CA Foundation Question Paper with Solution Dec 2023

CA Foundation Question Paper with Solution Dec 2023 - MATHS

Ca Foundation Question Paper with Solution | Maths Dec 23 Attempt

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7. If n^th terms of an AP series is 7n – 2, then sum of ‘n’ terms is :

(a) 0.5(7n² + 2n)

(b) 0.5(7n² - 3n)

(d) 0.5(7n² - 2n)

Answer : c

n^th term = 7n – 2

go by option :

i)Option A :

S_n = 0.5 ( 7n² + 2n )

n^th = 7n – 2

n = 1

1^st term = 7 X 1-2 = 5

Put n – 1 in S_n = 0.5 (7n² + 2n)

= 0.5 ( 7 X 1 + 2)

= 4.5

ii)key option c : S_n= 0.5 (7n² + 3n)

n^th = 7n -2 n=1 1^st term = 5

S_n = 0.5(7 X 1 + 3)

S₁= 0.5 X 10

= 5

Key n = 2

S₂ = 0.5(7 X 4 + 3 X 2)

= 0.5 (28 + 6)

= 0.5 (34)

=17

1^st term = 5

2^nd term = 7n – 2 = n = 2

= 7 X 2 – 2

= 14 -2 = 12

S₂ = 5 + 12 = 17

Thus ; option C is correct

8. In a certain language SIKKIM is written as THLIJL then how is TRAINING written in that code?

(a) SQBHOHOH

(b) UQBHOHOF

(d) UQBJOHOM

Answer : b

S	I	K	K	I	M
+1	-1	+1	-1	+1	-1
T	H	L	J	J	L

T	R	A	I	N	I	N	G
+1	-1	+1	-1	+1	-1	+1	-1
U	Q	B	H	O	H	O	F

9. Seven friends O, P, Q, R, S, T And U are watching movies sitting in a row , S is setting at one extreme end. Q is sitting second to the right of S. P is setting between O and Q Both U and O are not sitting at extreme end. R is sitting immediate lift of T. who is setting n the middle?

(a) O

(b) P

(d) U

Answer : b

Left

Right

P is Sitting in the middle of the Row.

10. DOCTOR In certain language, PEAR is coded as 7519, and TOIL is coded as 2693, then how DOCTOR be written in that code?

(a) 463293

(b) 463239

(d) 463296

Answer : c

P	E	A	R
7	5	1	9

T	O	I	L
2	6	9	3

D	O	C	T	O	R
4	6	3	2	6	9

11. Kamal walks 10 Km north from there he walks 6 Km towards south. Then he walks 3 Km towards east. How far and in which direction is he with reference to starting point?

(a) 5 Km south – east

(b) 7 Km north – east

(d) 7 Km south – east

Answer :

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12. There are six persons A, B, C, D, E and F in a family. B is the son of C is not the mother of B, A and C are a married couple. E is the brother of C. D is the daughter of A. F is the brother B. Who is the mother B?

(a) A

(b) E

(d) F

Answer :

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13. When Mr. P saw Mr. Q he recalled, “ He is the son of the father of my daughter’s mother.” Who is Mr. Q to Mr. P?

(a) Brother

(b) Cousin

(d) Brother-in-law

Answer :

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14. Introducing a boy , Akshat said, “His mother is the only daughter of my mother-in-law.” How is Akshat related to the boy?

(a) Uncle

(b) Father

(d) Husband

Answer :

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15. Showing the man playing the cricket, Ms. P said, “ He is the brother of my uncle’s daughter.” Who is the man to Ms. P?

(a) Son

(b) Cousin

(d) Brother-in-law

Answer :

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16. By plotting cumulative frequency against the respective class boundary, we get

(a) Frequency curve

(b) Ogives

(d) Histogram

Answer :

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17. The Frequency of visitor in an office is given below:

Time	9 AM - 11 AM	11 AM - 1 PM	1 PM- 3 PM	3 PM - 5 PM
Frequency	5	18	7	12

Find the cumulative frequency of visitors for the time 11 AM – 1 PM ?

(a) 5

(b) 23

(d) 30

Answer : b

Time	F	CF
9 AM - 11 AM	5	5
11 AM - 1 PM	18	23
1 PM- 3 PM	7	30
3 PM - 5 PM	12	42

18. If the AM and HM for two numbers are 5 and 3.2 respectively then the GM will be:

(a) 4.4

(b) 4.2

(d) 3.8

Answer : c

Here AM = 5 & HM = 3.2.

Let 2 numbers be ${x_1}\& {x_2}$

then $AM = \frac{{{x_1} + {x_2}}}{2}$

$5 = \frac{{{x_1} + {x_2}}}{2}$

$\therefore {x_1} + {x_2} = 10$ __________(1)

$HM = \frac{2}{{\sum\limits_{}^{} {\left( {\frac{1}{{{x_i}}}} \right)} }}$

$3.2 = \frac{2}{{\frac{1}{{{x_1}}} + \frac{1}{{{x_2}}}}}$

$3.2 = \frac{2}{{\frac{{{x_1} + {x_2}}}{{{x_1}{x_2}}}}}$

$\therefore \frac{2}{{3.2}} = \frac{{{x_1} + {x_2}}}{{{x_1}{x_2}}}$

$\therefore \frac{2}{{3.2}} = \frac{{10}}{{{x_1}{x_2}}}$ [ From (1)]

$\therefore {x_1}{x_2} = 16$

Now, GM = $\sqrt {\left( {{x_1}{x_2}} \right)}$

$= \sqrt {16}$

= 4

19. If the quartile deviation is 12 and the first quartile is 25, then the value of the third Quartile is :

(a) 37

(b) 49

(d) 60

Answer :

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20. If mode of a grouped data is 10 and median is 6, then what is the value of mean?

(a) 2

(b) 4

(d) 8

Answer : b

Mode = 3Me – 2

10 = 3 X 6 - 2

10 = 18 – 2

+ 2 = 18 –10

+ 2 = 8

= 8/2

= 4

21. In Standard Normal distribution, then the value of the mean (µ) and standard deviation () is:

(a) µ = 0 and = 0

(b) µ = 0 and = 1

(d) µ = 1 and = 1

Answer :

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22. If the regression line of y on x and of x on y are given by 10x - 290 = –20y and 7y - 104 = – 4x then the arithmetic means of x and y are given by

(a) 5, 12

(b) 7, 12

(d) 5,7

Answer : a

Y on n

10n – 290 = -20y

N on y

7y – 104 = -4n

Arithmetic mean =

Intersaction point of this 2 equation

10n – 290 = -20y

10n + 10y = 290

n + 2y = 29

multiply by 4

4n + 8y = 116

7y – 104 = -4n

4n + 7y = 104

Subtract 1 & 2

4n + 8y + 116

-4n – 7y = -104

Y = 12

Original equation =

n + 2y = 29

n + 2 x 12 = 29

n = 29 – 24

n = 5

Arithmetic mean = ( 5, 12 )

23. If mean and variance of a random variable which follows the Binomial Distribution are 7 and 6 respectively, then the probability od success is:

(a) 6/7

(b) 36/46

(d) 1/49

Answer :

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24. __________ may be defined as the ratio of covariance between the two variables to the product of the standard deviations of the two variables.

(a) Scatter diagram

(b) Karl Person’s correlation coefficient

(d) Correlation of concurrent deviations

Answer : b

25. The solution of cubic equation x³ – 23x³ + 142x – 120 = 0 is given by the triplet:

(a) (1, 10, 12)

(b) (1, -10, 12)

(d) (1, 10, -12)

Answer : a

Equation = n³ – 23n² + 142n – 120 = 0

go by option =

Try 1

1 -23 + 142 – 120 = 0

As such ; option c is ruled out

Try 12

(12)³ – 23 X (12)²

= 1728 – 3312 + 1704 – 120

= 0

As such ; option D is ruled out

Try 10

(10)³ -23 X (10)² + 142 X 10 – 120

= 1000 – 2300 + 1420 -120

= 0

As such ; option A is right

26. If 2^x = 4^y = 8^z and $\frac{1}{{2x}}$ + $\frac{1}{{4y}}$ + $\frac{1}{{6z}}$ = $\frac{{24}}{7}$ , then the value of z is:

(a) 7/16

(b) 7/32

(d) 7/64

Answer :

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27. The solution of the inequality $\frac{{5\, - \,2x}}{3}$ ≤ $\frac{x}{6}\, - \,5$ is:

(a) x ≥ 8

(b) x ≥ 7

(d) x ≤ 40/3

Answer :

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28. What is the effective rate of interest when principal amount of ₹ 50,000 deposited in a nationalized bank for one year, corresponding to a nominal rate interest 8% per annum compounded quarterly, given (1.02)⁴ = 1.0824

(a) 10.38%

(b) 8.08%

(d) 8.24%

Answer :

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29. Manoj invests ₹ 12,000 at 6% per annum simple interest to obtain a total amount of ₹ 14,880. What is the time for which the amount was invested?

(a) 3 years

(b) 4 years

(d) 5 years

Answer :

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30. Mr. X makes a deposit of ₹ 50,000 in the bank for a period of years. If the rate of interest is 12% per annum compounded half yearly, then the maturity value of the money deposited by Mr. X is: (Where (1.06⁾⁵ = 1.3382)

(a) ₹ 66,910

(b) ₹ 66,123

(d) ₹ 65,550

Answer :

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31. A,B,C,D,E,F,G,H are sitting in a circle facing the center. D sites 3^rd to left of A. E sits to the immediate right of A. B is third to left of D. G is second to right of B. C is neighbourer of B. C is 3^rd to left of H. who is sitting exactly in between F and E.

(a) C

(b) E

(d) A

Answer : d

A is sitting exactly between F and E.

32. Given an infinite geometric series with first term ‘a’ and common ratio ‘r’. If its sum is 4 and the second term is ¾ , than one of correct option is

(a) a = 1 and r = 1/4

(b) a = 3 and r = 3/4

(d) a = 1 and r = 1/2

Answer : c

A , ar , ar2, m³

1. S = $\frac{a}{{1\, - \,r}}\,$

4 = $\frac{a}{{1\, - \,r}}\,$

4 = 4r = a

4 = a + 4r

a + 4r

= 4

2. ar = $\frac{3}{4}\,$

1^st term = a

2^nd term = a X r = m

ar = $\frac{3}{4}\,$

2 equation

a + 4r = 4 ……(1)

ar = ……(2)

start by option

1. a = 1 r = $\frac{1}{4}\,$

equation (1) 1 + 4 X $\frac{1}{4}\,$ = 1 + 1 = 2 ≠ 4

rule out option A

2. a = 3 r = $\frac{3}{4}\,$

equation (1) a + 4r = 4

3 + $\frac{{4\,X\,3}}{4}\,$

= 3 + 3

= 6 ≠ 4

Option B thus wrong

3. option C =

a = 3 r = $\frac{1}{4}\,$

equation (1) a + 4r = 4

3 + $\frac{{4\,X\,1}}{4}\,$

= 3 + 1

= 4

equation (2) ar = $\frac{3}{4}\,$

$\frac{{3\,X\,1}}{4}\,$ = $\frac{3}{4}\,$

Thus option C is Right

33. Find the value of integral

(a)

(b)

(c)

(d)

Answer :

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34. If ¹⁵C_3r= ¹⁵C_r+3 then r equal to :

(a) 5

(b) 4

(d) 2

Answer : c

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35. Find odd one out of the series: 16, 25, 36, 72, 144, 196 and 225.

(a) 36

(b) 72

(d) 225

Answer : b

16	25	36	72	144	196	225
Hint: All these numbers are very close to perfect square.
16	25	36	72	144	196	225
from the pattern, we can understand that all the numbers are perfect square except 72, because 72 is not a perfect square.
16	25	36		144	196	225

36. In a certain system of coding the word “STATEMENT” is written as “TNEMETATS”. In the same system of coding the word “POLITICAL” written as:

(a) LACITILOP

(b) LACTILIOP

(d) LACATILOP

Answer : a

S	T	A	T	E	M	E	N	T
T	N	E	M	E	T	A	T	S

P	O	L	I	T	I	C	A	L
L	A	C	I	T	I	L	O	P

37. Five person are living in a five story building. Mr. Mahesh lives in flat above Mr. Ashok. Mr. Lokesh lives in a flat below Mr. Gaurav and Mr. Rakesh lives in a flat below Mr. Lokesh. Who possibly lives in the ground floor?

(a) Mr. Rakesh

(b) Mr. Lokesh

(d) Mr. Gaurav

Answer : a

	Case 1	Case 2
4^thFloor	Mahesh	Gaurav
3^rd Floor	Ashok	Lokesh
2^nd Floor	Gaurav	Rakesh
1^st Floor	Lokesh	Mahesh
Ground Floor	Rakesh	Ashok

Hence Ashok is not an option. Rakesh is the Correct Answer.

38. Sunita walked 30 meters towards the East, took a right turn and walked 40 meters. Then she took a left turn and walked 30 meters. In which direction is she now from the starting point?

(a) North-East

(b) East

(d) South

Answer :

39. If mean of 5 observations x + 1, x + 3, x + 5, x + 7 and x + 9 is given 15, then the value of x will be:

(a) 10

(b) 12

(d) 11

Answer :

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40. Consider the following data where class length is given as 5. Calculate the number of class intervals.

59, 68, 78, 57, 44, 73, 40, 60, 70, 47

(a) 5

(b) 6

(d) 8

Answer :

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41. The mean of the first three terms is 17 and mean of next four trems is 21. Calculate the mean of seven terms.

(a) 18.28

(b) 19.78

(d) 19.28

Answer :

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42. The mean of a set of 20 observations in 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

(a) 17.6

(b) 18.9

(d) 24.6

Answer :

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43. If P(A) = ½ and P(B) = 1/3 and P (A ∩ B)

(a) 1/4

(b) 2/3

(d) 1/2

Answer : c

P(A)=1/2 , P(b)=1/3

P(AՍB) =2/3 find P(AႶB)

P(AՍB)=P(A)+P(B)-P(A-B)

=1/6

44. If six coins are tossed simultaneously. The probability of obtaining exactly two heads are.

(a) 0.2343

(b) 0.9841

(d) 0.0156

Answer :

45. If ‘x’ and ‘y’ are related as 3x-4y = 20 and the quartile deviation of ‘x’ is 12, then the quartile deviation of ‘y’ is :

(a) 9

(b) 8

(d) 6

Answer :

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46. A box contain 20 electrical bulbs out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of them is defective.

(a) 7/19

(b) 4/19

(d) 15/19

Answer :

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47. If the coefficient of correlation is 0.8 and regression coefficient = 0.32 then what is the value of regression coefficient ?

(a) 2

(b) 1

(d) 0.48

Answer : a

r_xy= 0.8

b_xy = 0.32

To find

We know ;

0.8 =

Squaring both sides

0.64 = b_xy × 0.32

b_xy= 0.64/0.32

= 2

48. The gross monthly pay of an employee was ₹ 15,000 in a year 2020. The consumer price index number in 2023 is 155 with 2020 as base year. If employee is to rightly compensate what dearness allowance is required to be paid?

(a) ₹ 8,000

(b) ₹ 8,250

(d) ₹ 8,750

Answer : b

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49. If the Regression coefficient (ryx) of y on x is greater than unity, then other Regression coefficient (rxy) of x on y is:

(a) Less than one

(b) Greater than one

(d) Equal to zero

Answer :

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50. If 4y – 6x = 18 is regression line of y and x coefficient of correlation between x and y is 0.8. What is the value of regression coefficient of x on y?

