If x +y = 60; x, y > 0, then maximum value of xy3 is
The area bounded by the x-axis and the curve y = 4x - x2 - 3 is
If R → R is continuous such that then f(100) =
The value of arg [(1-i√3)/(1+i√3)] is
(x + y + z) (x + y ω + z ω2) (x + yω2 + z ω) =
Multiply R1, R2, R3 by a, b, c respectively and divide by abc
Take abc common from C3 so that C1, C3 are identical
Which equation has the solution y=A sinx+B cosx?
The solution of the differential equation x2 dy/dx-xy=1+cos y/x is
Let f(x) = log |x - 1|, x ≠ 1. The value of is
The solution of the equation (1+x2)(1+y)dy+(1+x)(1+y2)dx=0 is
If f x = log x , g x = x3 then f[ga]+f[gb]
If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + b
If then I is equal to
The valuie of sin-1 cos(sin-1 x) + cos-1 sin (cos-1 x) is
True statement for
Consider the sentence: x < 5
Which of the following integers makes this open sentence true?
The only number less than 5 in the list of answers is 4.
If |A| represents the determinant of a square matrix of order 3 then (-2A)=
If B is a non-singular matrix and A is a square matrix, then det (B-1AB) =
Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?
Two dice are thrown simultaneously. The probability of obtaining a total score of seven is
There are six possible ways as to the number of points on the first die; and to each of these ways, there corresponding 6 possible numbers of points on second die.
Hence total number of ways S = 6 x 6 = 36
We now find out how many ways are favorable to the total of 7 points.
This may happen only in following ways:
(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3).
Hence, required Probability = 6/36 =1/6.
If S is a sample space, , where A, B are two mutually exclusive events, then P(A) =
In a Poisson distribution mean is 16, then S.D is
In Δ A B C , i f A = 600then
113 + 123 + 133 + ... + 203 is
For a frequency distribution mean deviation from mean is computed by
The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by (1/2) kg ; the weight of the teacher is
If x = 2 + i √3, then the value of, 4x2 + 8x + 13 is____
A quadratic equation whose one root is the square root of -47+8√-3 is
The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 is
A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be
The angle between the two straight lines represented by 6y2 - xy - x2 + 30y + 36 = 0 is
Let a, b and c be distributed non-vegetative numbers. If the vectors aî + aĵ + ck̂, î + k̂ and cî̂ + cĵ̂ + bk̂ lie in a plane, then c is
If vectors i+2j+3k and 3i-2j+k represents the adjacent sides of a parallelogram, the area of parallelogram is