List of top Mathematics Questions

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=?

\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
Let a1, a2, a3,.....,an be positive real numbers.Then the minimum value of \(\frac{a_1}{a_2}+\frac{a_2}{a_3}+....+\frac{a_n}{a_1}\) is
Let f be a strictly decreasing function defined on R such that f(x)>0,∀x∈R. Let \(\frac{x^2}{f(a^2+5a+3)}+\frac{y^2}{f(a+15)}=1\) be an ellipse with a major axis along the y-axis. The value of 'a' can lie in the interval(s)
If R and R1 are equivalence relations on a set A, then so are the relations
A rectangle ABCD has its side parallel to the line y=2x and vertices A,B,D are on y=1,x=1 and x=-1 respectively. The coordinate of C can be
A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, Then 
Let f(x)=xm, m being a non-negative integer. The value of m so that the equality f'(a+b)=f'(a)+f'(b) is valid for all a,b>0 is