![Page 1: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/1.jpg)
Multiple Choice Questions
![Page 2: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/2.jpg)
CPT Section D, Quantitative Aptitude, Chapter 13 Prof(Dr.) P.R.Vittal
![Page 3: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/3.jpg)
(a)2/7 b)3 /7 c)4/7 (d)None of these
Solution :A leap year contains 52 weeks plus 2 days.The least 2 days can be [s,m],m,tu],[tu,wed],[wed,thurs],[thurs,fri],[fri,sat],[sat,sun]
P(53 sun or mon )=3/7
Answer: (b)
![Page 4: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/4.jpg)
(a)5:7 (b)4:7 (c)5:8 (d)4:5
Solution :
P(A)=7/12 No. of favourable ways =7 ,
No. of unfavourable ways =5
Hence odds against the event A is 5:7
Answer: (a)
![Page 5: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/5.jpg)
(a)1/15 (b)1/12 (c)5/18 (d)5/21
Solution :
The probability that all the 3 are white =(5C3/10C3)=1/12
Answer : (b)
![Page 6: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/6.jpg)
(a)5/396 (b)3/132 (c)1/36 (d)1/22
Solution :
P(3 are red) = ((3C3).(9C2)/12C5)=1/22
Answer : (d)
![Page 7: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/7.jpg)
(a)0.6 (b)0.06 (c)0.006 (d)0.96
Solution :
P(A∩B∩C)=P(A)P(B)P(C)=0.06
Answer : (b)
![Page 8: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/8.jpg)
There are 10 balls numbered from 1 to 10 in a box. If one of them is selected at random , the probability that the number printed on the ball would be an even number greater than 5 is
(a)3/5 (b)2/5 (c)3/10 (d)7/10
Solution :
The set of even numbers >5 is (6,8,10).
p(ball has even number>5)=3/10
Ans : (c)
![Page 9: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/9.jpg)
For two independent events A and B , P(A)=1/5 and P(AUB)=3/4. Then P(B) is (a)11/20 (b)11/16 (c)5 /15 (d)9/20
Solution :
P(AUB)=P(A)+P(B)-P(A)P(B)
¾ = 1/5 +P(B)-(1/5)P(B)
P(B)=11/16
Ans : (b)
![Page 10: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/10.jpg)
A problem on probability is given to two students A and B. Their chances of solving it are 1/3 and ¼.The probability that the problem is solved is
(a)11/12 (b)1/12 (c)3/4 (d)1/2
Solution :
P(A)=1/3, P(A’)=2/3 , P(B)=1/4 , P(B’)=3/4
P(problem solved)=1-P(A’)P(B’)=1-(2/3)(¾) =1/2
Answer : (d)
![Page 11: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/11.jpg)
If X is a random variable such that X : 1 2 3 4 P(x) : 0 k/10 3k/10 3k/5 The value of k is (a)1 (b)2 (c)10 (d)5 Solution : Since ∑p(x)=1 , 0+k/10 + 3k/10 + 3k/5 =1 K=1 Answer: (a)
![Page 12: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/12.jpg)
The random variable X has the following distribution X : 0 1 2 3 P(x) : 0 2k 3k k Then p(x<2) is (a)1/6 (b)1/3 (c)2/3 (d)0 Solution : Since ∑p(x)=1 , 0+2k+3k+ k=1 k=1/6 Hence p(x<2)=0+2k=2/6=1/3 Ans : (b)
![Page 13: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/13.jpg)
If X is a continuous random variable with pdf
f(x)= c/x2 , 2<x<∞
0 , otherwise The value of c is
(a)1 (b)2 (c)4 (d)3
Solution :
2∞∫f(x)dx=1 hence ∫c/x^2 dx =1
C=2
Answer : (b)
![Page 14: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/14.jpg)
The odds in favour of two mutually exclusive events are 2:5 and 3:7. The probability that atleast one of two events to occur is
(a)3/35 (b)1/2 (c)41/70 (d)29/70
Solution :
P(A)=2/7 p(B)=3/10p(AuB)=2/7+3/10 =41/70
Ans : (c)
![Page 15: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/15.jpg)
The probability that a person has a B.Com degree is 0.88 and he is CA is 0.30. The probability that he has at least one of these is 0.90. The probability that he has both is
(a)0.25 (b)0.15 (c)0.255 (d)0.745
Solution :
P(B.com and CA)=p(A∩B)=p(A)+p(B)-p(AUB)=0.85+0.30-0.90=0.25
Answer : (a)
![Page 16: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/16.jpg)
If a random variable takes values 0,1,2,3 with probabilities 0.4,0.3,0.2 and 0.1 then the expected value of x is
(a)0 (b)0.4 (c)1 ( d) (0.6)
Solution :
• Since ∑p(x)=1 , we have 0.3x1+0.2x2+0.1x3=1 • Answer : (c)
![Page 17: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/17.jpg)
The probabilities that there is atleast one error in an account statement prepared by three persons A,B,C are 0.2,0.1,and 0.05. If A,B,C prepares 200,500,1000 such statements the expected number of total correct statements is (a)1460 (b)1470 (c)1590 (d)1560
Solution :
Ans : (d)
P(atleast one error)
P(No. of error)
No.of statements
xp
A 0.2 0.8 200 160 B 0.1 0.9 500 450 C 0.05 0.95 1000 950
E(x)=1560
![Page 18: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/18.jpg)
A random variable X has the probability mass function X : 1 2 3 4 5 P(x) : 2k 3k 4k 3k^2 7k^2 Find p(x<2) (a)1/10 (b)1/3 (c)1/2 (d)3/10 Solution : Since ∑p(x)=1 we have 2k+3k+4k+3k^2+7k^2=1 10k^2+9k-1=0 K=1/10 , -1 Since k≠-1 we have k=1/10 P(x<2)=5k=5/10 = ½ Ans : (c)
![Page 19: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/19.jpg)
For the probability distribution f(x)=1, 0<x<1
0 otherwise
The expected value of x is (a)∞ (b)-0.5 (c)1 (d)0.5
Solution :
E(x)=∫xf(x)dx=1
Ans : (c)
![Page 20: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/20.jpg)
The random variable X has the following distribution X : -1 2 3 P(x) : 1/6 1/2 1/3 The value of E(3x^2-2x) is (a)28/6 (b)65/3 (c)56/3 (d)32/3 Solution : 3x^2-2x : 1 16 33 P(x) : 12/80 ½ 1/3 E(3x^2-2x)=56/3 Answer : (c)
![Page 21: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/21.jpg)
A random variable x takes the values 1,1/2,1/4 with respective probabilities ¼,1/2,1/4 Then the value of E(1/x^2) is (a)25/4 (b)17/4 (c)9/4 (d)11/4
Solution :
X : 1 ½ ¼
X^2 : 1 ¼ 1/16
1/x^2 : 1 4 16
p(x) : ¼ ½ ¼
E(1/x2)=1/4 +4/2+4 = 25/4 Ans: (a)
![Page 22: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/22.jpg)
The random variable X has the following distribution X : -2 3 1 P(x) : 1/3 1/2 1/6 The value of E(2x+5) is (a)6 (b)1 (c)7 (d)5 Solution : E(x)=-2/3+3/2+1/6 = 1 E(2x+5)=7 Ans: (c )
![Page 23: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/23.jpg)
The random variable X has the following probability distribution
X : -2 3 1
P(x) : 1/3 1/2 1/6
The value of E(x^2) is
(a)4 (b)6 (c)-4 (d)-6
Solution :
X^2 : 4 9 1
P(x) : 1/3 ½ 1/6
E(x^2)=4/3+9/2+1/6=6
Ans : (b)
![Page 24: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/24.jpg)
A bag contains 10 balls of which 3 are red. Five balls
are drawn from the bag . The probability that 3 of which are red is (a)1/6 (b)3/8 (c)1/12 (d)5/12
Solution : p(3 are red)= (3C3x7C2)/10C5 =1/12
Ans : (c)
![Page 25: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/25.jpg)
A and B are two independent events with p(A)=1/3 , p(AuB)=4/5 Then p(B) is
(a)7/8 (b)9/10 (c)11/12 (d)5/6
Solution :
P(AuB)=p(A)+p(B)-p(A)p(B)
4/5 = 1/3+p(B)-1/3 p(B)
P(B)=7/8
Ans : (a)
![Page 26: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/26.jpg)
The random variable X has the following probability distribution X : 0 1 2 3 P(x) : 0 k 2k 3k The n p(x<3) is (a)1/6 (b)1/3 (c)1/4 (d)1/2 Solution : Since ∑p(x)=1 , 6k=1 K=1/6 P(x<3)=3k=3/6=1/2 Ans : (d)
![Page 27: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/27.jpg)
If the expected values of two random variables X and Y are 8 and 5 respectively the expected value of 2x-3y is
(a)0 (b)31 (c)1 (d)-10
Solution : E(2x-3y)=2E(x)-3E(y)=16-15=1
Ans : (c)
![Page 28: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/28.jpg)
If the expected values of two independent random variables X and Y are 2 and 5 respectively the expected value of xy is
(a)15 (b)10 (c)7 (d)None of these
Solution : E(xy)=E(x)E(y)=2x5=10
Ans : (b)
![Page 29: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/29.jpg)
The probabilities of A and B winning in a race are 1/6 and 1/3 respectively . The probability of A or B winning is (a)2/3 (b)4/9 (c)1/2 (d)5/6
Solution :
P(AorB)=p(A)+p(B)=1/6 +1/3=1/2
Ans : (c)
![Page 30: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/30.jpg)
The probabilities of A,B,C winning a race are ½,1/4, 1/6
respectively. The probability one or others of A,B,C winning the race is (a)5/6 (b)2/3 (c)11/12 (d)3/4
Solution :
P(A)=1/2 p(B)=1/4 p(c)=1/6
P(Aor B or C )=1/2 + ¼ +1/6 =11/12
Ans : (c)
![Page 31: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/31.jpg)
If A and B toss a die, A gets a prize of Rs 600 , if both the dice show the same number , otherwise B wins. The expected amount of B winning is
(a)400 (b)500 (c)410 (d)550
Solution :
Let X denote the amount of B winning .
E(x)=600x5/6+0x1/6=500
Ans : (b)
![Page 32: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/32.jpg)
A business man ventures on a project in which he can make a profit of Rs3,00,000 or a loss Rs1,00,000.The probability of making a profit of Rs3,00,000 is 0.6.Then the expected gain or loss is
(a)Rs180,000 (b)Rs1,40,000 (c)2,00,000 (d)Rs60,000
Solution :
The expected gain = 300000x0.6-100000x0.4 = Rs1,40,000
Ans : (b)
![Page 33: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/33.jpg)
The wages of eight workers in rupees are 62,50,70,40,56,45,45,32.If one of the worker is chosen at random the probability that his wage is above the average is (a)2/5 (b)3/8 (c)1/2 (d)5/8
Solution : Mean = (62+50+70+40+56+45+45+32)/8 =50
P(Mean>50)=3/8
Ans : (b)
![Page 34: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/34.jpg)
If X and Y are independent random variables with standard deviation 3 and 4 then the standard deviation of (X+Y) is (a)7 (b)1 (c)25 (d)5
Solution : If X and Y are independent random variables the v(X+Y)=v(X)+v(Y)=9+16=25
Standard deviation of (X+Y) = √25=5
Ans : (d)
![Page 35: Multiple Choice Questions - ICAI Knowledge Gateway · Multiple Choice Questions . CPT Section D, Quantitative Aptitude, Chapter 13 . Prof(Dr.) P.R.Vittal ... There are 10 balls numbered](https://reader031.vdocument.in/reader031/viewer/2022011801/5ae2778a7f8b9a0d7d8c60f2/html5/thumbnails/35.jpg)