List of top Mathematics Questions asked in MHT CET

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:On a recent journey Aman drove from City A to city B to city C. His average speed for the whole journey was 60 km/hr. Find the average speed on his journey from city B to city C.Statement I:  Average speed during the journey from city A to city B is 48 km/hr Statement II: Total time taken for the entire journey is 3 hours Statement III: Ratio of distance travelled while going from A to B and B to C is 2 : 3

Find the area of the curve $y=4x^3$ between the end points $x=[-2,3]$

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.

General solution of $(x^2+y^2)dx-2xydy=0$ is:

$\frac{\sin 7x+6\sin 5x+17\sin 3x+12\sin x}{\sin 6x+5\sin 4x+12\sin 2x}$ equals:

Consider the following.1. $z\overline{z}=|z{|}^2$2. $z^{-1}=\frac{z}{|z{|}^2}$, where $z=$ complex numberWhich of the above statement is/are correct?

Find the value of $y-x$ from the following equation:$2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

Find the maximum value of 15sin θ + 20cos θ.

Consider the function $f(x)=|x|$ in the interval $-1\le x\le 1$. At the point $x=0,f(x)$ is:

If, $y=9\sqrt{x+\sqrt{x+\sqrt{x+....\infty }}}$ find $\left(\frac{dy}{dx}\right)$ at a point where y = 3.

What is the value of ${\int }_4^9\frac{1}{\sqrt{x}}dx$ ?

The maximum value of $\frac{\ln x}{x}$ is:

Evaluate ${\int }_0^{\frac{\pi }{2}}\frac{\cos x}{1+{\sin }^{2}x}dx$:

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is:

If ${\cos }^{-1}\left(\frac{p}{a}\right)+{\cos }^{-1}\left(\frac{q}{b}\right)=\alpha$, then $\frac{p^2}{a^2}+k\cos \alpha +\frac{q^2}{b^2}={\sin }^2\alpha$ where $\mathrm{k}$ is equal to:

Calculate the area under the curve $y=2\sqrt{x}$ and included between the lines $x=0,x=4$.

Find the equation of the line passing through $(-3,5)$ and perpendicular to the line through the points $(2,5)(-3,6)$.

If $2x^3-3y^2=7$, what is $\frac{dy}{dx}$ equal to $(y\ne 0)$:

Find the area of the region (in square unit) bounded by the curve $y=x-2$ and $x=0$ to $x=4$.

Find the equation of tangent of $y=x^2$ at $x=1$

If $A=\left[\begin{array}{ccc}1& -1& 0\\ 3& 2& -1\end{array}\right]$ and $B=\left[\begin{array}{l}1\\ 3\\ 5\end{array}\right]$, find $(AB{)}^T$.

Find the value $f^{\prime }(x)$, if $f(x)={\sin }^{-1}(1-x^2)$

What is the area of the parabola $x^2=y$ bounded by the line $y=1$?

If $\underset{x\to \mathrm{\infty }}{lim}(\frac{x^2+x+1}{x+1}-px-q)=-3$, then $p$ and $q$ is:

Find the equation of the line perpendicular to the line $x-3y+5=0$ and passes through the point $(2,-4)$.