Mathematics - Online Test
Q1. Equation of the tangent to the curve at the point (a, b) is
Answer : Option D
Explaination / Solution:
Q2. The next term of the sequence 1, 5, 14, 30, 55, …… is
Answer : Option C
Explaination / Solution:
Q3. If mean = ( 3 median – mode ) x , then the value of x is
Answer : Option A
Explaination / Solution:
We know that, 3median = mode + 2 mean
so, mean= (3 median - mode)/2 ........(1)
comparing equation(1) with the given equation
therefore, x=1/2
Q4. The area bounded by the curve and the line x + y = 3 is
Answer : Option B
Explaination / Solution:
Q5. The relation R on the set Z of integers given by R = {(a, b): 2 divides a – b} ,∀ a, b ∈ Z is
Answer : Option C
Explaination / Solution:
- Since a – a = 0 , and 0 is divisible by 2 , therefore, aRa i.e. R is reflexive.
- If aRb , then a – b is divisible by 2. - ( a- b ) is divisible by 2. (b – a ) is divisible by 2. bRa i.e. R is symmetric. .
- .
- If aRb and bRc , then a – b is divisible by 2 and b – c is divisible by 2 a – b = 2q and b – c = 2q’ where q and q’ are integers. ( a – b ) + ( b – c ) = 2 ( q + q’) a – c =2( q + q’) ,,but (q +q’) is an integer. (a –c ) is divisible by 2. aRc i.e. R is transitive. .
Q6. The determinant 
is equal to
is equal to
Answer : Option A
Explaination / Solution:
(Since C1 =0)
(Since C1 =0)
Q7. Given the 4 lines with equations x + 2y – 3 = 0, 2x + 3y – 4 = 0, 3x + 4y – 5 = 0, 4x + 5y – 6 = 0 , then these lines are
Answer : Option A
Explaination / Solution:
The lines are concurrent
On solving the lies 1 and 2 we get the point of intersection as (-1,2)
Similarly on solving lines 2 and 3, the point of intersection is (-1,2)
Similarly solving the lines 3 and 4, the point of intersection is (-1,2)
on solving lines 1 and 4 the point of intersection is (-1,2)
Since the point of intersection is the same for all the lines, the lines are concurrent.
Q8. “If the figure is a rhombus then the diagonals are perpendicular “. The contrapositive of the above statement is
Answer : Option B
Explaination / Solution:
p: the figure is a rhombus q: the diagonals are perpendicular
Contrapositive of
hence If the diagonals are not perpendicular, then the figure is not a rhombus
Q9. dx is equal to
Answer : Option D
Explaination / Solution:
Q10. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
Answer : Option C
Explaination / Solution:
