\(∫\frac{dx}{(x2+1) (x2+4)} =\)
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
If
then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is
If order and degree of the differential equation corresponding to the family of curves y2 = 4a(x+a)(a is parameter) are m and n respectively, then m+n2 =
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
If x = log (y +√y2 + 1 ) then y =
In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius is
The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
if |a| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =
If A(1,2,3) B(3,7,-2) and D(-1,0,-1) are points in a plane, then the vector equation of the line passing through the centroids of △ABD and △ACD is
If a + b + c = 0. |a| = 3, |b| = 5, |c| = 7, then the angle between a and b is
If 2i - j + 3k, -12i - j - 3k, -i + 2j -4k and λi + 2j - k are the position vectors of four coplanar points, then λ =
Let a = i + 2j -2k and b = 2i - j - 2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |x - y| =
The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
A random variable X has the following probability distribution
For the events E = {x/x is a prime number} and F = {x/x <4} then P(E ∪ F)
5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of the independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is