List of top Mathematics Questions asked in MHT CET

The equation of the circle whose end points of a diameter are the centres of the circles \[ x^2 + y^2 + 2x - 4y + 1 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 6y + 17 = 0 \] is

The area of the region bounded by the curve \( y = 4x - x^2 \) and the x-axis is

Evaluate the integral \[ \int \frac{(1 + \log x)}{\cos^2(\log x)} \, dx \]

If \[ \mathbf{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} - 4\hat{k}, \quad \mathbf{c} = \hat{i} + \hat{j} + \hat{k} \] then \( (\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{a} \times \mathbf{c}) = \)

The maximum value of the function \( \frac{\log x}{x}, x \neq 0 \) is

The approximate value of \( \cot^{-1} (1 \cdot 001) \) is

With usual notations, if in \( \triangle ABC \), \( s \) is the semi-perimeter and \( (s - a)(s - b) = (s - c) \), then \( \triangle ABC \) is

The direction cosines of a line which makes equal acute angles with the co-ordinate axes are

For \( \theta \in \left( 0, \frac{\pi}{2} \right) \), if \( \tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1 \), then \( \theta = \)

For the following shaded region, the linear constraints are:

If \[ y = \left( \frac{x^2 + 1}{x} \right)^x \text{ and } \frac{dy}{dx} = y \left[ g(x) + \log \left( \frac{x^2}{x+1} \right) \right], \text{ then } g(x) = \]

A metal has half-life period of 10 days. A sample originally has a mass of 1000 mg, then the mass remaining after 50 days is

If \[ A = \{ x / x \text{ is a prime number}, 0 \leq x \leq 9 \}, \text{ then the number of elements of the power set of } A \text{ is} \]

The solution of \( rdx + (x - r^2) dr = 0 \) is

The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are

The symbolic form of the following circuit is (where \( p, q, r \) represent switches \( s_1, s_2, s_3 \) which are closed respectively)

The general solution of \( \tan \theta + \tan 2\theta = \tan 3\theta \)

If the function \[ f(x)= \begin{cases} \dfrac{1-\sin2x+\cos2x}{1+\sin2x+\cos2x}, & x\neq \dfrac{\pi}{2}
k, & x=\dfrac{\pi}{2} \end{cases} \] is continuous at \( x=\dfrac{\pi}{2} \), then \( k \) is

The equation of a normal to the curve \[ x = 4\sec\theta,\qquad y = 4\tan^2\theta \] at \( \theta = \frac{\pi}{4} \) is

If \( \log_{10}\!\left(\dfrac{x^3-y^3}{x^3+y^3}\right)=2 \), then find \( \dfrac{dx}{dy} \).

If \( \vec{AB} = 3\hat{i} + 5\hat{j} + 4\hat{k} \), \( \vec{AC} = 5\hat{i} - 5\hat{j} + 2\hat{k} \) represent the sides of triangle \( ABC \), then the length of the median through \( A \) is

If a line in octant OXYZ makes equal angles with the coordinate axes, then

A tangent to the curve \( x = at^2,\; y = 2at \) is perpendicular to the X-axis. Then the point of contact is

If \( P(A') = 0.6 \), \( P(B) = 0.8 \) and \( P(B|A) = 0.3 \), then find \( P(A|B) \).

Given below is the probability distribution of a discrete random variable \( X \):
\[ \begin{array}{c|cccccc} X=x & 1 & 2 & 3 & 4 & 5 & 6
\hline P(X=x) & k & 0 & 2k & 5k & k & 3k \end{array} \] Then find \( P(X \ge 4) \).