Relation,Function & Inverse Trigo
If R = {(x,y): x + 2y = 8} is a relation on N, then write the range on N
Solution : Range = {3,2,1}
What is the value of the determinant
First Row 0 2 0
Second Row 2 3 4
Third Row 4 5 6
Solution : 8
If y = cosec-1x then dy/dx = ?
Solution= - 1/{x. (x2 - 1)1/2}
Write a unit vector in the direction of 2i - 6j + 3k
Solution :1/7.(2i - 6j + 3k)
If A and B are mutually exclusive events such that P(A) = 0.4 , P(B) = x and P(AUB) = 0.5 then x =?
solution : 0.1
If R: R --> R defined by f(x) = 3x + 2 then define f(f(x))
Solution: 9x + 8
Find |adj.A| if Matrix A = 5 2
7 3
Solution: | A| = 1
|adj. A| = |A| n-1
Answer = 1
Find the slope of the tangent to the curve y = 3x2 - 4x at the point (2,2)
Solution : 8
Find the cartesian equation of the line which passes through the point (-2,4, -5) and is parallel to the line
(x + 3)/ 3 = (4 - y)/5 = (z + 8)/6
Solution: (x + 2) /3 = (y - 4)/-5 = (z + 5)/6
The probabilities of A, B and C solving the problem are 1/6, 1/5 and 1/3 respectively. What is the probability that the problem is solved.
Solution: 5/9
Write the value of cos-1(-1/2) + 2 sin-1(1/2)
Solution: π (pi)
For what value of x the given matrix is singular?
(5 - x) (x + 1)
2 4
Solution : 3
Integrate 1 dx
(x2 - 6x + 10)1/2
Solution: log |(x -3) + (x2 - 6x + 10)1/2| + c
Find the sum of intercepts cut off by the plane 2x + y - z = 5 on the coordinate axes.
Solution: 5/2
Write the conditions and formulae of Bayes theorem for dependent event E with three other Events A, B and C.
Solution: A, B and C are Mutually exclusive and Mutually exhaustive.
P(A/E) = P(E/A) x P(A)
Total Probability
Relation R in a set of human beings in a town at a particular time is given by R = {(x,y), x is exactly 7cm taller than y}
Determine whether the relation is equivalence. If no then determine all possible relations
It is not equivalence, Not reflexive, Not symmetric and not Transitive.
For what value of x, is the matrix
0 1 -2
-1 0 3
x -3 0
a skew symmetric Matrix?
Solution: x = 2
Integrate from 0 to pi/2
sinx/(sinx + cosx)
Solution pi/4
Find the value of k such that the line
(x - 2)/6 = (y - 1)/k = (z + 5)/-4 is perpendicular to the plane
3x - y - 2z = 7
Solution: k = -2
Find the probability distribution of the number of heads when 3 coins are tossed.
Solution:
X : 0 1 2 3
P(x) : 1/8 3/8 3/8 1/8