Mathematics - Online Test
Q1. The lines y = mx , y + 2x = 0 , y = 2x + λ and y = - mx + λ form a rhombus if m =
Answer : Option B
Explaination / Solution:
Rhombus is a parallelogram in which the opposite sides are equaland parallel.
Therefore the lines y = mx and y = -2x are parallel, similarly y = 2x+ and y = -mx + are parallel.
If two lines are equal, then their slopes are qual
This implies m = -2
Q2. Which of the following is not a proposition ?
Answer : Option A
Explaination / Solution:
The above statement is a fact and the other options are mathematical statements which are proposition .
Q3. is equal to
Answer : Option B
Explaination / Solution:
Q4. Which of the following is a vector?
Answer : Option A
Explaination / Solution:
Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.and velocity specifies direction
Q5. If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∩ B)
Answer : Option A
Explaination / Solution:
We have ,
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
Q6. If x then sin 2 θ is equal to
Answer : Option B
Explaination / Solution:
.
Q7. Let f(x) = | x−1|, then
Answer : Option A
Explaination / Solution:
here f(x)=|x−1| x∈R. So f(x) is not derivable when x−1=0 i.e. at x=1
Q8. Three normals to the parabola are drawn through a point (c, 0) then
Answer : Option D
Explaination / Solution:
The equation of the normal to a parabola y2 = 4ax is
y = mx -2am - am3
Hence the equation of the normal to the given parabola y2 = x is
mx - -
Since it passes throught (c,0)
mc -- = 0
on solving we get
m = 0 or m2 = 4(c-1/2)
If m = 0 then the equation of the normal is y = 0
If m2 0, then 4(c-1/2) 0
Hence c-1/2 0 or c > 1/2
Q9.
If is divisible by 9 for all n N , then the least positive integral value of k is :
Answer : Option C
Explaination / Solution:
When n = 1 we have 58. Given that the expression is divisible by 9 . Hence the least value of k will be 5,so that the value becomes 63 which is divisible by 9.
Q10. In a triangle ABC, a = 13, b = 14, c = 15; then the radius of the incircle r of triangle ABC=
Answer : Option C
Explaination / Solution:
