List of top Mathematics Questions on Trigonometry asked in MHT CET

If \(\cos 4x = \cos 3x\), find the general solution for \(x\).

Evaluate the integral: \(\int \frac{\sin x}{\sin 4x} \, dx\)

If A and B are independent events such that \( P(A \cap B') = \frac{3}{25} \) and \( P(A' \cap B) = \frac{8}{25} \), then \( P(A) = \)}

Solution of \( (2y - x) \frac{dy}{dx} = 1 \) is

The probability distribution of a random variable X is given by

Then the variance of X is

If \( X \sim B(6, \frac{1}{2}) \), then \( P(|X - 2| \le 1) = \)}

If sin \( \theta \) = \( \frac{1}{2}\left(x + \frac{1}{x}\right) \), then sin \( 3\theta + \frac{1}{2}\left(x^3 + \frac{1}{x^3}\right) \) =}

Let \( \overline{\text{u}}, \overline{\text{v}}, \overline{\text{w}} \) be the vectors such that \( |\overline{\text{u}}| = 1, |\overline{\text{v}}| = 2, |\overline{\text{w}}| = 3 \). If the projection of \( \overline{\text{v}} \) along \( \overline{\text{u}} \) is equal to that of \( \overline{\text{w}} \) along \( \overline{\text{u}} \) and the vectors \( \overline{\text{v}}, \overline{\text{w}} \) are perpendicular to each other then \( |\overline{\text{u}} - \overline{\text{v}} + \overline{\text{w}}| \) equals

The first derivative of the function \( \left( \cos^{-1}\left(\sin\sqrt{\frac{1+x}{2}}\right) + x^x \right) \) with respect to \( x \) at \( x = 1 \) is

The derivative of \( y = (1 - x)(2 - x) \dots (n - x) \) at \( x = 1 \) is

Let \( \overline{\text{OA}} = \overline{\text{a}} \), \( \overline{\text{OB}} = \overline{\text{b}} \) and if the vector along the angle bisector of \( \angle \text{AOB} \) is given by \( x \frac{\overline{\text{a}}}{|\overline{\text{a}}|} + y \frac{\overline{\text{b}}}{|\overline{\text{b}}|} \) then

The last column in the truth table of the statement pattern \( [\text{p} \rightarrow (\text{q} \land \sim \text{p})] \lor [(\text{p} \lor \sim \text{q}) \land \text{p}] \) is

With usual notations, in a triangle $ABC$, if $\theta$ is any real number, then $a \cos(B - \theta) + b \cos(A + \theta)$ is

If $\tan^{-1}\left(\frac{x}{2}\right) + \tan^{-1}\left(\frac{y}{2}\right) + \tan^{-1}\left(\frac{z}{2}\right) = \frac{\pi}{2}$ then $xy + yz + zx =$}

If $A + B = \frac{\pi}{2}$ then the maximum value of $\cos A \cdot \cos B$ is

The value of $\sqrt{3} \cot 20^\circ - 4 \cos 20^\circ$ is equal to}

The smallest angle of the triangle whose sides are $6 + \sqrt{12}, \sqrt{48}, \sqrt{24}$ is

If $x + \log_{15}(5 + 3^x) = x \log_{15} 5 + \log_{15} 24$, then $x =$ ________

The solution of the differential equation $x \frac{\text{d}^2 y}{\text{d}x^2} = 1$ at $x = y = 1$ with $\frac{\text{d}y}{\text{d}x} = 0$ at $x = 1$, is

In a bank, the principal increases continuously at a rate of $x%$ per year. Then the rate $x$, if Rs.\ 100 doubles itself in 10 years, is ($\log 2 = 0.6931$)

$\int \frac{\text{d}x}{2\text{e}^{2x}+3\text{e}^x+1} =$

The first derivative of the function \( \left( \cos^{-1}\left(\sin\sqrt{\frac{1+x}{2}}\right) + x^x \right) \) with respect to \( x \) at \( x = 1 \) is

Let \( \overline{\text{u}}, \overline{\text{v}}, \overline{\text{w}} \) be the vectors such that \( |\overline{\text{u}}| = 1, |\overline{\text{v}}| = 2, |\overline{\text{w}}| = 3 \). If the projection of \( \overline{\text{v}} \) along \( \overline{\text{u}} \) is equal to that of \( \overline{\text{w}} \) along \( \overline{\text{u}} \) and the vectors \( \overline{\text{v}}, \overline{\text{w}} \) are perpendicular to each other then \( |\overline{\text{u}} - \overline{\text{v}} + \overline{\text{w}}| \) equals

The last column in the truth table of the statement pattern \( [\text{p} \rightarrow (\text{q} \land \sim \text{p})] \lor [(\text{p} \lor \sim \text{q}) \land \text{p}] \) is

Let \( \overline{\text{OA}} = \overline{\text{a}} \), \( \overline{\text{OB}} = \overline{\text{b}} \) and if the vector along the angle bisector of \( \angle \text{AOB} \) is given by \( x \frac{\overline{\text{a}}}{|\overline{\text{a}}|} + y \frac{\overline{\text{b}}}{|\overline{\text{b}}|} \) then