Mathematics - Online Test
Q1. If x and z = then
Answer : Option C
Explaination / Solution:
Q2. A pack of coffee powder contains a mixture of x grams of coffee and y grams of choco. The amount of coffee is greater than that of choco and each coffee powder pack is atmost 10 grams. Which of the following inequations describe the conditions given ?
Answer : Option C
Explaination / Solution:
Given in the mixture ,amount of coffee= x grams
Amount of choco=y grams
Amount of coffee is greater than that of choco
Each coffee powder pack is atmost 10 grams
Q3. The sum of first three terms of a G.P. is to the sum of next three terms is 125 : 27. The common ratio of the G.P. is
Answer : Option D
Explaination / Solution:
Q4. 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
Q5. 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.
Q6. 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 .
Q7. 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
Q8. 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 =
Q9. 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.
Q10. ∼(∼p)↔p is
Answer : Option A
Explaination / Solution:
