Mathematics - Online Test
Q1. The equation of the tangent to the curve at the point is
Answer : Option B
Explaination / Solution:
Q2. Ltx→0+x√16+x√√−4
Answer : Option D
Explaination / Solution:
Q3. Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Answer : Option B
Explaination / Solution:
Objective function is Z = x + y ……………………(1).
The given constraints are : x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Here , there is no common feasible region between the lines x – y = - 1 and - x + y = 0 .
Therefore , it has no solution. Thus , Z has no maximum value .
The given constraints are : x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Here , there is no common feasible region between the lines x – y = - 1 and - x + y = 0 .
Therefore , it has no solution. Thus , Z has no maximum value .
Q4. Solve the system of inequalities
Answer : Option A
Explaination / Solution:
Hence solution set is
which implies no solution exists.
Q5. If a, b, c are in A. P. as well as in G.P.; then
Answer : Option B
Explaination / Solution:
a,b,c are in A.P, .......................(i)
a,b,c are in G.P, .............................(ii)
from (i) and (ii), we get
using a=c in (ii)
so, a=b=c
Q6.
The area enclosed by the curve and the y – axis is
Answer : Option B
Explaination / Solution:
Q7. If a, b, c be any three positive numbers, then the least value of
Answer : Option A
Explaination / Solution:
A.M≥H.M⇒a+b+c3≥31a+1b+1c⇒(a+b+c)(1a+1b+1c)≥3×3≥9
Q8. A Relation is a
Answer : Option D
Explaination / Solution:
By definition of Relation, : A relation from a non-empty set A to a non empty set B is a subset of A x B . If ( x, y) ∈ R , then we write xRy and we say that x is related to y through R.
Q9. One of the factors of 
Answer : Option D
Explaination / Solution:
Therefore, one of the factors of given determinants is (a + b + c +d ).
Q10. The acute angle between the lines ax + by + c = 0 and ( a + b )x = ( a – b )y , a ≠ b , is
Answer : Option C
Explaination / Solution:
The slope of the first line is -(a/b) and slope of the second line is
Angle between the lines is =
Let m1 =-(a/b) and m2 =
Hence =[
On simplifying we get,
= 1
This implies = 450
