Mathematics - Online Test
Q1. Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.
Answer : Option D
Explaination / Solution:
Let the consecutive even positive integers be x and x+2.
By data, x>5 and
Now
So we have the least possible value of x is 6 and the maximum value of x is 10.
Therefore the possible pairs of consecutive even positive integers are (6,8) ,(8,10) ,(10,12).
Q2. If the numbers a,b,c,d,e are in A.P then find the value of a-4b+6c-4d+e
Answer : Option A
Explaination / Solution:
Q3. Which of the following is not a measure of dispersion ?
Answer : Option D
Explaination / Solution:
it is the measure of central tendency
Q4. Find the slope of the normal to the curve at
Answer : Option B
Explaination / Solution:
Q5. Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following is a function from A to B?
Answer : Option B
Explaination / Solution:
{(1, 3), (2, 3), (3, 3)} is a function ,because for each x ∈ A , there is a unique y ∈ B such that ( x , y) ∈f., i.e. xfy.
Q6. Find the area of triangle with vertices ( 1 ,1 ) , (2 ,2 ) and ( 3, 3 ).
Answer : Option C
Explaination / Solution:
AREA OF TRIANGLE= 
That is C1 and C2 are identical
so value of determinant =0
hence area of triangle =0
Q7. The orthogonal projection of the point ( 2 , - 3 ) on the line x + y = 0 is
Answer : Option B
Explaination / Solution:
Equation of the line which perpendicular to the given line is x - y + k = 0
Since this line passes through (2,-3)
2-(-3) + k = 0
This implies k= -5
Hence the equation og the line is x - y =5
On solving the lines x+y=0 and x-y=5, we get the point of intersection as x = 5/2 and y = -5/2
Hence (5/2,-5/2) is the coordinates of orthogonal projection.
Q8. Let p and q be two propositions. Then the inverse of the implication p→q is
Answer : Option D
Explaination / Solution:
inverse of p→q≡∼p→∼q
Q9. The area bounded by the curve y = x (x – 1 ) ( x – 2 ) and the x – axis is equal to
Answer : Option D
Explaination / Solution:
Q10. 
Answer : Option D
Explaination / Solution:
