Mathematics - Online Test
Q1. If, then x =
Answer : Option A
Explaination / Solution:
Because , ,
Q2. The area of the circle centred at (1,2) and passing through (4,6) is
Answer : Option C
Explaination / Solution:
Given centre = (1,2)
Therefore radius = = 5 units
Area of the circle is = sq units
Q3. Number of solutions of the equation tan x + sec x = 2 cos x. lying in the interval [0,2π] is
Answer : Option B
Explaination / Solution:
Q4. up to n terms is equal to
Answer : Option A
Explaination / Solution:
By the process of mathematical induction when n = 1 we have 1/15. When n = 2 we have LHS : 1/15+1/35=2/21, RHS :2/(3(4+3))=2/21, which is true
Q5. The probability that a card drawn at random from a pack of 52 cards is a king or a heart is
Answer : Option C
Explaination / Solution:
No Explaination.
Q6. The equations of y axis are
Answer : Option A
Explaination / Solution:
Since on Y axis x and z coordinate are 0 .
So , Equations of Y axis are X=0 and Z=0
Q7.
If A is square matrix such that , then is equal to
Answer : Option A
Explaination / Solution:
If A amd B are two square matrices of same order and the product AB= I, the matrix B is called inverse of matrix A.Therefore = I, then matrix A is the inverse of itself.
Q8. If , then is equal to
Answer : Option B
Explaination / Solution:
Q9. Number of all 4 digit numbers with distinct digits is
Answer : Option D
Explaination / Solution:
To form a four digit number with distinct digits we can use any four digits from the digits 0,1,2,3,4,5,6,7,8,9 without repetition
Since 0 cannot come as the first digit of a four digit number( then it will be a three digit number) the first place can be filled by any of the 9 digits other than 0.
Now we have 9 more digits left and since repetition is not allowed the second place can by filled by any of these 9 digits
Similarly the third and fourth can be filled by any of the 8 and 7 digits respectively
Hence we get the four places can be filled together by different ways.
Q10. In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0
Answer : Option C
Explaination / Solution:
We have ,
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0. Let
be the angle between the planes , then
As
Therefore , the given planes are perpendicular to each other.
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0. Let
be the angle between the planes , then
As
Therefore , the given planes are perpendicular to each other.
