Mathematics - Online Test
Q1. Let R be the relation on N defined as x R y if x + 2 y = 8. The domain of R is
Answer : Option A
Explaination / Solution:
As x R y if x + 2 y = 8 , therefore , domain of the relation R is given by x = 8 – 2y∈N. When y = 1, ⇒x = 6 ,when y = 2, ⇒x =4 , when y =3 , ⇒x = 2 . therefore domain is { 2, 4, 6 }.
Q2. The line through the points (a , b) and (- a , - b) passes through the point
Answer : Option C
Explaination / Solution:
Equation of a line passing through (x1,y1) and (x2,y2)
=
Substituting the given values we get,
=
That is =
On cross multiplying and reaaranging we get,
bx - ay = 0
If this passes through the given point (a2,ab) then
b(a2) - a(ab) = 0
Q3. Let p and q be two prepositions given by p : It is hot, q : He wants water Then , the verbal meaning of p→q is
Answer : Option C
Explaination / Solution:
→ symbol is replaced by if p then q
Q4. is equal to
Answer : Option A
Explaination / Solution:
Q5. Direction cosines
Answer : Option D
Explaination / Solution:
Cosines of the angles α,β,γ are called direction cosines.
Q6. A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Answer : Option A
Explaination / Solution:
Q7. If is equal to
Answer : Option A
Explaination / Solution:
secθ+ tanθsecθ−tanθ=1cosθ+sinθcosθ1cosθ−sinθcosθ=1+sinθ1−sinθ=1+351−35=4
Q8. If [x] stands for the integral part of x, then
Answer : Option D
Explaination / Solution:
The is defined as the value which takes the nearest small integer in every integer interval . For example in the interval the value of the function is 0 since it is the lowest integer in that interval . Hence which gives the value as 1,which is the lowest integer of that interval.
Q9. The smallest +ve integer n , for which holds is
Answer : Option A
Explaination / Solution:
when n = 2 , L H S : n ! = 2 ! = 2x1 = 2 RHS:
But if n = 1 , the inequation does not hold good.
Q10.
The equation represents
Answer : Option C
Explaination / Solution:
The general equation of the circle is x2+y2-2gh-2fy+c = 0. Sice the given equations satisfies the general equation, it represents the equation of the circle.