(a) 0.2448

(b) 0.4267

(d) 0.7441

Answer : b

4y – 6x = 18

line = y on x = 4y = 6x +18

y = 18/4 + 6x/4

To find = bxy

We know =

Equation :

4y = 6n + 18

b_yx = 6/4 = regression coefficient of x on y

Now ; orginal =

squaring both

bxy = 0.4267

51. Divide 27 into two parts, so that 5 times the first and 11 times the second together equal to 195, thren the ratio of first and second part is :

(a) 17:10

(b) 15:12

(d) 16:11

Answer : a

Divide 27 in two parts :- Part 1 and Part 2

5 time 1^st + 11 time 2^nd

= 195

Option A => 17 : 10

Let’s try if satisfies condition =>

5 × 17 + 11 × 10

=195 ® as gives in question’s condition.

option A is right

52. The solution of the linear simultaneous equations 2x-y=4 and 3x+4y=17 is

(a) x=3;y=2

(b) x=2;y=3

(d) x=-2;y=-3

Answer : a

2x – y = 4 …………………(1)

3x + 4y = 17 ……………..(2)

Multiple 4 is equation …….(1)

8x – 4y = 16 ………………(3)

3x + 4y = 17

11x = 33

x = 3

Equation (1)

2x – y =4

2 × 3 – y = 4

6 – 4 = y

y= 2

Option A is right.

53. If ,then the value of n is

(a) 2

(b) 0

(d) 4

Answer :

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54. The roots of the equation x³ + x² – x – 1 = 0 are

(a) x=1,x=-1,x=-1

(b) x=1,x=1,x=-1

(d) x=1,x=1,x=1

Answer : a

x³ + x² – x – 1 = 0
(A)x = 1,x = -1,x = -1
Put x= 1
1 + 1 – 1 - 1 = 0
Put x=-1
-1 + 1 + 1 - 1 = 0

Option A is Right

55. What will be the future value of an annuity of ₹ 2,500 made annually for 12 years at interest rate of 5% compounded annually if (1.05)¹² = 1.7958

(a) ₹ 37,588.58

(b) ₹ 39,790.00

(d) ₹ 42,603.68

Answer :

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56. If the initial investment of ₹ 4,00,000 becomes ₹ 6,00,000 in 24 months, then the Compound Annual Growth Rate (CAGR) is:

(a) 30.33%

(b) 22.4%

(d) 14.47%

Answer :

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57. Mrs. X invests in an annuity immediately that promises annual payment of ₹ 50,000 for the next 16 years. If the interest rate is 6% compounded annually then the approximate present value of this annuity is , where(1.06)15 = 2.3965.

(a) ₹ 5,51,217.75

(b) ₹ 5,75,900.00

(d) ₹ 5,35,612.45

Answer :

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58. If A = {2,4} and B = {1,2,3}, then (A Ս B) × (A Ո B) is equal to :

(a) {(1,2),(2,2),(3,2)}

(b) {(1,2),(2,2),(2,3),(2,4)}

(d) {(1,2),(2,2),(3,2),(4,2)}

Answer : d

A={2,4}

B={1,2,3}

(A Ս B)×(A Ո B)

A Ս B = {1,2,3,4}

A Ո B = {2}

To find :-

{1,2,3,4}×{2}

{(1,2),(2,2),(3,2),(4,2)}

59. Find the value of ‘X’ for the following data.

1 + 7 +13 +19 ...... + x = 225

(a) 56

(b) 63

(d) 42

Answer :

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60. If x³+ y³ – 3 axy = 0, then dy/dx is equal to:

(a)

(b)

(c)

(d)

Answer :

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61. Find ‘n’ if ⁿp₂=72

(a) 12

(b) 36

(d) 9

Answer : d

ⁿp₂= 72

(n)(n-1)=72

go by option try n =19

(9)(9-1) = 9 × 8 = 72

then n=9.

Nine friends, J,K,L,M,N,O,P,Q and R, are sitting in a row. L is to the right of M and is at the third place to the right of N, K is at one end of the row. Q is seated adjacent to both O and P. O is at the third place to the left of K. J is right next to L and the left of O.

