If x dy= y(dx + ydy), x(1)=1, y(x)>0, then y (-3) is?
If \(1+ (√1+x) tanx = 1+ (√1-x)\) then \(sin4x\) is ?
The area spherical balloon of radius 6 cm increases at the rate of 2 then find the rate of increase in the volume.
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
Find the coordinates of the point where the line through A (9, 4 , 1) and B (5, 1, 6) crosses X axis ?
What is the number of solutions of tanx + secx = 2 cosx if x belongs to (0, 2π)?
Find the differential equation of all circles passing through the origin and having their centres on the x-axis.
∫ex (1 - cotx + cot2x) dx = ?
∫01cos-1x dx = ?
∫0π (xtanx) dx/(secx + cosx) = ?
∫ (dx/(sinx + cosx)).dx = ?
Find cos248o - sin212o , if sin18o = (√5 - 1)/4
If a pair of line given by (xcosα + ysinα)2 = (x2 + y2)sin2α are perpendicular. What is the value of α?
Lim x -> 0 x.cot4x / (sin2x cot2(2x))
Solve for x, given tan-1 (1 - x/1 + x) = ½ tan-1x
If a, b, c are position vectors of points A, B, C respectively, with 2a + 3b -5c = 0 , then the ratio in which point C divides segment AB is
For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to
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
The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is
With reference to the principal values, if sin-1x + sin-1y + sin-1z = \(\frac {3π}{2}\), then x100 + y100 + z100 =?
If the standard deviation of first n natural numbers is 2, then the value of n is
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?