List of top Mathematics Questions asked in MHT CET

Which of the following statement patterns is a contradiction? 
\[ \begin{aligned} S_1 &: (p \to q) \land (p \land \sim q) \\ S_2 &: [p \land (p \to q)] \to q \\ S_3 &: (p \lor q) \to \sim p \\ S_4 &: [p \land (p \to q)] \leftrightarrow q \end{aligned} \]

If \[ y = \cot^{-1}\!\left(\sqrt{\frac{1-\sin x}{1+\sin x}}\right), \quad \text{then find} \quad \frac{dy}{dx}. \]

If the L.M.V.T. holds for the function \( f(x) = x + \dfrac{1}{x} \), \(x \in [1,3]\), then \(c =\)

If
\[ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ -\sin\theta & -\cos\theta \\ \end{bmatrix} \] then \(A^{-1} =\) 

If \(P(3,2,6)\), \(Q(1,4,5)\) and \(R(3,5,3)\) are the vertices of \(\triangle PQR\), then the measure of \(\angle PQR\) is
If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of \[ f\{f[f(2)]\} \] is
If \(3\cos x \ne 2\sin x\), then the general solution of \[ \sin^2 x-\cos 2x=2-\sin 2x \] is
The line cuts the \(X\)-axis and \(Y\)-axis at the points \(A\) and \(B\) respectively. The point \((5,6)\) divides the line segment \(AB\) internally in the ratio \(3:1\). Then the equation of the line is
If the acute angle between the lines \[ x^2-4xy+y^2=0 \] is \(\tan^{-1}(k)\), then \(k=\)
The vector equation of the line \[ \frac{x+3}{2}=\frac{2y-3}{5}, \quad z=-1 \] is
Evaluate \[ \int \frac{5^x}{\sqrt{5^{-2x}} - 5^{2x}}\,dx \]
The length of the perpendicular to the plane \[ \vec r \cdot (i - 2j + 3k) = 14 \] from the origin is
The differential equation of the family of lines having \(x\)-intercept \(a\) and \(y\)-intercept \(b\) is
Evaluate \[ \int_{-\pi/2}^{\pi/2} \sin^2 x\,dx \]
The negation of the statement \(\exists x \in A\) such that \(x+5>8\) is
The feasible region of the L.P.P.
\[ \text{Maximize } z = 70x + 50y \] subject to \[ 8x + 5y \le 60,\quad 4x + 5y \le 40,\quad x \ge 0,\; y \ge 0 \] is
The locus of the point of intersection of the two lines \[ x\sqrt{3} - y = k\sqrt{3} \quad \text{and} \quad \sqrt{3}x + ky = \sqrt{3}, \; k \in \mathbb{R}, \] describes
If \[ f(x)=\frac{(e^{2x}-1)\sin x^\circ}{x^2}, \quad x\neq0 \] is continuous at \(x=0\), then \(f(0)=\)
The differential equation obtained by eliminating the arbitrary constant from the equation \[ y^2 = (2x+c)^5 \] is
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get at least one correct answer is
If \(2\sin^2 x + 7\cos x = 5\), then the permissible value of \(\cos x\) is
If \(f'(x) = k(\cos x + \sin x)\) and \(f(0) = 9,\ f\!\left(\dfrac{\pi}{2}\right) = 15\), then \(f(x)=\)
Evaluate \[ \int \frac{dx}{(x+2)\sqrt{x+1}} \]
The eccentricity of the ellipse given by the equation \[ 9x^2 + 16y^2 = 144 \] is
If the lines \[ \frac{1-x}{2} = \frac{y-8}{\lambda} = \frac{z-5}{2} \quad \text{and} \quad \frac{x-11}{5} = \frac{y-3}{3} = \frac{z-1}{1} \] are perpendicular, then \(\lambda =\)