List of top Mathematics Questions asked in MHT CET

$\cosec 2\theta-\cot 2\theta=$

Evaluate the integral \[ \int_{-5}^{5} \log \left( \frac{7 - x}{7 + x} \right) \, dx \]

If \( a, b, c \) are lengths of the sides \( BC, CA, AB \) respectively of \( \triangle ABC \) and \( a\vec{AH} + b\vec{BH} + c\vec{CH} = \vec{0} \), then point \( H \) is the

For every value of \( x \), the function \( f(x) = \frac{1}{a^x}, a>0 \) is

If the equation \[ ax^2 + 2hxy + by^2 + 2gx + 2fy = 0 \] has one line as the bisector of the angle between the co-ordinate axes, then \[ (a + b)^2 = 4(h^2 + g^2) \]

If \[ 2 + 4 + 6 + \cdots \text{ up to } n \text{ terms} = \frac{37}{36}, \] then \( n = \)

If \( \tan^{-1}\!\left(\dfrac{1-x}{1+x}\right) - \dfrac{1{2}\tan^{-1}x = 0 \), for \( x>0 \), then the value of \( x \) is}

The eccentricity of the hyperbola \( 16x^2 - 3y^2 - 32x - 12y - 44 = 0 \) is

The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

If \(A(3,2,-1)\) and \(B(1,4,3)\), then the equation of the plane which bisects the segment \(AB\) perpendicularly is

The equation of the line passing through the point $(1,2,3)$ and perpendicular to the lines $\dfrac{x-1}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{3}$ and $\vec r = \lambda(-3\hat i + 2\hat j + 5\hat k)$ is

Evaluate: \[ \frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} \]

The perimeter of the triangle whose vertices have the position vectors \( \hat{i} + \hat{j} + \hat{k} \), \( 5\hat{i} + 3\hat{j} - 3\hat{k} \), and \( 2\hat{i} + 5\hat{j} + 9\hat{k} \) is

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is

The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is

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

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)

The bacteria increases at the rate proportional to the number of bacteria present. If the original number \( N \) doubles in 4 hours, then the number of bacteria in 12 hours will be

If \( f(x) = \sin^{-1} \left( \sqrt{\frac{1 - x}{2}} \right) \), then \[ f'(x) = \]

Evaluate $\displaystyle \int \frac{dx}{1+\sqrt{x}}$

The area bounded by the parabola \( y^2 = 16x \) and its latus-rectum in the first quadrant is

The coordinates of the foci of the ellipse \( 16x^2 + 9y^2 = 144 \) are

If the displacement of a particle at time \(t\) is given by \[ s = 3t^2 - 12t + 14, \] then the displacement of the particle when its velocity becomes zero is