Mean + Variance = 1.8, n = 5, Find p(probability of success).
Find variance of first 2n natural numbers.
\( \sum (x - x_i)^2 = 100 \), no. of observations = 20, \( \sum x_i = 20 \).
Find cos248o - sin212o , if sin18o = (√5 - 1)/4
If a pair of line given by \( (x \cos \alpha + y \sin \alpha)^2 = (x^2 + y^2) \sin^2 \alpha \) are perpendicular. What is the value of α?
\( \lim_{x \to 0} \frac{x \cdot \cot(4x)}{\sin(2x) \cdot \cot^2(2x)} = ? \)
\(\int \frac{1}{\cos^3 x \sqrt{\sin 2x}} \, dx\)
\( -\tan\left(\frac{1}{x}\right) + \frac{1}{x} + c = ? \)
\(\int \frac{1}{(x + 2)(1 + x)^2} \, dx\)
\( \int_0^\pi \frac{x \tan(x)}{\sec(x) + \cos(x)} \, dx = ? \)
\( \int \frac{(x^2 - 1)}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx = ? \)
\( \int_0^1 \cos^{-1}(x) \, dx = ? \)
\( \int e^x (1 - \cot(x) + \cot^2(x)) \, dx = ? \)
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.
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 ?