List of top Mathematics Questions asked in MHT CET

If [2132]\begin{bmatrix} 2 & 1 \\ 3 & 2\end{bmatrix} A [−325−3]\begin{bmatrix} -3 & 2 \\ 5 & -3\end{bmatrix} =[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}, then A =?

If a and b are two vectors such that Ia⃗\vec {a}I + Ib⃗\vec {b}I = 2\sqrt 2 with a⃗\vec {a}.b⃗\vec {b} = –1, then the angle between a⃗\vec {a} and b⃗\vec {b} is

A round table conference is to be held among 20 countries. If two particular delegates wish to sit together, then such arrangements can be done in __________ways.

The general solution of differential equation e12(dydx)e^{\frac {1}{2} (\frac {dy}{dx})} = 3x is (where C is a constant of integration.)

y=tan−1(4sin2xcos2x−6sin2x)y = tan^{-1} (\frac{4 sin 2x}{cos 2x - 6sin^2x}) then dydx\frac{dy}{dx} at x=0x=0.

A random variable X has the following probability distribution
probability distribution table
 then P (X ≥ 2) =?

Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?

Probability of getting odd numbers in first 100 numbers.

If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then

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
Letters in the word HULULULU are rearranged. The probability of all three L being together 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) =
If log⁡10(x3−y3x3+y3)=2\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2 then dydx= \frac{dy}{dx} =
If y=(tan⁡−1x)2y = \left(\tan^{-1} x\right)^{2} then (x2+1)2d2ydx2+2x(x2+1)dydx= \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} =
If f(x)={x2+αfor x≥02x2+1+βforx<0f(x) = \begin{cases} x^2 + \alpha & \text{for } x \ge 0 \\[2ex] 2\sqrt{x^2 + 1} + \beta & \text{for} x < 0 \end{cases} is continuous at x = 0 and f(12)=2f \left(\frac{1}{2} \right) = 2 then α2+β2\alpha^2+ \beta^2 is
If A, B, C are the angles of ΔABC\Delta ABC then cot⁡ A.cot⁡ B+cot⁡ B.cot⁡ C+cot⁡ C.cot⁡ A=\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =
If f:R−{2}→Rf : R - \{2\} \to R is a function defined by f(x)=x2−4x−2f(x) = \frac{x^2 - 4}{x - 2} , then its range is
The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is
The number of solutions of sin⁡ x+sin⁡ 3x+sin⁡ 5x=0\sin \, x + \sin \, 3x + \sin \, 5x = 0 in the interval [π2,3π2]\left[\frac{\pi}{2} , 3 \frac{\pi}{2}\right] is
Matrix A=[123115247]A = \begin{bmatrix}1&2&3\\ 1&1&5\\ 2&4&7\end{bmatrix}then the value of a31A31+a32A32+a33+A33a_{31} A_{31} + a_{32} A_{32} + a_{33 } + A_{33} is
The maximum value of 2x+y2x + y subject to 3x+5y≤263x + 5y \leq 26 and 5x+3y≤30,x≥0,y≥05x + 3y \leq 30, x \geq 0, y \geq 0 is
The sides of a rectangle are given by x=± ax = \pm \, a and y=± by = \pm \, b. The equation of the circle passing through the vertices of the rectangle is
The negation of the statement: "Getting above 95% marks is necessary condition for Hema to get the admission is good college"
The line 5x+y−1=05x + y - 1 = 0 coincides with one of the lines given by 5x2+xy−kx−2y+2=05x^2 + xy - kx - 2y + 2 = 0 then the value of k is
If ∫0Kdx2+18x2=π24\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}, then the value of K is