Mathematics - Online Test
Q1. Let p and q be two prepositions given by P : The sky is blue, q : Milk is white, Then , p and q is
Answer : Option D
Explaination / Solution:
using conjunction to combine statement
Q2. t dt is equal to
Answer : Option C
Explaination / Solution:
=[sint]π/2−π/2=sinπ2−sin(−π2)=1+1=2
Q3. Position vectors of points A, B, C, etc., with respect to the origin O are generally denoted by
Answer : Option B
Explaination / Solution:
Position vectors of any point in space are usually calculated from the origin, so we write three points A ,B,C in space to represent the origin as the initial point.
Q4. A coin is tossed three times, E : at most two tails , F : at least one tail. Find P(E|F)
Answer : Option C
Explaination / Solution:
Q5. The maximum value of sin x + cos x is
Answer : Option D
Explaination / Solution:
(12√)+(12√)=2–√
Q6. is equal to
Answer : Option B
Explaination / Solution:
Q7. If x -1 , then the statement is true for
Answer : Option D
Explaination / Solution:
For example , if x = 0 and n > 1 , say n = 2 then the given inequality will become 12 > 1 , which is not true. Hence both the conditions on x and n are needed.
Q8. The number of triangles that can be formed with 6 points on a circle is
Answer : Option D
Explaination / Solution:
To form a triangle 3 non collinear points are needed.
Number of ways of selecting 3 points out of 6 can be done in 6C3 = 20 ways.
Q9. The circles and
Answer : Option B
Explaination / Solution:
Circle touches externally if distance between the centers is equal to the sum of the radii .
After applying completing the square, we get
so the center is (-3,-3) and radius is
After applying completing the square
so the center is (6,6) and radius is
Distance between centres 
and sum of radii 
are equal.
and sum of radii are equal.Hence the circle touches externally.
Q10. Degree of a differential equation, when the equation is polynomial equation in y′ is
Answer : Option B
Explaination / Solution:
The power or index of the highest ordered derivative in the polynomial is the degree of the differential equation provided equation is in the standard form.
