List of top Questions asked in MHT CET

If the acute angle between the lines \[ x^2-4xy+y^2=0 \] is \(\tan^{-1}(k)\), then \(k=\)

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

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 \( f(x)=\dfrac{4x+7}{7x-4} \), 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

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

The vector equation of the line \[ \frac{x+3}{2}=\frac{2y-3}{5}, \quad z=-1 \] is

Evaluate \[ \int_{-\pi/2}^{\pi/2} \sin^2 x\,dx \]

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 negation of the statement \(\exists x \in A\) such that \(x+5>8\) is

The differential equation obtained by eliminating the arbitrary constant from the equation \[ y^2 = (2x+c)^5 \] 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 eccentricity of the ellipse given by the equation \[ 9x^2 + 16y^2 = 144 \] is

Evaluate \[ \int \frac{dx}{(x+2)\sqrt{x+1}} \]

If \(f'(x) = k(\cos x + \sin x)\) and \(f(0) = 9,\ f\!\left(\dfrac{\pi}{2}\right) = 15\), then \(f(x)=\)

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

Evaluate \[ \int_{0}^{a} (a-x)^{\frac{3}{2}} x^2 \, dx \]

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 \(\lambda =\)

Evaluate \[ \sec 2\theta - \tan 2\theta = \]

The area bounded by the curve \(y = x^3\), the \(x\)-axis and the lines \(x = 1\) and \(x = 4\) is

The displacement of a particle at time \(t\) is \[ s = t^3 - 4t^2 - 5t \] Then the velocity of the particle at \(t = 2\) sec is