NDA II - Mathematics Question Paper 2015


120 Questions MCQ Test NDA (National Defence Academy) Past Year Papers | NDA II - Mathematics Question Paper 2015


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QUESTION: 1

Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is

Solution:

a ~ b≤ 5
Let b ~ c ≤ 5
so a ~ c ≤ 10
as (a ~ b) ∈ Rand (b ~c) ∈R
but (a ~ c) ∉ R
So it is not a transitive relation.
By considering all the options, we come to the conclusion that only option (d) is correct.

QUESTION: 2

The matrix A=  will have inverse for every real number x except for

Solution:

|A| = 1 [(x -1 )(x-3) - 7] - 3 [(x - 3) - 2] + 2[7-2(x- 1)]
= x2 -11x + 29 = 0

QUESTION: 3

If the value of the determinant  is positive, where a ≠ b ≠ c, then the value of abc

Solution:

=> a(bc-1) - l(c-1)+ 1(1 - b)>0
=> abc-a-c+l + l- b>0
=> abc + 2-(a + b + c)>0
=> abc >(a + b + c)-2
Let; a = -l;b = 0& c = l
Then; 0 > -2 [which is correct]
Hence, abc = 0
After considering all the option; (b) is correct option.

QUESTION: 4

Consider the following statements in respect of the determinant

where α, β are complementary angles
1. The value of the determinant is 
2. The maximum value of the determinant is 1/√2

Q. Which of the above statements is/ are correct?

Solution:

QUESTION: 5

What is (1000000001)2 - (0.0101)2 equal to?

Solution:

(1000000001)2

= 1 x2° + 0x21+0x22+          + 1 x29
= 1 + 0 + 0+....... +512
=(513)10
(0.0101)2 =0 x2-1 + 1 x2-2 + 0 x 2-3 + 1 X2-4

= 1/4 + 1/16 = 5/16 = (0.3125)10

(1000000001)2 - (0.0101)2 = 513 - 0.312

=(512.6875)10 

QUESTION: 6

If A = , then the matrix X for which 2X+3A= 0 holds true is 

Solution:

QUESTION: 7

If Z1 and z2 are complex numbers with |z1|= |z2|, then which of the following is/are correct?
1. z1 =z2
2. Real part of z1 = Real part of z2.
3. Imaginary part of z1 = Imaginary part of z2

Q. Select the correct answer using the code given below:

Solution:

It is true for many values of a1, a2 & b1, b2. So a1 must not equal to a2, and b1 must not equal to b2

QUESTION: 8

If A =  and B =  then which of the following is/are correct ?
1. A and B commute.
2. AB is a null matrix.

Q. Select the correct answer using the code given below:

Solution:

asAB ≠ BA
So A and B are not commute.

QUESTION: 9

The number of real roots of the equation x2 - 3 |x| + 2 = 0 is

Solution:

QUESTION: 10

If the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of their squares, then

Solution:

QUESTION: 11

 then which of the following is/ are correct?
1. (A ∩ B) = (-2,1)
2. (A\B) = (-7,-2)

Q. Select the correct answer using the code given below:

Solution:

x2 + 6x - 7 < 0
=> ( x + 7 ) ( x - 1 ) < 0
=> x = ( - 7 , l )
=> A= {- 7 ,- 6 ,- 5 ,- 4 ,- 3 ,- 2 ,- 1,0,1}
=> x2+ 9 x + 1 4 > 0
=> (x + 7 )(x + 2 )> 0
=> x = (-∞, - 7 ) ∪ ( - 2 , ∞)
=> B = R - { - 7 , - 6, - 5, - 4 , - 3, - 2 }

So A ∩ B = ( - 2 , l )
A/B = (- 7, - 2).

QUESTION: 12

A, B, C and D are four sets such th at A ∩ B = C ∩ D = ø Consider the following:
1. A ∪ C and B ∪ D are always disjoint.
2. A ∩ C a n d B ∩ D are always disjoint

Q. Which of the above statements is/are correct ?

Solution:

LetA= {1,2}
B = {3 ,4 ,0 }
C = {5 ,6 ,0 }
D = { 7 , 8 }
Such that (A ∩ B) = (C ∩ D) = ø
=> (A ∪ C) = { 1 , 2 , 5 , 6 , 0 }
=> ( B ∪ D ) = {3 ,4 ,7 ,8 ,0 }
=> (A ∪ C )∩(B ∪ D )={0}
So (A ∪ C) and (B ∪ D) are not always dispoint
=> ( A ∩ C ) = ø and (B ∩ D ) = ø
So (A ∩ C) and (B ∩ D) are always disjoint.

QUESTION: 13

If A is an invertible matrix of order n and k is any positive real number, then the value of [det(kA)]-1 det A is

Solution:

If A is matrix that is invertible then det- (kA) will be kn. det(A), where n is the order.

QUESTION: 14

The value o f the infinite product is

Solution:

QUESTION: 15

If the roots of the equation
x2 - nx + m = 0
differ by 1, then

Solution:

QUESTION: 16

If different words are formed with all the letters of the word 'AGAIN' and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be

Solution:

QUESTION: 17

The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

Solution:

If captain is always included then we can choose 10 more players out of the remaining 14 players. So

QUESTION: 18

In the expansion of the value of constant term (independent of x) is

Solution:

Equating the coefficient of x to zero. 

QUESTION: 19

The value of sin2 5° + sin2 10° + sin2 15° + sin220°+.... + sin2 90° is

Solution:

QUESTION: 20

On simplifying  , we get, sin A cos A

Solution:

= 3 - 3 sin2A - 3cos2A + 3
= 6 - 3 (cos2A + sin2A)
= 6 - 3 (1)
=3

QUESTION: 21

The value of tan  is

Solution:

QUESTION: 22

Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15° with the horizontal. The distance between the poles is approximately equal to

Solution:

QUESTION: 23

If  then which one of the following is correct

Solution:

f(x)=x
g(x)= 1/x
Putting these values in the options, only (b) is correct.

QUESTION: 24

Consider the following:

Q. which of the above is/are correct ?

Solution:

Statement (1) is correct Again
Statement (2) is incorrect.

QUESTION: 25

If A is an orthogonal matrix of order 3 and B = , then which of the following is/are correct?
1. |AB| = ±47
2. AB = BA

Q. Select the correct answer using the code given below:

Solution:

The determinent of a orthogonal matrix is always ±1 |A |= ± 1

Taking A as identity matrix we can prove AB = BA

QUESTION: 26

If a,b,c are the sides o f a triangle ABC, then  where p> 1, is

Solution:

Consider any equilateral triangle:
c = b = a = 1 unit

By considering all the options carefully; we came to a conclusion that opton (b) is correct.

QUESTION: 27

If a,b,c are real numbers, then the value of the determinant  is

Solution:

QUESTION: 28

If the point z1 = 1 + i w here i = V-1 is th e reflection of a point z2 = x + iy in the line iz  - iz = 5, then the point z2 is

Solution:

Let Z = a+ bi

QUESTION: 29

If sin x + sin y = a and cos x + cos y = b, then  is equal to 

Solution:

Squaring of eq (1) & (2) and adding -

QUESTION: 30

A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower ?

Solution:

as ∠CPA=45°

QUESTION: 31

Consider the expansion of (1 + x)2n+1

Q. If the coefficients of xr and xr+1 are equal in the expansion, then r is equal to

Solution:

QUESTION: 32

Consider the expansion of (1 + x)2n+1

Q. The average of the coefficients of the two middle terms in the expansion is

Solution:

Total no. of terms in the expansion is 2n + 2. The middle two terms will be nth, (n + l)th term. So.

QUESTION: 33

Consider the expansion of (1 + x)2n+1

Q. The sum of the coefficients of all the terms in the expansion is

Solution:

Sum of all coefficient

QUESTION: 34

The nth term o f an AP. is  then the sum o f first 105 terms is

Solution:

QUESTION: 35

A polygon has 44 diagonals. The number of its sides is

Solution:

=> n2- 3n - 88 = 0
=> (n - 11) ( n + 8) = 0
n ≠ - 8
n= 11

QUESTION: 36

If p,q,r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in

Solution:

Let the common ratio be K1 for p, q and r.
q = K1p
& r = (K1)2p
Let the common ratio be K2 for a, b and c
b = K2a
& c = (K2)2a
bq = (K1K2)ap
&Cr = (K1K2)2ap
So ap, bq, cr are in GP.

QUESTION: 37

Consider a triangle ABC satisfying

Q. The sides of the triangle are in

Solution:

=> a + c = 2b
So a, b, care inA.P.

QUESTION: 38

Consider a triangle ABC satisfying

Q. sin A, sin B, sin C are in

Solution:

As we have already proven
2b = a + c
as
a = RsinA
b = RsinB
c = RsinC
=> 2(RsinB) = RsinA + RsinC
=> 2R(sinB) = R(sinA + sinC)
2sinB = sinA + sinC

QUESTION: 39

If p = , then which of the following is/are correct?
1. The value of p x r is 2.
2. p, qandrare inG.P.

Q. Select the correct answer using the code given below:

Solution:

So p, q,r are in G.P.
Statement (2) is correct.

QUESTION: 40

The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

Solution:

Each employee is eligible for 1 or more of the tickets.
No. of ways = 20 x 20 x 20 = 8000.

QUESTION: 41

What is the sum of n terms of the series √2 + √8 + √18 + √32 + .. ?

Solution:

QUESTION: 42

The coefficient o f x99 in the expansion o f (x - 1) (x - 2) (x - 3) .... (x-100) is

Solution:

QUESTION: 43

 represents a circle with

Solution:

Centre (-3 ,-1)
radius = 3

QUESTION: 44

The number of 3-digit even numbers that can be formed from the digits 0, 1,2, 3,4 and 5, repetition of digits being not allowed, is

Solution:

No. of digits to be filled at one’s place = 3
No. of digits to be filled at 10’s place = 50
No. of digits to be filled at 100’s place = 4
Total no. o f digits formed = 3 x 5 x 4 = 60
If zero is at 100’s place;
Then; no. of digits to be filled at one’s place = 2
& no. of digits to be filled at 10’s place = 4
No. of digits formed with zero at 100’s place = 1 x 2 x 4 = 8
Required no. of digits formed = 60 - 8 = 52.

QUESTION: 45

If log8m +log8 1/6 = 2/3, then m is equal to

Solution:

QUESTION: 46

The area of the figure formed by the lines ax + by + c = 0, ax - by + c = 0, ax + by - c = 0 and ax - by - c = 0 is

Solution:

Area of triangle

Total area 
= 4 x area ΔAOB
= 4 x c2/2ab
= 2c2/ab

QUESTION: 47

If a line is perpendicular to the line 5x - y = 0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is

Solution:

5 x - y = 0
y = 5 x                  ...(1)
Slope = 5
Slope of perpendicular line will be -1/5.
 Let equation of line is
                        ......(2)

Putting y= 0
x = 5 c
OB = 5c
Intersecting point A

QUESTION: 48

Consider any point P on the ellipse x2/25 + y2/9= 1 in the first quadrant. Let r and s represent its distances from (4,0) and ( - 4 , 0 ) respectively, th en (r + s) is equal to

Solution:

QUESTION: 49

A straight line x = y + 2 touches the circle 4(x2 + y2) = r2. The value of r is

Solution:

Eq. of line is ; x - y - 2 = 0
Line touches the circle.

QUESTION: 50

The three lines 4x + 4y = 1, 8x - 3y = 2, y=0 are

Solution:

So from the figure it is clear that all the three lines are concurrent at point P.

