Mathematics - Online Test
Q1. 5 boys and 5 girls are to be seated around a table such that boys and girls sit alternately. The number of ways of seating them is
Answer : Option C
Explaination / Solution:
If there are n objects to be arranged in circular order the no of permutations possible=
First we will make the 5 girls around the table and this can be done in , different ways
Now we have 5 places available between these girls and the 5 boys can be seated in these 5 available places in , different ways
Hence the 5 boys and 5 girls can be arranged in ways
Q2. If x = a then is equal to
Answer : Option B
Explaination / Solution:
dydx=dydtdxdt=3asin2tcost3acos2t(−sint)=−tant
Q3. Find the distance of the point (– 6, 0, 0) from the plane 2x – 3y + 6z – 2 = 0
Answer : Option B
Explaination / Solution:
Q4. can be expressed as
Answer : Option D
Explaination / Solution:
Q5. Solution of is
Answer : Option C
Explaination / Solution:
Q6. If in the expansion of, the coefficients of (2r+1)th and (r+2)th terms are equal , then r is equal to
Answer : Option B
Explaination / Solution:
Q7. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are
Answer : Option B
Explaination / Solution:
Let A and B be two sets having m and n elements respectively.Then,
Number of subsets of A=2m,Number of subsets of B=2n
It is given that 2m-2n=56
so,2n(2m-n-1)=23(23-1)
n=3 and m-n=3n=3 and m=6
Q8. 
is equal to
is equal to
Answer : Option D
Explaination / Solution:
Q9. If a, b ,c are real numbers such that a > b , c > 0, then
Answer : Option A
Explaination / Solution:
The inequality remains same if both sides of an inequality are multiplied by the same positive real number.
Q10. Sum of an infinitely many terms of a G.P. is 3 times the sum of even terms. The common ratio of the G.P. is
Answer : Option D
Explaination / Solution:
