List of top Mathematics Questions asked in MHT CET

If the lines $x = ay - 1 = z - 2$ and $x = 3y - 2 = bz - 2$ ($ab \neq 0$) are coplanar, then \dots

Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?

$\int_{\pi/4}^{\pi/2} 2\sin^{-4} x dx = \_\_\_\_\_\_.$
Note: The initial OCR showed "$23.4 \frac{/2}{/4}$". The "4" was a misread coefficient. The mathematical evaluation of the options indicates a coefficient of 2 is present in the intended question.

A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.

The order of the differential equation whose general solution is given by $y = (C_1 + C_2) \sin(x + C_3) - C_4 e^{x+C_5}$ is \dots}

A doctor assumes patient has $d_1, d_2,$ or $d_3$ with equal probability. A test is positive with probability 0.7 for $d_1$, 0.5 for $d_2$, and 0.8 for $d_3$. If the test is positive, what is the probability the patient has $d_2$?

$\int \frac{dx}{x(x^3 + 1)} = \dots$

The area bounded by the curve $y = 4x - x^2$ and X-axis in square units, is \dots

The angle $\theta$, at which the curves $y = 3^x$ and $y = 7^x$ intersect, is given by ______.

The equation of the curve passing through origin and satisfying $(1 + x^2) \frac{dy}{dx} + 2xy = 4x^2$ is ______.

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the coordinates of the point of contact are \dots

The eccentricity of the hyperbola which passes through the points $(3, 0)$ and $(3\sqrt{2}, 2)$ is \dots

Let $f : \mathbb{R} - \{2\} \rightarrow \mathbb{R} - \{1\}$ defined by $f(x) = \frac{x-3}{x-2}$ and $g : \mathbb{R} \rightarrow \mathbb{R}$ defined by $g(x) = 3x - 2$, then sum of all values of $x$ for which $f^{-1}(x) + g^{-1}(x) = 19/6$ is ______.

If $f(x) = \log(1 + x) - \frac{2x}{2 + x}$, then $f(x)$ is increasing in ______.

The function $f(x) = x^3 - 6x^2 + ax + b$ satisfies the conditions of Rolle's theorem in $[1, 3]$. Then the values of $a$ and $b$ are respectively \dots

If the line $\frac{x-3}{2} = \frac{y+5}{1} = \frac{z+2}{2}$ lies in the plane $\alpha x + 3y - z + \beta = 0$, then values of $\alpha$ and $\beta$ respectively are \dots}

$\cos^4(\pi/8) + \cos^4(3\pi/8) + \cos^4(5\pi/8) + \cos^4(7\pi/8) = \dots$

If $\tan^{-1}(x + 1) + \tan^{-1} x + \tan^{-1}(x - 1) = \tan^{-1} 3$, then for $x < 0$ the value of $500x^4 + 270x^2 + 997 = \dots$

If $(\tan^{-1} x)^2 + (\cot^{-1} x)^2 = 5\pi^2/8$, then $x^2 + 1 = \dots$

$\lim_{x \to 0} \frac{63^x - 9^x - 7^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}} = \dots$

The straight line passing through $(-3, 6)$ and midpoint of the line segment joining the points $(4, -5)$ and $(-2, 9)$ have inclination ______.

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students selected at random 4 are swimmers is ______.

Let $\vec{a} = \hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = 5\hat{i} - 3\hat{j} + 2\hat{k}$ and if $\vec{b} \times \vec{c} = \vec{a}$ then $|\vec{b}|$ = ______.

If $\theta$ is an obtuse angle between vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}| = 5, |\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 5\sqrt{5}$ then $\vec{a} \cdot \vec{b} = \dots$

$\int_{\log(1/2)}^{\log 2} \sin \left( \frac{e^x - 1}{e^x + 1} \right) dx = \_\_\_\_\_\_.$