Mathematics - Online Test
Q1. The number of selections of n different things taken r at a time which exclude m particular things is
Answer : Option A
Explaination / Solution:
No: of combinations of n different things taken r at at a time is given by nCr
No: of combinations of n different things taken r at a time and excluding m particular things is n - mCr = C(n-m,r)
Q2. The order of the equation = 0 is
Answer : Option B
Explaination / Solution:
Since the highest derivative term is hence the order is 3.
Q3. If l, m, n are the direction cosines and a, b, c are the direction ratios of a line then
Answer : Option D
Explaination / Solution:
using direction ratio a,b,c we got a vector along the line ,for direction cosine find unit vector then 
where l,m,n represent direction cosine
where l,m,n represent direction cosine
Q4.
In a (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to
Answer : Option B
Explaination / Solution:
Q5. AOB is the positive quadrant of the ellipse in which OA = a and OB = b . The area between the arc AB and chord AB of the ellipse is
Answer : Option B
Explaination / Solution:
Required area :
= area of ellipse – area of right angled triangle AOB.
= area of ellipse – area of right angled triangle AOB.
= ab – ab = ( - 2 ) .
Q6. How many lines through the origin make equal angles with the coordinate axes ?
Answer : Option C
Explaination / Solution:
hence the lines will be 8
Q7. The number of all the possible matrices of order 2 × 2 with each entry 0, 1 or 2 is
Answer : Option A
Explaination / Solution:
The number of elements in a 2 x 2 matrix is the product 2 x 2 =4
Each element can either be a 0,1 or 2.
Given this, the total possible matrices that can be selected is 34
Q8. The function f (x) = 2 – 3 x is
Answer : Option C
Explaination / Solution:
f (x) = 2 – 3x f ‘ (x) = - 3 < 0 for all x R . so, f is strictly decreasing function.
Q9. If A and B be any two sets , then (A∩B) ‘ is equal to
Answer : Option B
Explaination / Solution:
Q10. If then a and b are respectively :
Answer : Option A
Explaination / Solution:
