List of top Mathematics Questions asked in MHT CET

ABCD is a parallelogram. \(P\) is the midpoint of \(AB\). If \(R\) is the point of intersection of \(AC\) and \(DP\), then \(R\) divides \(AC\) internally in the ratio

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

Which of the following have the same value:
(a) \( \sin 120^\circ \)
(b) \( \cos 930^\circ \)
(c) \( \tan 840^\circ \)
(d) \( \cot(-1110^\circ) \)

Evaluate the sum of the series: \[ \frac{1^2}{2} + \frac{1^2 + 2^2}{3} + \frac{1^2 + 2^2 + 3^2}{4} + \frac{1^2 + 2^2 + 3^2 + 4^2}{5} + \cdots \quad \text{upto 8 terms} \]

If the function \[ f(x)= \begin{cases} \dfrac{\log 10 + \log(0.1+2x)}{2x}, & x \neq 0 \\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then \(k+2=\)

\(y = mx + \dfrac{2}{m}\) is the general solution of

In a triangle \(ABC\) with usual notations, \[ \frac{\cos A - \cos C}{a - c} + \frac{\cos B}{b} = \]

The approximate value of \( \log_{10}99 \) is (Given \( \log_{10}e = 0.4343 \))

The equation of a line passing through the point of intersection of the lines \[ x + 2y + 8 = 0 \quad \text{and} \quad 3x - y + 4 = 0 \] and having x– and y–intercepts zero is

The maximum value of \(Z = 10x + 25y\) subject to \[ 0 \le x \le 3,\; 0 \le y \le 3,\; x + y \le 5,\; x \ge 0,\; y \ge 0 \] is

Evaluate the integral: \[ \int \frac{\sin x}{\sin\left(x-\frac{\pi}{4}\right)}\,dx \]

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

In a triangle \(ABC\) with usual notations, if \(\tan A,\tan B,\tan C\) are in H.P., then \(a^2,b^2,c^2\) are in

The joint equation of a pair of lines passing through \((2,3)\) and parallel to the lines \[ x^2 - y^2 = 0 \] is

If \((\sim p \wedge q)\rightarrow r\) is false, then the truth values of \(p,q,r\) respectively are

The equation of a plane passing through the intersection of the planes \(x + 2y - 3z + 2 = 0\) and \(6x + y + z + 1 = 0\) and parallel to the line \(x - 1 = y + 2 = 7 - z\) is

The area bounded by the circle \(x^2 + y^2 = 16\) and the lines \(x = 0\) and \(x = 2\) is

Given \(A = \{1,2,3,4,5\}\), \(B = \{1,4,5\}\). If \(R\) is a relation from \(A\) to \(B\) such that \((x,y) \in R\) with \(x>y\), then the range of \(R\) is

The value of \(x\) such that the matrix \[ \begin{bmatrix} x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5 \end{bmatrix} \] is not invertible is

If \[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} \] then

Evaluate the integral \[ \int_{0}^{\pi} \frac{x \cos x \sin x}{\cos^3 x + \cos x}\,dx \]

If the population grows at the rate of 5% per year, the time taken for the population to become double is (Given \( \log 2 = 0.6912 \))

Evaluate the integral: \[ \int \left[ \log(1+\cos x) - x \tan\left(\frac{x}{2}\right) \right] dx \]

A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =