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Maths Question Bank Solutions A17
Computer Science, Engineering (CSC502)
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SAMPLE QUESTION BANK
Program: BE (Mechanical Engineering) Curriculum Scheme: Rev2019 C Scheme SE Semester IV Course Code: MEC401 and Course Name: Engineering Mathematics-IV ===================================================================== MCQ- SAMPLE SET
ý⃗=(ć + Ĉ)ÿ +(Ć + Ĉ)Ā +(Ć + ć)ā ÿā Option A: Solenoidal and not irrotational Option B: Neither solenoidal nor irrotational Option C: Solenoidal and irrotational Option D: Not solenoidal but irrotational
If S is a closed surface enclosing a volume V and 𝔹⃗= ÿĆÿ +ĀćĀ + āĈā , Ă/ăÿ , 𝔹.⃗⃗⃗⃗ÿ Ăā is Option A: (a+b+c)V Option B: a+b+c Option C: abcV Option D: Abc
The value of + 1 𝔶 ÿ2𝕎ĂĈ;Where C is the circle with centre at z=a and radius c units is equal to Option A: 0 Option B: 2πi Option C: 2π Option D: πi
Value of + (Ĉ + 1)ĂĈ 𝕐 ; where ā:ĀĀăÿĂÿĀć ĀĄ Ă/ă āÿăÿĀă ąÿĂ/ ĄăĀĂÿāăā ÿĂ (0,0);(1,0);(1,1);(0,1) ÿā Option A: 2i Option B: 3+2i Option C: 5 Option D: 0
Residue of f(z) = 1 ÿ 3 (ÿ+4) ÿĂ Ĉ = 0 ÿā Option A: Ā ąă Option B: 1 32 Option C: 21 64 Option D: 21 32
If f(a)=+ 4ÿ 2 +ÿ+ 𝕐 ÿ2𝕎 ĂĈ where c is an ellipse
ý 2 4 +
þ 2 9 = 1 then the value of f(i) is Option A: 2π+2πi
Option B: 0 Option C: 2π 2 2πi Option D: 2 2π+2πi
Given: ∑ÿ = 21 ;∑Ā = 24;∑ÿĀ = 75; ∑Ā 2 = 106 ;ÿ = 6 Line of best fit to the above data for determining the best estimate of X corresponding to specified value of Y is Option A: X=0 2 7. Option B: X=7 2 0 Option C: Y=7+0 Option D: Y=7 2 0
The Regression line of X on Y is 3Y 2 5X= 2 180 and Var(X)= 9 16 Var(Y) .The Karl Pearson9s correlation coefficient is equal to Option A: 2 0. Option B: 0. Option C: 0. Option D: 20. 93
Given: ∑Ćć = 2 93; ∑Ć 2 = 140 ;∑ć 2 = 398 ; [x and y denote the deviations of X and Y from their respective means] .The regression coefficients of X on Y and Y on X are respectively Option A: {0 ;0} Option B: { 2 0 ; 20. 234} Option C: { 2 0 ; 0. 234} Option D: { 2ÿ. āĂă;2ÿ. ąąă }
Given: Rank correlation coefficient between X and Y is 2/3 .The number of pairs of observations is 10.{No ranks are repeated in both X and Y series} .Then the sum of the squares of the differences between the corresponding rank is Option A: 110 Option B: 55 Option C: 165 Option D: 330
Given: P(A)= 1 12 ; P(B)=
5 12 ; P (þ/ý)= 1 15 ; / ăÿ P(AUB) is equal to Option A: ÿĀ
Āÿÿ Option B: 8 9 Option C: 17 18 Option D: 91 180
- A R. X has a probability density function Ą(Ć)= { Ćă2ý ; Ć g 0 0 ;ĀĂ/ăĀąÿāă }. Then mean of X is Option A: 6
Option C: (113,216) Option D: (159,170)
- Given:the observed frequencies {200,300} and the corresponding expected frequencies{300,200} , the value of the Chi-square Statistic is Option A: 1 6 Option B: 500 3 Option C: āĄÿ
Ă Option D: 5 6
Two sample of size 10 and 12 are drawn from two normal population sum of the squares of the deviations from the respective means are 120 and 314 respectively the calculated value of the F-Statistic is Option A: 2. Option B: 2. Option C: 0. Option D: 1.
Find the value of a if 𝔹=(Ć 2 2Ĉ)ÿ +(ć 2 5Ć)Ā + ( ÿĈ + 2Ć)ā is solenoidal Option A: ÿ = 2 Option B: 𝖂 = 2ā Option C: ÿ = 24 Option D: ÿ = 4
Vector field is Irrotational if Option A: 𝗁 × 𝖇⃗⃗ = 0
Option B: ∇ .Ą⃗ = 0 Option C: ∇ × Ą⃗ b 0 Option D: ∇ .Ą⃗ = 1
The residue at the pole z =-1 of Ą(Ĉ) = 1 (ÿ+1)(ÿ22) 2 is Option A: 1/ Option B: -1/ Option C: 1/ Option D: -1/
The poles of Ą(Ĉ) = 3ÿ (ÿ+1)(ÿ22) are Option A: 1,- Option B: -1,- Option C: -1, Option D: 1,
Value of + āÿÿ2Ĉ ĂĈ ý(Ĉ + /3) 4 ĂĈ is where C:|Ĉ|= 2
Option A: 4 𝖊 / Option B: ÿ/ Option C: 2ÿ/ Option D: 4 ÿ
/ă ĄÿĂăă ĀĄ +1+ÿĈ̅ 0 dz along straight line y=x is Option A: 0 Option B: 2 Option C: 3 Option D: 1
If the two regression coefficient are -8/15 and -5/6 then the correlation coefficient is Option A: 0. Option B: - 0. Option C: -0. Option D: 0.
Line of regression y on x is 8x-10y +66 =0. Line of regression x on y is 40x -18y -214 =0. The value of variance of y is 16. The standard deviation of x is Option A: 3 Option B: 2 Option C: 6 Option D: 7
∑Ćć = 2638, Ć̅ = 14,ć =17, n=10 then cov (x,y) is Option A: 24. Option B: 25. Option C: 23. Option D: 20.
Least square fit for the straight line y= ax + b to the data
x 1 2 3 y 5 7 Option A: y = 2x + Option B: y = 2x - Option C: y = 2x + Option D: y = 3x - 4
A random variable X has the following probability distribution. The value of K is x 2 3 4 5 P(x) 5/K 7/K 9/K 11/K Option A: 16 Option B: 8 Option C: 48 Option D: 32
If observed frequencies are 5,10,15 and expected frequencies are each equal to 10 then chi square value is Option A: 20 Option B: 10 Option C: 15 Option D: 5
Among 64 offspring of a certain cross between guinea pig 34 were red,10 were black and 20 were white, According to genetic model these number should in the ratio 9:3:4. Expected frequencies in the order Option A: 36,12, Option B: 12,36, Option C: 20,12, Option D: 36,12,
41. Find the constants a, b, c if F = +( axy bz i 3 ) (+ − + 3 x 2 cz j ) ( 3 xz 2 − y k )
is irrotational. Option A: a = 6 , b = 1, c = 1 Option B: a = 6 , b = – 1, c = 1 Option C: a = 6 , b = – 1, c = – 1 Option D: a = 6 , b = 1, c = – 1
If ( )
4 2 5
=
C
z z f a dz z a
++
−
where C is a ellipse
2 2 1, 4 9
x y +=then what is the
value of f ' 1 ?( )−
Option A: 0
Option B: − 14 i
Option C: 14 i
Option D: 18 i
- If null hypothesis is H 0 := 10 and alternate hypothesis is Ha :ü10, then the test is Option A: right tailed Option B: left tailed Option C: two tailed Option D: cross tailed
44. If X is a Poisson variate with mean m , then P X ( = x ) is given by
Option A: !
e m m x x
−
Option B: !
e m x x x
−
Option C: !
e x m m x
−
Option D: !
e x x m x
−
If two lines of regression are x + 3y = 5 and 4x + 3y = 8 , then the correlation coefficient is Option A: 2 Option B: 1 Option C: 0. Option D: 0.
If we have two samples of sizes n 1 and n 2 with standard deviations s 1 and s 2 respectively, then to test the equality of population variances, the test statistic F is given by
Option A: ( )
( )
2 1 1 2 2 2
1
1
s n F s n
−
=
−
Option B: ( )
( )
2 1 1 1 2 2 2 2
1
1
n s n F n s n
−
=
−
Option C: ( )
( )
2 1 1 2 2 2 2 1
1
1
n s n F n s n
−
=
−
Option D: ( )
( )
2 2 1 2 1 2
1
1
s n F s n
−
=
−
- Find
( )( )
2
C 34
z dz z z
+
−−
where C is z = 1.
Option A: 2 i
Option B: − 10 i
Option C: 0
Option D: 6 i
Fit a straight line y = a + bx into the given data. x: 10 20 30 40 50 y: 22 23 27 28 30 What is the value of b? Option A: 2. Option B: 0. Option C: 1. Option D: 0.
If the probability density function of a continuous random variable is given by
f x ( )= kx 2 , 0 x 1, then what is the value of k?
Option A: 1 Option B: 2 Option C: 3 Option D: 4
50.
What is the value of ( )
1 2 0
i x y ix dz
−+ along the line from z = 0 to z = 1 + i?
Option A: 1 3
− i
Option C: a removable singularity Option D: a non-isolated essential singularity
- If a random variable X has probability density function
( )
( )
3
2 , 0 2
4
0 ,
x x x f x elsewhere
ü ÿ − =ý ÿþ
, then what is E(X)?
Option A: 1 Option B: 1 2 Option C: 3 Option D: 1 3
- If X is normal variate with mean 10 & standard deviation 4, then what is
P X ( 12 )? (Given: Area from z = 0 to z = 0 is 0)
Option A: 0. Option B: 0. Option C: 0. Option D: 0.
When the values of two variables move in the same direction, correlation is said to be Option A: Linear Option B: Non-linear Option C: Positive Option D: Negative
What is the scalar potential of the vector function
F = ( y 2 cos x z i + + 3 ) (2 sin y x − + 4 ) j ( 3 xz 2 + 2 ) k?
Option A: 2 y 2 sin x xz + − + 34 y 2 z Option B: y 2 sin x xz + − + 34 y 2 z Option C: y 2 sin x + + − 2 xz 34 y 2 z Option D: y 2 sin x xz − + + 34 y 2 z
The means of two independent samples of size 8 and 7 are 1134 and 1024 respectively. The standard deviation of these two samples is 35 and 40 respectively. What is the value of test statistic t in order to test the significance of difference between sample means? Option A: 5. Option B: 6. Option C: 5. Option D: 4.
The order of the pole of Ą(Ĉ)=ýÿ𝕛/ÿ ÿ 7 Option A: 7
(ÿ21) 2 (ÿ+2)
If F =(x + 2y + 4z)i +(ax 2 3y 2 z )j +(4x 2 y +2z )k is irrotational
If a random variable X follows Poisson distribution such that𝕃(ÿ = 1)=
If X is a normal variate with mean 10 and standard deviation 4. The value of
Given 𝕁 =10,∑Ăÿ 2 = 96. Find the rank correlation coefficient R.
- Option B:
- Option C:
- Option D:
- Find the residue at z = -2 of the function Ą(Ĉ)= ÿ
- Option A:
- Option B: 5/
- Option C: 4/ - Option D: - Option A: 63. What is the expectation of heads if an unbiased coin is tossed 12 times - Option B: - Option C:
- Option D:
- 64. Find r if ∑Ćć = 24,∑Ć 2 = 36 and ∑ć 2 =
- Option A: 0.
- Option B: 0.
- Option C: 0.
- Option D: 0.
- Option A: then find the constants a
- Option B:
- Option C: -
- Option B: 0.
- Option D:
- Option A: 𝕃(ÿ = 2) Find the mean.
- Option B:
- Option C:
- Option D:
- Option A: standard normal variate Z is
- Option B:
- Option C:
- Option B:
- Option D: 2. - Option B: = 0. Option A: 𝕹 = ÿ.ăĀÿĀ - Option C: = 0. - Option D: = 0.
Option A:
Option B: 5/
Option C:
Option D:
- What is r -th Moment about origin μr′?
Option A: 0.
Option B:
Option C:
Option D:
- Which of the following can9t be Probability Option A: 5% Option B: 3 8
Option C: 0.
Option D: -0.
What is the size of Large sample Option A: Less than 30 Option B: More than 30 Option C: More than 50 Option D: Less than 50
Chi Square test used to analyze Option A: Mean Option B: Variance Option C: Frequencies Option D: Rank
Descriptive Questions SAMPLE SET
Q1.
If 𝔹⃗= (Ĉ 2 + 2Ć + 3ć)ÿ + (3Ć + 2ć + Ĉ)Ā + (ć + 2ĆĈ)ā is irrotational, then (i) Find the scalar potential associated with 𝔹⃗ such that φ(1,1,0)= (ii) Also the work done in moving a particle under 𝔹⃗ from A(0,1,1) to B(3,0,2)
Q2. Evaluate:+ ÿ 2 𝕐 (ÿ21) 2 (ÿ22)ĂĈ ; ā ÿā
|Ĉ|= 2.
Q4.
The chance that a doctor will diagnose a disease correctly is 60%. The chance that a patient will die by his correct diagnosis is 40% and that by his wrong diagnosis is 70%. A patient dies on a particular day. What is the chance that he was diagnosed correctly?
Q5.
(i) Verify whether probability mass function of R.V. p(x)=
(|𝕋|+1) 2 9 ĄĀĀ Ć = {21,0,1}ÿā ąăĂĂ ĂăĄÿÿăĂ (ii) If so find its mean and variance.
Q6.
Discuss whether drug and sugar pills differ in curing cold(at 5% level of significance)and Table value of Chi-square statistic is 3 using the data:- Helped Harmed Drug 150 30 Sugar pills 130 40
Q7.
Evaluate: + 𝔹⃗. ĂĀ⃗⃗⃗⃗⃗ ; where 𝔹⃗=(Ć 2 2 ć 2 )ÿ +(Ć + ć)Ā and c is the triangle with vertices (0,0),(1,1),(2,1) using Green9s theorem.
Q8.
Expand: f(z)= 7ÿ ÿ(ÿ+1)(ÿ22)ÿĀĀăĂ Ĉ = 21,ĄĀĀ 1 <|Ĉ + 1|< 3 as a Laurent9s Series
Maths Question Bank Solutions A17
Course: Computer Science, Engineering (CSC502)
University: Datta Meghe Institute of Medical Sciences
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