Mathematics - Online Test
Q1. 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
Q2. 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
Q3. If x then sin 2 θ is equal to
Answer : Option B
Explaination / Solution:
.
Q4. 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
Q5. 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
Q6.
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.
Q7. 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:
Q8.
Find the values of p so that the linesare at right angles.
Answer : Option B
Explaination / Solution:
Q9.
If then n is
Answer : Option A
Explaination / Solution:
Q10. The line is
Answer : Option C
Explaination / Solution:
The line is parallel to Z- axis as here value of x and y is fixed . Here whatever be the value of z , x and y will be fixed So it represent a plane parallel to Z axis
