Mathematics - Online Test
Q1. Direction angles are
Answer : Option C
Explaination / Solution:
the angles are called direction angles, which the position vector makes with the positive x-axis ,y-axis and z-axis respectively
Q2. A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
Answer : Option C
Explaination / Solution:
n(S)=36.
Let A = event of getting sum greater than 9.
= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
And B = event of getting 5 on black die.
={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}
Let A = event of getting sum greater than 9.
= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
And B = event of getting 5 on black die.
={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}
Q3. The minimum value of sin x −− cos x is
Answer : Option B
Explaination / Solution:
(−12√)+(−12√)=−2–√
Q4. is equal to
Answer : Option D
Explaination / Solution:
Q5. If P ( n ) = 2+4+6+………………..+2n , n N , then P ( k ) = k ( k + 1 ) + 2 P ( k + 1 ) = ( k + 1 ) ( k +2 ) + 2 for all k N . So we can conclude that P ( n ) = n ( n + 1 ) +2 for
Answer : Option B
Explaination / Solution:
Because the statement is incomplete without the conclusion/ RHS
Q6.
The equation represents
Answer : Option C
Explaination / Solution:
The above circle can be written as 
Here the center is (0,0) and radius is also 0 units.
Here the center is (0,0) and radius is also 0 units.So it is a degenerate circle as degenerate circle is a circle( a point) where radius is zero units.
Q7. Number of ways in which 10 different things can be divided into two groups containing 6 and 4 things respectively is
Answer : Option A
Explaination / Solution:
If there are 10 things and we have to make them in to two groups containing 6 things and 4 things respectively , you have to select 6 to form first group , then automatically another group would have formed of 4 remaining things.
Now 6 things can be selected from 10 things in different ways
Also we have
Q8. The order of the equation is
Answer : Option B
Explaination / Solution:
Since the equation has 2nd derivative as the highest derivative term.hence the order 2
Q9. If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are
Answer : Option C
Explaination / Solution:
If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are Proportional to the direction cosines of the line.
Q10. There exists a triangle ABC satisfying the conditions
Answer : Option D
Explaination / Solution:
when k=1 we have
But we have in a triangle the sum of the three angles is 180 degrees ,so if B=90 degrees then