Answer the following Question :(Q 62 & 63)

62. Who is immediate left to M?

(a) N

(b) R

(d) J

Answer : b

Left

Right

The Immediate Left of M is R

63. Who is sitting at the center of the row?

(a) I

(b) J

(d) Q

Answer : b

J is sitting at the center of the row.

64. Mr. X walks 14 kilometers towards north. From there, he walks 8 kilometers towards south. Then he walks 8 kilometers towards the West. How far and in which direction is he with reference to his starting point?

(a) 10 kilometers North-West

(b) 10 kilometers West

(d) 7 kilometers West

Answer :

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65. Find the missing number ?

2, 3, 8, ? 3968

(a) 65

(b) 63

(d) 80
Answer : b

2	3	8	?	3968
Hint : we can observe a pattern like.
2	3	8	?	3968
	2² - 1	3² - 1	8² - 1	63² - 1
From the pattern, we can understand that the next Value would be 8² - 1 = 63. Hence, our term would be 63.
2	3	8	63	3968

66. If A.M. and G.M. of two positive numbers a and b are 12 and 12, respectively, find the numbers.

(a) 18 and 16

(b) 15 an d 9

(d) 12 and 12

Answer :

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67. In a cumulative frequency curve, what is represented on the Y-axis ?

(a) Class interval

(b) Cumulative frequency

(d) Relative density

Answer :

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68. If the range of the data is 20 and it's smallest value is 5, then what is the largest value of data is ?

(a) 20

(b) 25

(d) 30

Answer : b

Range = < - 5

20 = < - 5

< = 25

69. Ina a frequency distribution, the relative frequency of the class is :

(a) The ratio of the class frequency to the total number of classes

(b) The ratio of the class frequency to the total frequency

(d) The ratio of the class mid point to the class frequency

Answer :

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70. If a card is drawn at random from a pack of 52 cards, what is the chancof getting a club or a king?

(a) 13/52

(b) 4/52

(d) 16/52

Answer : d

Card drawn at random from 52 cards

P (club or king)

P(club) = 13/52 = 1/4

P(King) = 4/52 = 1/13

P(both) = 1/52

P(club or king) = P(club) + P (king) = P(both)

= 13/52 + 4/52 + 1/52

=16/52

71. If ‘x’ and ‘y’ are independent normal variate with mean and Standard deviation µ1,µ2 andrespectively, then for z = x + y which also follows normal distribution mean and SD are:

(a) Mean = µ1 + µ2, SD = $\sqrt {{\sigma _1}^2 + {\sigma _2}^2}$

(b) Mean = (µ1 + µ2)/2, $SD = \sqrt {({\sigma _1}^2 + {\sigma _2}^2)/2}$

(d) Mean = (µ1 - µ2)/2, $SD = \sqrt {({\sigma _1}^2 - {\sigma _2}^2)/2}$

Answer :

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72. For a binominal distribution the mean and standard deviation are 10 and 3 respectively. Find the value of n.

(a) 30

(b) 9

(d) 100

Answer :

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73. An Index constructed to measure the relative change in the price of an item or a group of item is called :

(a) Quantity index number

(b) Price index number

(d) Composite index number

Answer :

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74. Fisher's index does not satisfy following test.

(a) Unit Test

(b) Time Reversal Test

(d) Factor Reversal Test

Answer :

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75. If the Laspeyre's index is 110 and Passche's index is 108, then what is the value of Fisher's index?

(a) 106.50

(b) 107.60

(d) 109.88

Answer : c

f = $\sqrt { \prec \, \times \,P}$

f = fisher’s index

$\prec$ = Laspeyre’s index

P = Passche’s index

f =

= 108.99

76. From the year 2013 to 2023, Consumer price index number is increased from 135 to 180. During this period, salary of the employees as increased from 135 to per pay commission recommendations was revised from ₹ 23,000 to ₹ 29,500. In real terms, an employee should get following additional amount (upto nearest whole number) to maintain his previous standard of living.