QUESTION: 51

The line 3x + 4y - 24 = 0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is

Solution:

Since circumcentre of right angled triangle lies on the midpoint of hypotenuse.
So mid point of AB is 

QUESTION: 52

The eccentricity of the hyperbola 16x2 - 9y2 = 1 is

Solution:

16x2 - 9y2 = 1

QUESTION: 53

The product of y the perpendiculars from the two points (± 4,0) to the line 3x cos ø + 5y sin ø=15 is

Solution:

If length of perpendicular be P1 from the point (4,0) 

If length of perpendicular be p2 from the point (- 4 ,0)

QUESTION: 54

If the centre of the circle passing through the origin is (3,4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

Solution:

Equation of circle having radius r and centre (3,4) is
= (x - 3 )2 + ( y - 4 )2 = r2
if it is passing through (0,0)
(0 - 3)2 + (0 - 4)2 = r2
=> r2 = 25
equation of circle is
(x - 3)2 + (y - 4)2 = 25
putting y = 0
x = 6 unit = interception x-axis intercept on y axis (putting x = 0) is
y = 8 unit

QUESTION: 55

The lines 2x = 3y = - z and 6x = - y = - 4z

Solution:

2x = 3y = - z

cosθ = 0
θ = 90°
So lines are perpendicular

QUESTION: 56

Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

Solution:

Coordinates of Q are (3,0) & it passes through PQ.
Putting the values of(x=3) & (y=0) m options we get:
Equation of line PQ = 7x + y - 21 = 0

QUESTION: 57

The radius of the sphere 3x2 + 3y2 + 3z2- 8x + 4y + 8z - 15 = 0 is

Solution:

So radius is 3.

QUESTION: 58

The direction ratios of the line perpendicular to the lines with direction ratios < 1, -2, -2 > and < 0,2,1 > are

Solution:

Let the direction ratio be <a, b, c>

Fromeq. (1)&(2)
a = - 2b; c = - 2b 

QUESTION: 59

What are the co-ordinates of the foot of the perpendicular drawn from the point (3,5,4) on the plane z = 0?

Solution:

Plane z = 0 is simply
xy plane, so z quadrant value will be zero.

So, from options (b) is correct option. 

QUESTION: 60

The lengths of the intercepts on the co-ordinate axes made by the plane 5 x + 2y + z - 1 3 = 0 are

Solution:

5x + 2y + z - 13 = 0
Putting y = 0 & z = 0

QUESTION: 61

The area of the square, one of whose diagonals is  is

Solution:

Length of diagonal

QUESTION: 62

ABCD is a parallelogram and P is the point of intersection of the diagonals. If O is the origin, then  is equal to

Solution:

QUESTION: 63

If are the position vectors of the points B and C respectively, then the position vector of the point D such that is

Solution:

QUESTION: 64

If the position vector a of the point (5, n) is such that |a | = 13, then the value/values of n an be

Solution:

QUESTION: 65

If  , then is equal to

Solution:

QUESTION: 66

Consider the following inequalities in respect of vectors

Q. Which of the above is/are correct? 

Solution:

both are correct.

QUESTION: 67

If the magnitude of difference of two unit vectors is √3 then the magnitude of sum of the two vectors is

Solution:

QUESTION: 68

If the vectors  lie on a plane, where α, β and γ are distinct non-negative numbers, then y is

Solution:

If three vectors are co-planar. 

QUESTION: 69

The vectors  are such th at  and  Which of the following is/ are correct?

Q. Select the correct answer using the code given below:

Solution:

So both (1) and (2) are correct.

QUESTION: 70

The value of

Solution:

a + b = 0 =>a = - b

So f(x) is odd hence
I=0

QUESTION: 71

If  equal to?

Solution:

It is 0/0 (undefined condition) so using L’hospital’s rule

QUESTION: 72

Consider the function

Q. What is the value of a for which f(x) is continuous at x = - 1 and x = 1 ?

Solution:

if f(x) is continuous at x = - 1

QUESTION: 73

 The function f(x) =  is not defined at x = π.
The value of f(π) so that f(x) is continuous at x = π is 

Solution:

Using L’hospital’s rule

QUESTION: 74

Consider the following functions :

Q. Which of the above functions is/are derivable at x = 0 ?

Solution:

as there is a discontinuity at x = 0, so function is not differentiable at x = 0

It is differentiable at x = 0
Only (2) is differentiable at x = 0

QUESTION: 75

The domain of the function  is 

Solution:

it is possible only when x is negative.

