Mathematics - Online Test
Q1. If is equal to
Answer : Option A
Explaination / Solution:
secθ+ tanθsecθ−tanθ=1cosθ+sinθcosθ1cosθ−sinθcosθ=1+sinθ1−sinθ=1+351−35=4
Q2. If [x] stands for the integral part of x, then
Answer : Option D
Explaination / Solution:
The is defined as the value which takes the nearest small integer in every integer interval . For example in the interval the value of the function is 0 since it is the lowest integer in that interval . Hence which gives the value as 1,which is the lowest integer of that interval.
Q3. The smallest +ve integer n , for which holds is
Answer : Option A
Explaination / Solution:
when n = 2 , L H S : n ! = 2 ! = 2x1 = 2 RHS:
But if n = 1 , the inequation does not hold good.
Q4.
The equation represents
Answer : Option C
Explaination / Solution:
The general equation of the circle is x2+y2-2gh-2fy+c = 0. Sice the given equations satisfies the general equation, it represents the equation of the circle.
Q5. 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)
Q6. The order of the equation = 0 is
Answer : Option B
Explaination / Solution:
Since the highest derivative term is hence the order is 3.
Q7. 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
Q8.
In a (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to
Answer : Option B
Explaination / Solution:
Q9. 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 ) .
Q10. The two vectors [1,1,1] and [1, a, a2], where a = 
, are
, are
Answer : Option B
Explaination / Solution:
Dot product of two vectors = 1 + a + a2 = 0
So orthogonal
