List of top Mathematics Questions on Integral Calculus asked in MHT CET

In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is

The area bounded by the curve \( y = x^2 + 3, y = x, x = 3 \) and \( y \)-axis is

If \( \theta \) is the angle between the lines whose direction cosines are given by \( 6mn - 2nl + 5lm = 0 \) and \( 3l + m + 5n = 0 \), then \( \sin \theta = \)}

If \( A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix} \), \( B = \text{adj } A \) and \( C = 5A \), then \( \frac{|\text{adj } B|}{|C|} = \)}

The Cartesian equation of plane through A$(7, 8, 6)$ and parallel to the XY plane is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

The values of $b$ and $c$ for which the identity $f(x + 1) - f(x) = 8x + 3$ is satisfied, where $f(x) = bx^2 + cx + d$, are

$p$ : If 7 is an odd number then 7 is divisible by 2.
$q$ : If 7 is prime number then 7 is an odd number. If $V_1$ and $V_2$ are respective truth values of contrapositive of p and q then $(V_1, V_2) \equiv$

Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$

The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is: