Mathematics - Online Test

Q1. Roots of the algebraic equation x3 + x2 + x + 1 = 0 are
Answer : Option D
Explaination / Solution:



Q2. In a multiple choice question, there are 4 alternatives, of which one or more are correct. The number of ways in which a candidate can attempt this question is
Answer : Option B
Explaination / Solution:

Since given there are four alternatives in which one or more are correct,we have to consider the following four cases

The candidate choose 1 correct answer, 2 correct answers,3 correct answers or 4 correct answers.

1 correct answer can be chosen in 4C1 ways = 4 ways

 2 correct answer can be chosen in 4C2 ways= 6 ways

 3 correct answers can be chosen in  4C3ways  = 4 ways

4 correct answers can be chosen in4C4 ways = 1 way

 Hence the totalnumber of ways = 4 + 6 + 4+ 1=15ways


Q3. If the line 2x – y +  = 0 is a diameter of the circle  then  =
Answer : Option A
Explaination / Solution:

Equation of circle is 


Applying completing the square method


Comparing the above equation with   we get center as (-3,3) and radius as    .

As centre of the circlre lies on diameter , it will satisfy the equation of diameter, so on putting (-3,3) in equation of diameter we get


=> 

=>


Q4. The domain of the function √cosx-1
Answer : Option B
Explaination / Solution:

This function exists only if cosx−1≥0 ⇒cosx≥1 ⇒cosx>1 OR cosx=1 since maximum value of cosine function is 1 so, cos x >1 is not possible so, cosx=1 cosx=cos2nπ ⇒x=2nπ(n∈I)
Q5. Differential equations are equations containing functions y = f(x), g(x) and
Answer : Option C
Explaination / Solution:

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

Q6. Direction cosines of a line are
Answer : Option D
Explaination / Solution:

a line when intersect another line or axis two kind of angle form ,as an assumption we take positive side of axis, to define the direction of line we take angle made from all three axis.and we take cos not other trigonometric function like sin,tan because we can define Direction cosines of a line are coefficient of i,j,k of a unit vector along that line.

Q7. In a triangle ABC, tan , then tan  is equal to
Answer : Option C
Explaination / Solution:



Q8. The area of ellipse  is
Answer : Option D
Explaination / Solution:

Area of standard ellipse is given by :πab.

Q9. The distance of the point ( 3, 4, 5) from X- axis is
Answer : Option B
Explaination / Solution:

The distance of the point ( 3, 4, 5) from X- axis is

let L be the foot of perpendicular from the point ( 3, 4, 5) to X axis ,then coordinate of L will be (3,0,0)       [ because on X axis y and z coordinate are zero]

then distance of the point ( 3, 4, 5) from X- axis i.e. from L (3,0,0) is given by 


Q10. If A and B are symmetric matrices of the same order, then
Answer : Option C
Explaination / Solution:

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.