NDA II - Mathematics Question Paper 2014 - Defence MCQ

X = Set of all citizens of India

 (R is not reflexive)

 (R is symmetric)

(R is not transitive)
 

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.

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

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.

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

(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

 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.

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.

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.

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

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

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

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

I : Variance is not dependent on change of origin. Therefore, if every x_i 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 x_i is squared the variance of the new set is V²
V_xi x  V_xi =V = V .V = v²

Mean of the squares of the first 20 natural number

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 = 

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

Number of words =  

Statement 1 :
n (X) = 2

arithmetric mean of X = np

Statement 2: Standard deviation of 


Hence, statements 1 and 2 both are correct. 

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

This is a Geometric Progression with a = 3 ,

Therefore, (251)₁₀=(11111011)₂

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.

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

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