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 ?
\( \int \left( \frac{1}{7} - 6x - x^2 \right) \, dx \)
\( \int \frac{dx}{\sin(x) + \cos(x)} = ? \)
Find ∫(cos√x) dx=?
If surrounding air is kept at 20 °C and body cools from 80 °C to 70 °C in 5 minutes, then the temperature of the body after 15 minutes will be
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?
20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
Give that f(x) =\(\frac {1-cos4x}{x^2}\) if x < 0 ,f(x) = a if x = 0 , f(x) =\(\frac {\sqrt {x}}{\sqrt {16 + \sqrt {x} }- 4}\) if x > 0, is continuous at x = 0, then a will be
In a triangle ABC, with usual notations ∠A = 60°, then (1 + \(\frac {a}{c}\) + \(\frac {b}{c}\))(1 + \(\frac {c}{b}\) - \(\frac {a}{b}\)) = ?