Mathematics - Online Test
Q1. Let P ( n ) denote the statement is odd , It is seen that , therefore P ( n ) is true for all
Answer : Option A
Explaination / Solution:
Since if n = 1 the answer is 2 which is even . also p ( 1 ) = p ( 2 ) is also not true since p(2 ) is 6 which is even.
Q2. Two perpendicular tangents to the circle meet at P. The locus of P is
Answer : Option C
Explaination / Solution:
locus of P is a circle with centre at origin and radius .This is known as the director circle of the circle
Q3. Determine order and degree (if defined) of +sin(y’’’) = 0
Answer : Option A
Explaination / Solution:
Order = 4 , degree not defined , because the function y’’’ present in the angle of sine function.
Q4. 5 persons board a lift on the ground floor of an 8 storey building. In how many ways can they leave the lift?
Answer : Option A
Explaination / Solution:
Since they are boarding from ground floor and we are considering the number of ways they leave the lift ,we can consider there are 7 floor sas we exclude the ground floor)
As each of the 5 persons can leave the lift in 7 ways, required number of ways= 75
Q5. If and are the direction cosines of two lines; and is the acute angle between the two lines; then
Answer : Option A
Explaination / Solution:
If and are the direction cosines of two lines; and is the acute angle between the two lines; then the cosine of the angle between these two lines is given by : .
Q6. The area of a triangle is and its perimeter is 8 cm. The radius of its inscribed circle is
Answer : Option A
Explaination / Solution:
Q7.
The area bounded by y = 2cosx , x = 0 to x =2π and the axis of x in square units is
Answer : Option C
Explaination / Solution:
$= = == 2
Therefore , total area from x= 0 to x = 2 is 4 X 2= 8 sq. units.
Therefore , total area from x= 0 to x = 2 is 4 X 2= 8 sq. units.
Q8. The lines, which do not lie in the same plane, are called ?
Answer : Option C
Explaination / Solution:
Lines which lie in same plane can be parallel, coincident or intersecting.
Skew lines are those lines which lie in different planes and never meet to each other
Q9. If a square matrix A has two identical rows or columns , then det.A is :
Answer : Option C
Explaination / Solution:
If two rows or column of a matrix are identical then determinant of such a matrix is zero.
Q10. The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all x∈R , if
Answer : Option D
Explaination / Solution:
f ( x) = mx + c is strict decreasing on R
if f ‘ ( x) < 0 i.e. if m < 0 .
