Mathematics - Online Test
Q1. The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y – 13 = 0 is
Answer : Option A
Explaination / Solution:
Distance between parallel lines is given by
Now substituting the values we get,
=
Q2. Let p and q be two prepositions given by p : A parallelogram is a rhombus. q : The diagonals are at right angles. The compound proposition “ A parallelogram is a rhombus iff its diagonals are at right angles “ is represented by
Answer : Option B
Explaination / Solution:
iff means a double implication statement so symbolic form has ↔
Q3. (tan x) dx is equal to
Answer : Option D
Explaination / Solution:
Q4. The unit vector in the direction of a given vectoris denoted by
Answer : Option D
Explaination / Solution:
, is called the unit vector of a given vector in the direction of
Q5. If A and B are events such that P(A|B) = P(B|A), then
Answer : Option B
Explaination / Solution:
It is given that :
Q6. tan x is periodic with period
Answer : Option C
Explaination / Solution:
The values of tanx repeats after an interval of π.
Q7. If k be an integer, then (x –[x])
Answer : Option C
Explaination / Solution:
= k - (k - 1) = 1 for all
Q8. The greatest positive integer, which divides , is
Answer : Option D
Explaination / Solution:
If n = 0 the given expression becomes 1.2.3.4........r = r! Also when n = 1 one more extra term will be there in the product 2.3.4........which is also divisible by r!.
Q9. The number of tangents to the circle which pass through the point ( 3, - 2), is
Answer : Option D
Explaination / Solution:
After completing the square,we get
so center is (4,3) and radius is 4.
Distance between center and given point 
which is greater than 4.
hence point lies outside the circle .
Since point lies outside of the circle there will be 2 tangents since two tangents can be drawn from external point to a circle.
Q10. Determine order and degree (if defined) of y’ + 5y = 0
Answer : Option C
Explaination / Solution:
Order = 1 , degree = 1. Since the equation has the highest derivative as y' and its power is 1
