Mathematics - Online Test
Q1. The mean of 50 observations is 36, if two observations are 30 and 42 are deleted , then the mean of the remaining observations is
Answer : Option D
Explaination / Solution:
After deleting the observations 30 and 42
new sum
new mean
Q2. Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0 } then
Answer : Option D
Explaination / Solution:
Since given f(x) is differentiable in (2,3) and f(2) = f(3) we have conditions of Rolle′s Theorem are satisfied by f(x) in [2,3]. Hence there exist atleast one real c in (2,3) s.t.f′
(c) = 0. Therefore, the set S contains atleast one element.
Q3. Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is
Answer : Option D
Explaination / Solution:
We have Z = px + qy , At ( 3, 0 ) Z = 3p ……………………………….(1) At ( 1 , 1) Z = p + q …………………………(2) Therefore , from (1) and (2) : We have : p = q/2 .
Q4. The range of the function f(x) = [sin x] is
Answer : Option B
Explaination / Solution:
The only possible integral values of sin x are { -1 ,0, 1 }.As −1≤sinθ≤1
Q5. If A is a non singular matrix of order 3 , then =
Answer : Option A
Explaination / Solution:
If A is anon singular matrix of order , then =
Q6. The number of lines that are parallel to 2x + 6y – 7 = 0 and have an intercept 10 units between the coordinate axis is :
Answer : Option B
Explaination / Solution:
Thslope of the given line 2x+6y = 7 is -1/3
Hence the line which is parallel to the above line is
y = (-1/3)x+c
That is the y intercept is (0,c) and the x intercept is (3c,0)
Using the distance formula
d2 = (0-3c)2 + (3c-0)2
= 10c2
since the distance is 10 is given,
100 = 10c2
therefore c = 10
Since two values are possible, two lines can be drawn.
Q7. ∼(∼p)↔p is
Answer : Option A
Explaination / Solution:
Q8.
Answer : Option A
Explaination / Solution:
The tangents are
since .
It passes through ( -2 , 0 ).
The tangents are :
Required area :
since .
It passes through ( -2 , 0 ).
The tangents are :
Required area :
Q9. If a unit vector makes angles , then find
Answer : Option C
Explaination / Solution:
Let
It is given that
, then,
Putting these values in (1), we get:
It is given that
, then,
Putting these values in (1), we get:
Q10. If f (x) = f (a –x), then , is equal to
Answer : Option C
Explaination / Solution:
