List of top Mathematics Questions asked in MHT CET

If \(f(x) = |5x-3|\) is defined on interval \([0,1]\), then the value of \(\int _0^1f(x)\,dx\) is...

If the rate of increase of surface area of a spherical balloon is \(5\,\text{cm}^2/\text{sec}\) and rate of increase of volume of a spherical balloon is \(10\,\text{cm}^3/\text{sec}\), then the radius of the balloon at that time 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...

If \(3y^2-2xy-x = 0\), then the value of \(\frac{dy}{dx}\) at \(y = 2\) is...

If \(u\) and \(v\) are functions of \(x\), then \(\int \frac{1}{v^3}(uv\frac{du}{dx}-u^2\frac{dv}{dx})dx =\)

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

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

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

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

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 \(\angle A =\)

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

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...

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?

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