightarrow r)∧(\sim q\rightarrow r)\)
(IV) \(p\rightarrow (q\rightarrow r)\equiv q\rightarrow (p\rightarrow r)\)

The tangent to the circle \(x^2+y^2 = 10\) at the point \((3,1)\) touches the circle \(x^2+y^2-2\sqrt{10}\,x-20y+k = 0\), then the value of \(k\) is...

The area of the region (in sq. unit) bounded by x-axis, the tangent and normal to the circle \(x^2+y^2 = 4\), drawn at a point \((1,\sqrt{3})\) is

If the eccentricity of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1,(a > b)\) is \(\frac{2}{3}\) and its focal chord is \(3x+2y-6 = 0\), then the value of \(a^2+b^2\) is...

The line \(L_1\) given by \(\frac{x}{p}+\frac{y}{2} = 1\) passes through the point \((5,0)\). The line \(L_2\) given by \(\frac{x}{10}+\frac{y}{q} = 1\) is parallel to \(L_1\). Then the distance between the lines \(L_1\) and \(L_2\) is...

Two lines are given by \(x^2-4xy+4y^2+kx-2ky = 0\), then the value of k so that the distance between them is 3 is

The value of \((\frac{-1+i\sqrt{3}}{2})^{18}+(\frac{-1-i\sqrt{3}}{2})^{18}\) is

11 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keeper and the captain never sit together is ___

In \(△ABC\), if \(\angle C = \frac{π}{3}\), then the value of \(cos^2A+cos^2B+cosAcosB\) is...