List of top Mathematics Questions asked in MHT CET

The value of $\frac{d}{dx}{x}^{2x}=$

Direction: Below given a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:A metal block of density ‘D’ and mass ‘M’, in the form of a cuboid, is beaten into a thin square sheet of thickness ‘t’, and rolled to form a cylinder of the same thickness. Find the inner radius of the cylinder –Statement I: Cuboid has dimensions 10cm x 5 cm x 12 cmStatement II: Thickness ‘t’ = 1.5cm Statement III: Mass of block, M = 216kg

If $\sin (\alpha +\beta )=6\sin (\alpha -\beta )$ and $k=\frac{\tan \alpha }{\tan \beta }$, then, what is the value of $k$ ?

Suppose $\sin 2\theta =\cos 3\theta$, here $0<\theta <\frac{\pi }{2}$ then what is the value of $\cos 2\theta ?$

$\overrightarrow{A}\times \overrightarrow{B}=\frac{1}{2}AB,$ what is the angle between $A$ and $B?$

Order of $\left[\begin{array}{lll}2& 7& 4\\ 3& 1& 0\end{array}\right]\left[\begin{array}{l}5\\ 4\\ 3\end{array}\right]$ is:

The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is:

The solution of the differential equation $\frac{dy}{dx}=\sec \left(\frac{y}{x}\right)+\frac{y}{x}$ is:

Find $\frac{z_1}{z_2}$, when $z_1=6+2i$ and $z_2=2-i$.

A box contains $100$ round discs, $50$ square - shaped discs and $30$ triangular discs. All the discs are made up of iron and have an equal probability of getting attracted by a magnet. If a magnet which can attract only one disc in one pass and the disc is passed over them twice. What is the probability that both times a triangular disc is attracted? The disc attracted in one pass does not fall into box again, however each time a square shaped disc is kept into the box.

Region represented by the in equation system $x+y\le 3,y\le 6$ and $x\ge 0,y\ge 0$ is:

Maximam value of $:Z=10x+25$ y Subject to : $x\le 3,y\le 3,x+y\le 5,x\ge 0,y\ge 0$ at:

The integrating factor of the differential equation $2y\frac{dx}{dy}+x=5y^2$ is, $(y\ne 0)$:

Find the value of $\sqrt{(5+12i)}$, where $i=\sqrt{-1}$.

Maximize $Z=4x+9y$, subject to the constralnts $x=0$, y $=0,x+5y\le 200,2x+3y\le 134$.

Find the position vector of the midpoint of the vector joining the points $P(2,3,4)$ and $Q(4,1,-2)$.

Find the centre and radius of $x^2+y^2+6y=0$.

The differential equation of the family of curves $y=c_1{e}^x+c_2{e}^{-x}$ is:

Form the differential equation of $y=a{e}^{3x}\cos (x+b)$ Where $y^{\prime }=\frac{dy}{dx}$ and $y^n=\frac{d^{2}y}{d{x}^2}$?

The following table gives the weights of one hundred persons. Copute the coefficient of dispersion by the method of limits.Class-interval$40-45$$45-50$$50-55$$55-60$$60-65$$65-70$$70-75$$75-80$$80-85$$85-90$No. of persons$4$$13$$8$$14$$9$$16$$17$$9$$8$$2$

Consider the following statements:1. If $y=\ln (\sec x+\tan x)$, then $\frac{dy}{dx}=\sec x$.2. If $y=\ln (\mathrm{cosec}x-\cot x)$, then $\frac{dy}{dx}=\mathrm{cosec}x$.Which of the above is / are correct?

If $n=100!$, then what is the value of the following?$\frac{1}{{\log }_{2}n}+\frac{1}{{\log }_{3}n}+\frac{1}{{\log }_{4}n}+\dots \dots +\frac{1}{{\log }_{100}n}$

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{array}\right]$ then $A{A}^T$ is equal to: (where $A^T$ is the transpose of $A)$

Cards numbered from $107$ to $1006$ are put in a bag. A card is drawn from it at random. Find the probability that the number on the card is not divisible both by $11$ and $37$?

If ${\sec }^2\theta +{\tan }^2\theta =3$ then find the value of $\cot \theta$.