QUESTION: 76

Consider the following statements:
1. The function f (x) = x2 + 2cos x is increasing in the interval (0, π)
2. The function f(x) =  is decreasing in the interval (-∞,∞)

Q. Which of the above statements is/are correct?

Solution:

f(x) = x2 + 2cosx
f'(x ) = 2x -2sin x
= 2[x-sinx]

Between (0,π),(x-sinx)isalways+ve, soif'(x) is always+ve. Hence it is increasing.

As f' (x) is -ve always, so this function is decreasing always.

QUESTION: 77

The derivative of ln(x+ sin x) with respect to (x+ cos x) is

Solution:

derivative of ln(x + sinx) w.r.t (x + cosx) is

QUESTION: 78

If y = , where,  then dy/dx is equal to 

Solution:

QUESTION: 79

The function f (x) = monotonically increasing if

Solution:

as ex is always positive and for monotonically increasing; 2x - x2 > 0
x2- 2 x < 0
=> x (x -2 )< 0
=> x = ( 0 , 2)

QUESTION: 80

If , then the value of  is equal to

Solution:

differentiating both sides w.r.t 'x'

QUESTION: 81

If f : IR → IR, g : IR → IR be two functions given by f(x) = 2x - 3 and g(x) = x3 + 5, then (fog)-1 (x) is equal to

Solution:

QUESTION: 82

If  is equal to 

Solution:

QUESTION: 83

 is equal to

Solution:

QUESTION: 84

If f(x) = , then  is equal to

Solution:

It is 0/0 (undefined) condition so using L’hospital’s rule

QUESTION: 85

Consider the following statements:
1. f(x) = In x is an increasing function on (0, ∞).
2. f(x) = ex - x (In x) is an increasing function on (1, ∞).

Q. Which of the above statements is/are correct ?

Solution:

f(x) = logx
Clearly f(x) is increasing on (0,∞)
f(x) = ex-xlogx
f '(x) = ex - (log x +1)

From the figure it is clear that f'(x) > 0 on (1, ∞).
So both statements (1) & (2) are correct.

QUESTION: 86

If  is equal to

Solution:

QUESTION: 87

Consider the following statements:
Statement 1 : The function f: IR → IR such that f ( x ) = x3 for all x ∈ IR is one-one.
Statement 2 : f (a) => f (b) for all a, b ∈ IR if the function f is one-one.

Q. Which one of the following is correct in respect of the above statements ?

Solution:

So it is one-one function
Hence option (a) is correct.

QUESTION: 88

 is equal to

Solution:

QUESTION: 89

 is equal to

Solution:

QUESTION: 90

The area bounded by the coordinate axes and the curve √x + √y = 1, is

Solution:

QUESTION: 91

Consider the function

Q. At what value of x does the function attain maximum value ?

Solution:

For max. or min. value dy/dx = 0

QUESTION: 92

Consider the function

Q. The maximum value of the function is

Solution:

QUESTION: 93

Consider  such that f(0) = 0 and f(3) =15

Q. The value of k is

Solution:

QUESTION: 94

Consider  such that f(0) = 0 and f(3) =15

 is equal to

Solution:

QUESTION: 95

Consider the function
f(x)=-2x3-9x2-12x+ 1

Q. The function f(x) is an increasing function in the interval

Solution:

QUESTION: 96

Consider the function
f(x)=-2x3-9x2-12x+ 1

Q. The function f (x) is a decreasing function in the interval

Solution:

QUESTION: 97

Consider the integrals

Q. Which one of the foilwing is correct ?

Solution:

QUESTION: 98

Consider the integrals

Q. What is the value of B?

Solution:

QUESTION: 99

Consider the function

Which is continuous everywhere.

