A condition for a function y = f(x) to have inverse is that it should be
The area bounded by the x-axis and the curve y = 4 x − x2 − 3 is
y = 0, y = 4x - x2 - 3
⇒ 4x - x2 - 3 = 0
⇒ x2 - 4x + 3 = 0
⇒ (x - 1) (x - 3) = 0
⇒ x = 1, 3
If the function f is defined by then at what points is f differentiable
If z2 + z + 1 = 0, where z is a complex number then the value of
If is continuous at π/4 , then a =
The solution of the differential equation cos(x + y)dy = dx is
The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is
The roots of the equation are
The degree of the differential equation
The differential equation which represents the family of plane curves y=exp. (cx) is
y = ecx
dy dx = c. ecx
y' = cy
If x=a[(cost)+(log tan(t/2))], y=a sint, (dy/dx)=
The range of the function f(x) = x2 - x/x2 + 2x is
If where n > 1 , then In − In − 2
sec2(tan-1 2) + cosec2(cot-1 3) =
What is the value of
The value of
Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?
Statements are logically equivalent to their contrapositives.
If A is a singular matrix, then A adj (A)
If A and B both are of order 2 x 3 , which one of these is not defined ?
Twelve students compete for a race. The number of ways in which first three prizes can be taken is
An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is
A committee of 5 is to be chosen from a group of 9 people. What is the probability that a certain married couple serve together or not at all ?
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.
In a triangle , then b =
If the sum of n terms of the series 23 + 43 + 63 + ... ∞ is 3528, then n equals
The Quartile Deviation of the daily wages (in Rs) of 7 persons given below :
12, 7, 15, 10, 17, 19, 25 is
The S.D. of 5 scores
1 2 3 4 5 is
If x is positive, the greatest value of 5+4x-4x2 is
The degree of the equation is ____
A st. line which makes an angle of 600 with each of y and z axes, inclines with x-axis at an angle
The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are
If sin2x+sin4x=2sin3x, then x=
Locus of centroid of the triangle whose vertices are (a cost, a sint), (b sint, -b cost) and (1, 0), where t is a parameter, is
In a ∆ABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is
If θ is the angle between vectors a and b and |axb|=a.b, then θ=
The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k is