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NDA II - Mathematics Question Paper 2014 - NDA MCQ


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30 Questions MCQ Test NDA (National Defence Academy) Past Year Papers - NDA II - Mathematics Question Paper 2014

NDA II - Mathematics Question Paper 2014 for NDA 2024 is part of NDA (National Defence Academy) Past Year Papers preparation. The NDA II - Mathematics Question Paper 2014 questions and answers have been prepared according to the NDA exam syllabus.The NDA II - Mathematics Question Paper 2014 MCQs are made for NDA 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for NDA II - Mathematics Question Paper 2014 below.
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NDA II - Mathematics Question Paper 2014 - Question 1

Let X be the set of all citizens of India. Elements x, y in X aresaid to be related if the difference of their age is 5 years. Which one of the following is correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 1

X = Set of all citizens of India

 (R is not reflexive)

 (R is symmetric)

(R is not transitive)
 

NDA II - Mathematics Question Paper 2014 - Question 2

2.    Consider the following relations from A to B where A = {u, v, w, x, y, z} and B= {p,q, r, 5}.
1.    {(u,p), (y,p), (w,p), (x, q), (y, q), (z, q)}
2.    {(u,p),(y,q),(w,r),(z,s)}
3.    {(«, s), (v, r), (w, q), (u,p), (v, q), (z, q),}
4.    {(u, q), (v,p), (w, s), (x, r), (y, q), (z, $),}

Which of the above relations are not functions ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 2

Given that, A = {u, v, x, y, z}; B = {p, q, r, s} As we know, a mapping f : x y is said to be a function, if each element in the set x has its image in set y. It is also possible that these are few elements in set y which are not the image of any element in set x. Every element in set x should have one and only one image.


(ii) and (iii) are not functions.

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NDA II - Mathematics Question Paper 2014 - Question 3

If a and P are the roots of the equation ax2 + bx + c = 0, where a 0, then (aα + b){aβ+ b) is equal to:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 3

Given equation ax2 + bx + c = 0 (where a 0) α and β are roots of given equation.
(aα + b) (aβ + b) = a2 aβ + abα + abβ + b2
= a2αβ + ab (α + β) + b2
From the given quadratic equation

NDA II - Mathematics Question Paper 2014 - Question 4

Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S. Then R is :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 4

S = Set of all integers and
R = {(a, b), a , b ∈ S and a b≥ 0 }
For reflexive: aRa ⇒ a.a = a2 ⇒ 0
for all integers a. a ≥ 0
For symmetric : aRb ⇒ ab ⇒ 0 a, b ∈ S
If ab > 0, then ba ≥ 0 ⇒ bRa
For transitive:
If ab≥ 0 , be≥ 0, then also ac≥ 0
Rlation R is reflexive, symmetric and transitive.
Therefore relation is equivalence.

NDA II - Mathematics Question Paper 2014 - Question 5

The roots of the equation a2x2 - 2 abx + b2 = 0 when a < 0 and b > 0 are:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 5

We have, 2a2 x2 - 2abx + b2 = 0
Discriminent, D=( - 2ab)2 - 4 (2a2) (b2)
= 4a2b2 - 8 a2b2 = - 4 a2b2 < 0
Roots are always complex.

NDA II - Mathematics Question Paper 2014 - Question 6

What is the sum of the two numbers (11110)2 and (1010)2 ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 6

(11110)2 = 24 x l + 23 x l + 22 x 1 + 21 x l + 20 x 0
= 16 + 8+4 + 2 + 0 = 30
(1010)2 = (23 x 1 + 22 x 0 + 21 x 1 + 20 x 0 = 8 + 0 + 2 + 0)= 10
Sum = 30 + 10=40
=(101000)2

NDA II - Mathematics Question Paper 2014 - Question 7

Let N denote the set of all non-negative integers and Z denote the set of all integers. The function Z → N given by  is:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 7

 f : Z → N and f ( x ) = |x|
When we drawa parallel line to x-axis.
It cuts the curve into more than one point. Therefore,f(x) = |x| is not one-one.

NDA II - Mathematics Question Paper 2014 - Question 8

If P and Q are two complex numbers, then the modulus of the quotient of P and Q is :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 8

The two complex numbers are 
P =x+ iy and Q = α+iβ


Hence, the quotient of their modulus is equal to the quotient of their moduli.

NDA II - Mathematics Question Paper 2014 - Question 9

Let z = x + iy Where x, y are real variables i = √-i. If |2z -1| = |z - 2|, then the point z describes :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 9


Squaring both sides
4x2 + 1- 4 x + 4y2 = x2 + 4 - 4 x + y2
⇒ 3x2 + 3y2 = 3
⇒ x2 + y2 = 1
It is the equation of a circle.
∴ The point z describes a circle.

