List of top Mathematics Questions

The value of integral \(\int x^3cosx\,dx\) is...

Rolle's theorem holds for monic quadratic polynomial \(f(x)\) on the interval \([α,α+3]\) where \(f(α) = 0\). Similarly, \(g(x) = f(x)+2\) also follows Rolle's theorem in the interval \([β,3]\) where \(g(3) = 0\), such that the value of \(c\) is the same for both \(f(x)\) and \(g(x)\). Then the value of \((f\circ g)(α)\) is...

Let \(f(x) = 1-\frac{1}{x},g_2(x) = f(f(x)),g_3(x) = f(f(f(x)))\) and so on. If \(\int x\cdot g_{2026}(x)\,dx = \int g_{2025}(x)\,dx+h(x)+c\), then \(h(x) =\)...

If \(g(x) = 1-\sqrt{x}\) and \(f(g(x)) = 5+4\sqrt{x}+x\), then the value of \(f(6)\) is...

If \(f(x)\) and \(g(x)\) are inverse functions of each other and \(f(x) = x+e^x\), then \(g^'(x) =\)...

If \(y = sin^{-1}(\frac{25-x^2}{25+x^2})\), then \(y^'(1)\) is...

If \(x^m+y^m = k,(m\neq 1)\) and \(y^{''} = \frac{ax^b}{y^c}\) such that \(a+b+c = 0\), then the value of k is...

If the function \(f(x) = (\frac{5x-8}{8-3x})^{\frac{3}{2x-4}}\), for \(x\neq 2\) is continuous at \(x = 2\), then the value of \(f(2)\) is...

If ABC is a triangle of area \(\Delta\) with \(a = 2,b = \frac{7}{2},c = \frac{5}{2}\), where \(a,b,c\) are the lengths of the sides of the triangle opposite to angles A, B and C respectively, then \(\frac{2sinA-sin2A}{2sinA+sin2A}\) is equal to...

In \(△ABC\), with usual notations, \((a+b+c)(b+c-a)(c+a-b)(a+b-c) = 3b^2c^2\), then \(\angle A =\)

If \(\sim p\rightarrow q\) is false and \(q\leftrightarrow r\) is false, then the truth value of \((p,q,r)\) is...

The inverse of the matrix \(A = \left[ \begin{array}{ccc}2 & -1 & 4 \\ 4 & -3 & 1 \\ 1 & 2 & 1\end{array} \right]\) is \(B = \frac{1}{37}\left[ \begin{array}{ccc}-5 & 9 & 11 \\ -3 & -2 & 14 \\ 11 & -5 & k\end{array} \right]\), then the value of \(k\) is...

If matrix \(A = \left[ \begin{array}{ccc}-1 & 2025 & 2026 \\ 0 & 2 & 2027 \\ 0 & 0 & -1\end{array} \right]\), then the sum of all elements in \(\text{adj}(A^{-1})\) is equal to...

The value of \(sin^{-1}(sin\frac{5π}{6})+cos^{-1}(cos\frac{7π}{6})+tan^{-1}(tan\frac{2π}{3})\) is equal to...

If \(\underset{x\rightarrow 1}{lim}\frac{x^3+ax^2+bx+c}{x^2-2x+1} = 2026\) then the value of \(a-c\) is...

Let PA and PB be the tangent segments drawn from point P\((6,8)\) to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

A circle passes through the point \((0,1)\) and touches the parabola \(y = x^2\) at the point \((1,1)\). The centre of the circle is...

If p, q, r are simple propositions with truth values T, F, T respectively, then which of the following is not a true statement?

If the truth value of \([(p∨q)∧(q\rightarrow r)∧(\sim r)]\rightarrow (p∧q)\) is false, then which of the following is NOT true?

The eccentricity of the ellipse represented by the equation \(7x^2+16y^2-14x+64y-377 = 0\) is...

If \(z = \sum _{n = 0}^{2026}i^n\), where \(i = \sqrt{-1}\), then one of the values of \(\sqrt{z}\) is...

If two lines represented by \(x^2-(1+\sqrt{3})xy+\sqrt{3}y^2 = 0\) make angles \(α\) and \(β\) with the X-axis, then \(tan(α+β)\) is...

The family of straight lines \(4ax+3by+c = 0\) such that \(a+b+c = 0\) (where a, b, c are real constants) are concurrent at the point...

Point A\((5,12)\) rotated about the origin O in the XY-plane through an angle of \(30^{\circ}\) in the anticlockwise direction to a new position B. The ordinate of point B is...

If \(^nC_4,^nC_5\) and \(^nC_6\) are in arithmetic progression (A.P.), then the value of n is...