Mathematics - Online Test
Q1. The area bounded by the curve y =x, the x – axis and the ordinates x = 1 and x = -1 is given by
Answer : Option B
Explaination / Solution:
Q2. The scalar product of two nonzero vectors 
is defined as
is defined as
Answer : Option B
Explaination / Solution:
The scalar product of two nonzero vectors 
is defined as : 
is defined as :
Q3. ∫cosx(1+sinx)(2+sinx)dx=
Answer : Option D
Explaination / Solution:
Q4. The relation is valid for
Answer : Option C
Explaination / Solution:
The relation is true for all real values of x greater than or equal to 1.
Q5. The line y = c is a tangent to the parabola x2 = y - 1 if c is equal to
Answer : Option C
Explaination / Solution:
putting the value y=c into parabola,we get
x2=c-1
or x2-(c-1)=0
here discriminat=
line y=c is tangent when discriminant is equal to 0.
putting disriminant =0 we get c=1.
(0, c) will be a point on the parabola.
Q6. The general value of satisfying the equation is
Answer : Option B
Explaination / Solution:
Q7.
is equal to
Answer : Option D
Explaination / Solution:
Q8. upto n terms is equal to
Answer : Option B
Explaination / Solution:
Replace n = 1 we have 1/2. When n = 2 we have 1/2+1/6=2/3,( by the principle of mathematical induction when n = 1 we need to take one term from LHS. and for n = 2 we need to take the sum of two terms from the LHS. .....)
Q9. In a certain town , 40% persons have brown hair , 25% have brown eyes , and 15% have both. If a person selected at random has brown hair , the chance that a person selected at random with brown hair is with brown eyes
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. The centre of the sphere , which passes through ( a , 0 , 0 ) , ( 0 , b , 0 ) ( 0 , 0 , c ) and ( 0 , 0 ,0 ) is ? where abc ≠ 0
Answer : Option D
Explaination / Solution:
General equation of the sphere is ---------------------1)
Since 1) passes through the point (0,0,0) using this in 1) we get d=0
Similarly 1) passes through ( a , 0 , 0 ) , ( 0 , b , 0 ) ( 0 , 0 , c ) using these values in 1)
But as abc0 So , a 0 ,b 0 ,c 0
So from above equations , we have a = - 2g , b= - 2f , c = -2h
centre is (-f ,-g , -h) = ( a/2 , b/2 , c/2 )
