The area of the circle with centre (h,k) and radius a is
[(1+cosθ+i sinθ)/(i+sinθ+i cosθ)]^{4} = cos nθ + isin nθ, then n=
The differential equation which represents the family of plane curves y=exp. (cx) is
If the domain of function f(x) = x^{2}  6x + 7 is (∞, ∞), then the range of function is :
In the following question, a Statement1 is given followed by a corresponding Statement2 just below it. Read the statements carefully and mark the correct answer
Let a, b, c, p, q be real numbers. Suppose α,β are the roots of the equation x^{2} + 2px + q = 0 and a, 1/β are the roots of the equation ax^{2} + 2bx + c = 0, where β^{2} ∉ {1, 0, 1}
Statement1:
(p^{2}q)(b^{2}ac)≥0
Statement2:
b≠pa or c≠qa
The angle between the pair of tangents drawn from the point (1,2) to the ellipse 3x^{2} + 2y^{2}= 5 is
(d/dx)[cos(1x^{2})^{2}]=
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): e^{x} , log_{e} x are two functions such that each is the image of the other with respect to the line x = y
Reason (R): The inverse of every bijective function is symmetric about the line x = y
A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)^{2} rupees. The dimensions of the tank for the least total cost are
The same roots of 34 i are
Everybody in a room shakes hands with every body else. The total number of hand shakes is 66. Then the number of persons in the room is
There are n people in the room
n(n  1)/2 = 66
n^{2}  n = 132
n^{2}  n  132 = 0
n^{2}  12n + 11n  132 = 0
n(n  12) + 11(n  12) = 0
(n + 11) (n  12) = 0
n = 12,  11
Hence total no of persons = 12
If the sum of the squares of the roots of x^{2} + px  3 = 0 is 10, then the values of p =
Three identical dice are rolled. The probability that the same number will appear on each of them, is
If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon
M telegrams are distributed at random over N communication channels (N > M). The probability of the event
A = {not more than one telegram will be sent over any channel} is
The total no. of ways of distributing M telegrams over N channels = N^{M}
The number of ways of choosing M channels out of N to send one telegram over each channel = ^{N}C_{M}
∴ Total no. of ways to send M telegrams over each channel = ^{N}C_{M} . M!
∴ Required probubility
The equation of a line passing through (a,0) and form a triangle of area 'T' with coordinates axes, is
If then value of L/128 is :
If the function is continuous in the interval (–∞, 6) then value of is
Value of is equals to
(where [.] denotes greatest integer function)
If the area bounded by curve x + y = 1 and the yaxis is k, then k/4 is equals to
If value of is k then k/4 is
k = 3
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