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Revision Quiz | Mathematical Reasoning and Statistics

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Question 1

Show that for every natural number relatively prime to X, there is another natural number all of whose digits are 1’s such that divides and that every positive rational number can be expressed in the form for some natural numbers .
X can be ?

Question 2

For all positive integral values of n, 33n – 2n + 1 is divisible by

Question 3

The smallest positive integer for which the inequality n! < {(n + 1)/2}n holds is

Question 4

If n is any natural number, (2n)! is divisible by

Question 5

For all positive integral values of n, 10n+1 + 10n + 1 is divisible by

Question 6

The contrapositive statement of the statement “If x is prime number, then it is odd” is

Question 7

The biconditional of the following statements is
P: Today is 1st October
Q: Tomorrow is Gandhi Jayanti

Question 8

Statement 1: (p^~q)^(~p^q) is a fallacy
Statement 2: is a tautology.

Question 9

The contrapositive of the following statement,
“If the side of a square doubles, then its area increases four times”, is:

Question 10


The negation of ~ s ∨ (~r ∧ s) is equivalent to :

Question 11

If and then the standard deviation of the 9 items is :

Question 12

All the students of a class performed poorly in Maths. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

Question 13

The mean deviation of the series a, a + d, a + 2d, ......, a + 2nd from its mean is

Question 14

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ... , 1 + 100d from their mean is 255, then the d is equal to

Question 15

Variance of the data given below is
Size of item 3.5 4.5 5.5 6.5 7.5 8.5 9.5
Frequency 3 7 22 60 85 32 8
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Oct 28JEE & BITSAT