NDA II - Mathematics Question Paper 2014 - Question 10

The sum of an infinite GP is x and the common ratio r is such that |r| < 1. If the first term of the GP is 2, then which one of the following is correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 10

GP = x
  x(where, a = 1st term and r = common ratio)

from equation (i) x > 1 Hence, 1 <x<

NDA II - Mathematics Question Paper 2014 - Question 11

A box contains 3 white and 2 black balls. Two balls aredrawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 11

Total number of balls
= 5 Number of black balls
= 2 Required probability

NDA II - Mathematics Question Paper 2014 - Question 12

For two variables x and y, the two regression coefficients are byx = -3/2 and bxy = - 1/6. The correlation coefficient between x and y is :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 12


bxy and byx both have negative sign. Therefore we have to take negative sign
bxy and byx both have negative sign. Therefore we have to take negative sign
Hence, correlation coefficient (r) 

NDA II - Mathematics Question Paper 2014 - Question 13

The variance of numbers x1,x2,x3,.......xn, is V Consider the following statements :
1. If every xi is increased by 2, the variance of the new set of the new set of numbers is V.
2.  If the numbers xi is squared, the variance of the new set is V2.

Which of the following statements is/are correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 13

I : Variance is not dependent on change of origin. Therefore, if every xi is increased by 2, the variance of the new set of numbers is not changed.
II: Variance is dependent on change of scale.
If the number xi is squared the variance of the new set is V2
Vxi x  Vxi =V = V .V = v2

NDA II - Mathematics Question Paper 2014 - Question 14

What is the mean of the squares of the first 20 natural numbers ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 14

Mean of the squares of the first 20 natural number

NDA II - Mathematics Question Paper 2014 - Question 15

p, q, r, s, t, are five numbers such that the average ofp,q and r is 5 and that of s and t is 10. What is the average of all the five numbers ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 15

According to question p + q + r = 5><3=15...(i)
s+t = 10 x 2 = 20 ...(ii)
From equations (i) and (ii), p + q + r + s+1 = 15 + 20 = 35
Average p, q, r, s and t = 

NDA II - Mathematics Question Paper 2014 - Question 16

The cumulative frequency of the largest observed value must always be:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 16

The cumulative frequency of the largest observed value must always be less then the total number of observations.

NDA II - Mathematics Question Paper 2014 - Question 17

It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternately, is :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 17

NDA II - Mathematics Question Paper 2014 - Question 18

Out of 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 18

Number of words =  

NDA II - Mathematics Question Paper 2014 - Question 19

Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:
1. The arithmetic mean o f X is 6.
2. The standard deviation ofX is 2.

Which of the above statements is/are correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 19

Statement 1 :
n (X) = 2

arithmetric mean of X = np

Statement 2: Standard deviation of 


Hence, statements 1 and 2 both are correct. 

NDA II - Mathematics Question Paper 2014 - Question 20

How many different words can be formed by taking four letters out of the letters of the word 'AGAIN' if each word has to start with A ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 20

As 'A’ must be first letter of each word. Total number ofwords = 4! = 24

NDA II - Mathematics Question Paper 2014 - Question 21

The sum of the series formed by the sequence 3, √3, 1. upto infinity i s :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 21


This is a Geometric Progression with a = 3 ,

NDA II - Mathematics Question Paper 2014 - Question 22

 then the locus o f z is:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 22

NDA II - Mathematics Question Paper 2014 - Question 23

The number 251 in decimal system is expressed in binary system by :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 23


Therefore, (251)10=(11111011)2

NDA II - Mathematics Question Paper 2014 - Question 24

What is the argum ent o f the complex number 

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 24


NDA II - Mathematics Question Paper 2014 - Question 25

Consider the following statements in respect of the matrix

1. The matrix A is skew-symmetric.
2. The matrix A is symmetric.
3. The matrix A is invertible.

Which of the above statements is/are correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 25


NDA II - Mathematics Question Paper 2014 - Question 26

Consider two matrices  

Which one of the following is correct ?

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 26


NDA II - Mathematics Question Paper 2014 - Question 27

One of the roots of

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 27



NDA II - Mathematics Question Paper 2014 - Question 28

If A is any matrix, then the product AA is defined only when A is a matrix o f order m x n where :

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 28

A A is defined only when A is a matrix of order m x n where m = n.
A x A = (m x n) (m x n) = (m x n) (n x n) if m = n = mxn = nxnorm xm.
= A is a square matrix.

NDA II - Mathematics Question Paper 2014 - Question 29

The determinant of an odd order skew symmetric matrix is always:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 29

We know that, elements of principal diagonals of a skew-symmetric matrix are all zero.

NDA II - Mathematics Question Paper 2014 - Question 30

If any two adjacent rows or columns of a determinant are intercharged in position, the value of the determinant:

Detailed Solution for NDA II - Mathematics Question Paper 2014 - Question 30

If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant changes its sign.

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