List of top Mathematics Questions asked in MHT CET

\( \int e^x (1 - \cot(x) + \cot^2(x)) \, dx = ? \)

Find the differential equation of all circles passing through the origin and having their centres on the x-axis.

In a certain culture of bacteria the rate of increase is proportional to the no.of bacteria present at that instant it is found that there are 10000 bacteria present in 3 hours and 40000 bacteria at the 5 hours the number of bacteria present in the beginning is?

The area spherical balloon of radius 6 cm increases at the rate of 2 then find the rate of increase in the volume.

The radius of a cylinder is increasing at the rate 2 cm/sec and its height is decreasing at the rate 3 cm/sec, then find the rate of change of volume when the radius is 3cm and the height is 5 cm.

Out of five siblings, what is the probability that the eldest and youngest children have the same gender?

If ax + by + c = 0 is normal to xy = 1, then determine if a and b are less than, greater than, or equal to zero.

If \(\int_0^{\pi/2} \log(\cos x) \, dx = \frac{\pi}{2} \log\left(\frac{1}{2}\right)\), then find \(\int_0^{\pi/2} \log(\sec x) \, dx\).

Find the general solution of the differential equation: cosx (1 + cosy) dx - siny (1 + sinx) dy = 0

Three vectors a, b and c are given. Find the equation of a vector that lies in the plane of vector a and vector b and whose projection on vector c is 1/√3.

What is the number of solutions of tanx + secx = 2 cosx if x belongs to (0, 2π)?

Find the coordinates of the point where the line through A (9, 4 , 1) and B (5, 1, 6) crosses X axis ?

Find k if \(\int_{0}^{\frac{1}{2}}[\frac{x^2dx}{(1-x^2)^{\frac{3}{2}}}]=\frac{k}{6}\).

\( \int \frac{dx}{\sin(x) + \cos(x)} = ? \)

A man takes a step forward with a probability 0.4 and backward with a probability 0.6. The probability that at the end of eleven steps, he is one step away from starting point is?

Find \(tan^{-1}[\frac{(1-sin\,x+cos\,x)}{(1+sin\,x-cos\,x)}]\) = ?

Two lines \(2x=3y=-z\) and \(6z=-y=-4z\) intersect at a point, then find the angle between them.

Find the equivalent of \( p \land (q \lor r) \lor \neg (r \land \neg (p \land q)) \).

Find the value of \(\int\frac{dx}{\,sin^2x\,cos^2x}\) = ?

Find ∫(cos√x) dx=?

Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?

∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then

If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then equation of the circle is (Taken π=\(\frac {22}{7}\))

If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is