List of top Questions asked in MHT CET

The eccentricity of the hyperbola \( 16x^2 - 3y^2 - 32x - 12y - 44 = 0 \) is

\( y = c^2 + \dfrac{c}{x} \) is the solution of the differential equation

If \( y\sqrt{1-x^2} + x\sqrt{1-y^2} = 1 \), then \( \dfrac{dy}{dx} = \)

If the vectors \( (2\mathbf{i}-q\mathbf{j}+3\mathbf{k}) \) and \( (4\mathbf{i}-5\mathbf{j}+6\mathbf{k}) \) are collinear, then the value of \( q \) is

If the vectors \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar, then \( \dfrac{\left| \vec{a} + 2\vec{b} \;\; \vec{b} + 2\vec{c} \;\; \vec{c} + 2\vec{a} \right|} {\left| \vec{a} \;\; \vec{b} \;\; \vec{c} \right|} \) is

The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to

Evaluate the integral \( \displaystyle \int \frac{e^x}{\sqrt{x}}(1+2x)\,dx \)

Simplify \( \cos\left(\dfrac{3\pi}{4}+x\right) - \sin\left(\dfrac{\pi}{4}-x\right) \)

Evaluate \( \displaystyle \int_{-\pi}^{\pi} \frac{2x}{1+\cos^2 x}\,dx \)

If \( f(x) = [x]^2 - 5[x] + 6 = 0 \), where \( [x] \) denotes the greatest integer function, then \( x \in \)

If \( \int_{0}^{1} (5x^2 - 3x + k) \, dx = 0 \), then \( k = \)

For a sequence \( (t_n) \), if \( s_n = 7(3^n - 1) \), then \( t_n = \)

If \( \int x^x (1 + \log x) \, dx = k x^x + c \), then \( k = \)

A particle moves according to the law \( s = t^3 - 6t^2 + 9t + 25 \). The displacement of the particle at the time when its acceleration is zero is

If the population grows at the rate of \( 8% \) per year, then the time taken for the population to be doubled is \([ \log 2 = 0.6912 ]\)

Which among the following compounds is obtained when calcium formate is dry distilled alone?

A solution is \(0.25%\) by mass. What is the weight of solvent containing \(1.25~\text{g}\) solute?

What is the IUPAC name of 3–chloropropyl ethyl ether?

Which of the following can form a colloidal sol with water?

The area of the region bounded by the curve \( y = \log x \), x-axis and the lines \( x = 1 \), \( x = e \) is

The measure of the acute angle between the lines given by the equation \( 3x^2 - 4\sqrt{3}xy + 3y^2 = 0 \) is

Which of the following halogens combine with dihydrogen at the lowest temperature?

Identify product ‘C’ in the following reaction:
\[ \text{Propylene dibromide} \xrightarrow[\text{Alcohol}]{\text{Zn},\,\Delta} A \xrightarrow{\text{HBr}} B \xrightarrow[\text{ether}]{\text{Na}} C \]

Which of the following oxides is NOT volatile?

The edge length of an fcc type unit cell of copper having atomic radius \(127.6~\text{pm}\) is equal to