Q. The value of A is

Solution:

QUESTION: 100

Consider the function

Which is continuous everywhere.

Q. The value of B is

Solution:

QUESTION: 101

The degree o fthe differential equation  is

Solution:

Order of the above differential equation = 1 & degree = 5

QUESTION: 102

The solution of  is

Solution:

QUESTION: 103

The differential equation of the family of circles passing through the origin and having centres on the x-axis is

Solution:

Eq. of family of circles passing through the origin & having centres on the x-axis is :

QUESTION: 104

The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a> 0, are respectively

Solution:

The eq. of parabolas having vertex at (0,0) & focus at (a, 0), where (a >0) is:
y2 = 4ax    ...(1)

QUESTION: 105

f(xy) = f(x) + f(y) is true for all

Solution:

Let f(x) = logx
f(y) = log y
& f(xy) = log (xy) = logx + logy
=> f(xy) = f(x) + f(y)

QUESTION: 106

Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?

Solution:

Total no. of 3-digit numbers = 9 x 8 x 7 = 504
For product to be odd, we have to choose only from odd numbers.
Total no. of 3-digit no. whose product are odd = 5 x 4 x 3 = 60
Required probability = 60/504 = 5/42

QUESTION: 107

Two events A and B are such that P(not B) = 0.8, P(A∪B) = 0.5 and P(A|B) = 0.4. Then P(A) is equal to

Solution:

QUESTION: 108

If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is

Solution:

QUESTION: 109

Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads ?

Solution:

Let X denote the no. of coins showing 3 or more heads in a set of 7 coins.
X follows binomial distribution with n = 7
p = probability of getting a head in a single toss of a coin

QUESTION: 110

A coin is tossed five times. What is the probability that heads are observed more than three times ?

Solution:

Let P denote the probability of getting head in a single toss of a coin.

Let X denote the no. of heads in 5 tosses of a coin, then, X is a binomial variate with parameters; n = 5 & p= 1/2

QUESTION: 111

The geometric mean ofthe observations x1 x2, x3, ..... xn is G1, The geometric mean ofthe observations y1, y2, y3,....yn is G2. The geometric mean of observations 

Solution:

QUESTION: 112

The arithmetic mean of 1,8,27,64, up to n terms is given by

Solution:

QUESTION: 113

An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is/are correct?
1. The probability that no head is observed is 1/16
2. The probability that the experiment ends with three tosses is 1/8

Q. Select the correct answer using the code given below:

Solution:

S = {H, TH, TTH, TTTH, TTTT}
P (T)= P (H) = 1/2
[Probability of getting head or tail in a single toss] Probability that no head is observed = P(TTTT)
= P(T) P(T) P(T) P(T)
1/24 = 16
And the probability that the experiment ends with 3 tosses
= P (TTH)
= P(T) P(T) P(H)
= 1/8
Hence, both statements are correct.

QUESTION: 114

If x ∈ [0,5], then what is the probabil lty that x2 - 3x + 2 > 0 9

Solution:

QUESTION: 115

A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

Solution:

QUESTION: 116

A problem in statistics is given to three students A, B and C whose chances of solving it independently are 1/2, 1/3,  and 1/4 respectively. The probability that the problem will be solved is

Solution:

QUESTION: 117

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01,0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

Solution:

Let Ej, E2, E3 & A be events defined as follows.
E1 = person chosen is a scooter driver
E2 = person chosen is a car driver.
E3 = person chosen is a truck driver &
A = person meets with an accident

QUESTION: 118

A coin is tossed 5 times. The probability that tail appears an odd number of times, is

Solution:

Let p denote the probability of getting tail in a single of a coin.

Let X denot no. of tails in 5 tosses of coin.

QUESTION: 119

The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

Solution:

QUESTION: 120

What is the probability that the sum of any two different single digit natural numbers is a prime number ?

Solution:

Total no. of two different single digit natural number = 9C2=36
The number of two different single digit natural no.s whose sum is a prime number ( 3,5 ,7 ,11,13 & 17) = 14

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