Mathematics - Online Test
Q1. 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.
Q2. “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
Q3. dx is equal to
Answer : Option D
Explaination / Solution:
Q4. 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:
Q5. The value of is
Answer : Option D
Explaination / Solution:
Q6. If the lines 3x-4y + 4 = 0 and 6x -8y - 7 = 0 are tagents to the circle then the radius of the circle is
Answer : Option D
Explaination / Solution:
The given lines are paralle. Hence the tangents are parallel tangents. Distance between these lines is equal to the diameter
D = = 3/2
Therefore the radius is 3/4
Q7. is equal to
Answer : Option C
Explaination / Solution:
=
Q8. The general solution of the equation sin x + cos x = 2 is
Answer : Option D
Explaination / Solution:
Q9. If is divisible by 64 for all n N , then the least negative integral value of is
Answer : Option C
Explaination / Solution:
When n = 1 we have the value of the expression as 65 . Given that the expression is divisible be 64. Hence the value is -1.
Q10. The probability of having atleast one head in 5 throws of a coin is
Answer : Option A
Explaination / Solution:
No Explaination.
