List of top Questions asked in MHT CET- 2025

The approximate value of \(\cos \left(59^{\circ} 30^{\prime}\right)\) is (given \(1^{\circ}=0.0175^{\mathrm{c}}, \sin 60^{\circ}=0.8660\) )

If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x^2+y^2+z^2=\)

\[ \int_0^{\frac{\pi}{2}} \frac{d x}{1+(\cot x)^{101}}= \]

In a triangle \(A B C\), with usual notations, \(3 \mathrm{~b}=\mathrm{a}+\mathrm{c}\), then \(\cot \frac{\mathrm{A}}{2} \cdot \cot \frac{\mathrm{C}}{2}=\)

The rate of reduction of a persons assets is proportional to the square root of the existing assets. The assets reduced from 25 lakhs to 6.25 lakhs in 2 years. This rate of reduction of his assets will make him bankrupt in

The solution of \(\left(1+y^2\right)+\left(x-\mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0\) is

\[ \int_0^3 \frac{d x}{(x+2) \sqrt{x+1}}= \]

AOB is the positive quadrant of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) in which \(\mathrm{OA}=5, \mathrm{OB}=3\). The area between the arc AB and the chord AB of the ellipse in sq. units is

In a triangle ABC , the sides \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are such that they are the roots of the equation \(x^3-11 x^2+38 x-40=0\) Then

\[ \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}= \]

In a triangle ABC with usual notations if \(\mathrm{a}=13\), \(b=14, c=15\) Then \(\sin A=\)

If \(2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)\), then the value of \(x\) is

The possible values of \(\theta \in(0, \pi)\) such that \(\sin \theta+\sin (4 \theta)+\sin (7 \theta)=0\) are

If \(2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0\) and \(y=5 x^2 \mathrm{f}(x)\), then \(y\) is strictly increasing in

If the equation \(\mathrm{k} x y+10 x+8 y+16=0\) represents a pair of lines, then

If the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{x}{y}=\frac{\mathrm{a}}{y}\) where a is constant, represents a family of circles then the radius of the circle is \(\qquad\)

A manufacturer produces \(x\) items per week at a total cost of ₹ \(\left(x^2+78 x+2500\right)\). The price per unit is given by \(8 x=600-\mathrm{p}\) where ' p ' is the price of each unit. Then the maximum profit obtained is

If \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\) are unit vectors and \(\theta\) is the angle between them, then \(\tan \frac{\theta}{2}=\)

\[ \int \log (2+x)^{2+x} d x= \]

If the points \(\mathrm{A}(1,1,2), \mathrm{B}(2,1, \mathrm{p}), \mathrm{C}(1,0,3)\) and \(D(2,2,0)\) are coplanar then the value of \(p\) is

The equation of the plane passing through the point of intersection of the planes \(2 x-y+z-3=0\) and \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{2}=\frac{y+3}{4}=\frac{z-3}{5}\) is \(\alpha x+\beta y+\gamma z+d=0\) Then \(\alpha+\beta+\gamma+d=\)

If the projection of \(\bar{a}\) on \(\bar{b}+\bar{c}\) is twice the projection of \(\bar{b}+\bar{c}\) on \(\bar{a}\) also if \(|\bar{b}|=2 \sqrt{2},|\bar{c}|=4\) and the angle between \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(\frac{\pi}{4}\) then \(|\overline{\mathrm{a}}|=\)

\[ \int \frac{\mathrm{e}^{\tan ^{-1} 2 x}}{1+4 x^2}= \]

If the equation of the median through vertex \(\mathrm{A}(3, \mathrm{k})\) of \(\triangle \mathrm{ABC}\) with vertices \(\mathrm{B}(2,1)\) and \(\mathrm{C}(-4,5)\) is \(x+4 y=\mathrm{p}\), then \(\mathrm{k}=\) where p and k are constants

Calculate the standard enthalpy change of following reaction.

\[ \mathrm{C}_2 \mathrm{H}_{4(\mathrm{~g})}+3 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(l)} \]

If \(\Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{C}_2 \mathrm{H}_4\right)=-52 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

\[ \begin{aligned} & \Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{CO}_2\right)=-390 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{H}_2 \mathrm{O}\right)=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned} \]

If \(\bar{a}=\hat{i}+\hat{j}, \bar{b}=2 \hat{i}-\hat{k}\) then the point of intersection of the lines \(\overline{\mathrm{r}} \times \overline{\mathrm{a}}=\overline{\mathrm{b}} \times \overline{\mathrm{a}}\) and \(\overline{\mathrm{r}} \times \overline{\mathrm{b}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) is