Mathematics - Online Test
Q1. General solution of
Answer : Option D
Explaination / Solution:
Q2. If then is equal to:
Answer : Option A
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Q3. The coefficient of in the binomial expansion of is
Answer : Option C
Explaination / Solution:
Q4. If n (A ) =3 and n ( B ) = 6 and A⊆ B , then n(A∩B) is equal to
Answer : Option B
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Q5. The curve y = is inclined at to the X – axis at (0, 0) but it touches X – axis at (1, 0) , then the values of a, b, c, are given by
Answer : Option B
Explaination / Solution:
At ( 0 , 0) , slope of tangent = = 1. c = 1. At ( 1 ,0 ) , slope of tangent = 0.3a+2b+c=0. Also, when x = 1 , y = 0 , therefore , a + b + c = 0
At ( 0 , 0) , slope of tangent = = 1. c = 1. At ( 1 ,0 ) , slope of tangent = 0.3a+2b+c=0. Also, when x = 1 , y = 0 , therefore , a + b + c = 0
Q6.
The area between the hyperbola , then x – axis and the ordinates at a and b with a > b is :
Answer : Option C
Explaination / Solution:
Required area :
= = = =
= = = =
Q7. If k be an integer, then is equal to
Answer : Option C
Explaination / Solution:
Q8. The solution set for ( x + 3 ) + 4 > − 2x + 5:
Answer : Option B
Explaination / Solution:
Q9. Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.
Answer : Option A
Explaination / Solution:
Objective function is Z = x + 2 y ……………………(1).
The given constraints are : 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0 .
Corner points | Z = x + 2y |
A(0 ,3 ) | 6…………………..(Minimum) |
B(6,0) | 6………………………(Minimum) |
Here , Z = 18 is minimum at ( 0, 3 ) and ( 6 , 0 ) .
Minimum Z = 6 at all the points on the line segment joining the points (6, 0) and (0, 3).
Q10. The sum of first four terms of an A. P. is 56 and sum of last four terms is 112. If the first term is 11, then the number of terms is
Answer : Option B
Explaination / Solution:
