List of top Mathematics Questions asked in MHT CET

If \( \tan \text{A} = \frac{1}{\sqrt{x(x^2+x+1) \), \( \tan \text{B} = \frac{\sqrt{x}}{\sqrt{x^2+x+1}} \) and \( \tan \text{C} = \sqrt{x^{-1} + x^{-2} + x^{-3}} \) then}

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) 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

In triangle \( ABC \), the point \( P \) divides \( BC \) internally in the ratio \( 3 : 4 \) and \( Q \) divides \( CA \) internally in the ratio \( 5 : 3 \). If \( AP \) and \( BQ \) intersect in a point \( G \), then \( G \) divides \( AP \) internally in the ratio

The differential equation of all straight lines passing through the point \( (1, -1) \) is

If \( X \sim B(n, p) \) then \( \frac{P(X=k){P(X=k-1)} = \)}

The area enclosed between the curves \( y^2 = 4x \) and \( y = |x| \) is

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 position of a point in time \( t \) is given by \( x = \text{a} + \text{b}t - \text{c}t^2 \), \( y = \text{a}t + \text{b}t^2 \). Its resultant acceleration at time \( t \) in seconds is given by

A straight line through the origin \( O \) meets the line \( 3y = 10 - 4x \) and \( 8x + 6y + 5 = 0 \) at the points \( A \) and \( B \) respectively. Then \( O \) divides the segment \( AB \) in the ratio

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

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

If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:

The projection of the line segment joining P(2, -1, 0) and Q(3, 2, -1) on the line whose direction ratios are 1, 2, 2 is

The equation of the curve passing through $(2, \frac{9}{2})$ and having the slope $(1 - \frac{1}{x^2})$ at $(x, y)$ is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

The general solution of the differential equation $\frac{\text{d}y}{\text{d}x} + \sin \left( \frac{x+y}{2} \right) = \sin \left( \frac{x-y}{2} \right)$ is

The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is

In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

$\int \text{e}^{2x} \frac{(\sin 2x \cos 2x-1)}{\sin^2 2x} \text{d}x =$

If four digit numbers are formed by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$