List of top Mathematics Questions asked in MHT CET

The shaded region in the following figure represents the solution set for a certain linear programming problem. Then linear constraints for this region are given by}
The mirror image of $P(2, 4, -1)$ in the plane $x - y + 2z - 2 = 0$ is $(a, b, c)$, then the value of $a+b+c$ is
The function $f$ defined on $\left(-\frac{1}{3}, \frac{1}{3}\right)$ by $f(x) = \left\{ \begin{array}{ll} \frac{1}{x} \log\left(\frac{1+3x}{1-2x}\right) & , x \neq 0 \\> k & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then $k$ is
If $|\vec{a}| = 2$, $|\vec{b}| = 3$, $|\vec{c}| = 5$ and each of the angles between the vectors $\vec{a}$ and $\vec{b}$, $\vec{b}$ and $\vec{c}$, $\vec{c}$ and $\vec{a}$ is $60^\circ$, then the value of $|\vec{a} + \vec{b} + \vec{c}|$ is
Let $\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \hat{j}$. If $\vec{c}$ is a vector such that $\vec{a} \cdot \vec{c} = |\vec{c}|$, $|\vec{c} - \vec{a}| = 2\sqrt{2}$ and the angle between $\vec{a} \times \vec{b}$ and $\vec{c}$ is $\frac{2\pi}{3}$, then $|(\vec{a} \times \vec{b}) \times \vec{c}|$ is
If the statement $p \leftrightarrow (q \rightarrow p)$ is false, then true statement/statement pattern is
If both mean and variance of 50 observations $x_1, x_2, \ldots, x_{50}$ are equal to 16 and 256 respectively, then mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is
Let $z \in C$ with $\text{Im}(z) = 10$ and it satisfies $\frac{2z-n}{2z+n} = 2i - 1$, $i = \sqrt{-1}$ for some natural number $n$, then}

The number of solutions of tanx+secx=2cosx, n(0,2π) are?

\(f(x) = x^2 + 1\), \(g(x) = \frac{1}{x}\). Find \(f(g(g(f(x))))\) at \(x = 1\)
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

If the line ax+by+c=0 is a normal to the curve xy=1, then 
 

Area of the Region bounded by the curve y=√49-x2 and x-axis is .

Considering only the principal value of an inverse function, the set: A= { x ≥ 0, tan-1x + tan-16x = \(\frac{\pi}{4}\)}, then A is... 
 
Ki are possible values of K for which lines \(Kx + 2y + 2 = 0\), \(2x + Ky + 3 = 0\), \(3x + 3y + K = 0\) are concurrent, then \(∑k_i\) has value.
The solution of \( e^{y-x} \frac{dy}{dx} = \frac{y(\sin x + \cos x)}{1 + y \log y} \)
The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is? 
 

\( \int \left( \frac{1}{7} - 6x - x^2 \right) \, dx \)

If x = 3 tan t and y = 3 sec t, then find \(\frac{d^2y}{dx^2} \, at\,t=\frac{\pi}{4}\), is:

The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?

If \(A=\begin{bmatrix} 2a & -3b\\ 3 & 2\end{bmatrix}\) and \(\text{adj}A = AA^T\), then 2a+3b is?

The differential equation dy/dx=√1-y2/y determines a family of circles with

Solve for x, given \( \tan^{-1}\left(\frac{1 - x}{1 + x}\right) = \frac{1}{2} \tan^{-1}(x) \)

If \(1+ (√1+x) tanx = 1+ (√1-x)\)  then \(sin4x\)  is ?

 

Find area bounded by region, y=3x+1, y=4x+1 and x=3?