(a) ₹1168

(b) ₹666

(d) ₹6500

Answer : a

CPi₂₀₁₃= 135, salary = 23,000

CPi₂₀₂₃ = 180 , salary = 29,500

1. ideal salary that should have been in 2023.

= Salary₂₀₁₃ $\times$

= 23000 180 / 135

= 30667

2. actual salary in 2013 = 29,500

To compenare

Additional

Salary should be = 30667 – 29500

= 1167 approx.

77. Given x = and y = then find the value of

(a) 63

(b) 61

(d) 60

Answer :

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78. If $\alpha$ and $\beta$ are the roots of the equation x² – 4x +1 = 0 , then value of will be $^{{\alpha ^3}\, + \,{\beta ^3}}$

(a) 76

(b) -76

(d) -52

Answer : c

x² – 4x + 1 = 0

$\alpha \, + \,\beta$ = -(-4/1) = 4

$\alpha \beta$ = 1

Value of ${{\alpha ^3}\, + \,{\beta ^3}}$

= ( $\alpha \, + \,\beta$ )³- 3( $\alpha \, + \,\beta$ )

=(4)³ – 3(1)(4)

= 64-12

= 52

79. A software company should recruit more than or equal to 10 employees at a time in their recruitment drive. Under these conditions, company recruits experienced (x) and freshers (y) employees. The values of x and y can be related by the following inequality.

(a) x + y ≤ 10 x ≥ 0, y ≥ 0

(b) x + y ≥ 10 x ≥ 0, y ≥ 0

(d) x + y ≥ 10 x ≤ 0, y ≤ 0

Answer :

80. A machine costing ₹ 1,00,000 has useful life of 10 years. If the rate of depreciation 12%, what is scrap value of the machine at the end of life? Given ${\left( {0.88} \right)^{10}} = 0.27850$

(a) ₹ 22,850

(b) ₹ 26,850

(d) ₹ 28,850

Answer :

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81. Compute the compound interest on ₹ 6,000 for $1\frac{1}{4}$ years at 8% per annum. Interest will be compounded quarterly.

(a) 642

(b) 630.78

(d) 624.48

Answer :

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82. The population of city increases at the rate of 5% every year. What will be the population of the city in the year 2023, if its population in 2021 was 1,00,000?

(a) 1.05,500

(b) 1,10,250

(d) 1,20,550

Answer : b

Population of city 5% every year

P₂₀₂₁ = 1,00,000

P₂₀₂₂ = 1,00,000 + 1,00,000 5%

= 1,05,000

P₂₀₂₃ =1,05,000 + 1,05,000 5%

= 1,10,250

83. Mr. XYZ invested ₹ 60,000 in a nationalized bank in the form of fixed deposit at the rate of 7.5% per annum simple interest rate. He received ₹ 73,500 after the end of the term of fixed deposit. Calculate the period for which ₹ 60,000 was invested in fixed deposit.

(a) 3 years

(b) 3.5 years

(d) 4.5 years

Answer :

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84. Calculate the present value of ₹ 2,000 to be required after 10 years Compounded annually at 5% per annum given (1.05)¹⁰ = 1.62889

(a) 1227.82

(b) 1282.48

(d) 1822.65

Answer :

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85. If x=5t² + 3 and y =2t² + 1, then dy/dx can be calculated as

(a) 2

(b) 1

(d) 2/5

Answer :

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86. IF B = {1,2,3,4,5}, then the number of proper subset of B is

(a) 120

(b) 30

(d) 32

Answer : c

B = {1,2,3,4,5}

Proper subsets = 2ⁿ- 1

=2⁵-1

=32-1

=31

87. If A={1,2}, B={3,4}, C = {5,6} then the value of A × (B U C)

(a) {(1,2)(3,4) (5,6)}

(b) {(1,3)(2,3)(1,4)(2,4)(2,5)(1,5)(1,6)(2,6)}

(d) {(3,1)(2,3)(4,1)(2,4)(2,5)(1,5)(1,6)(2,6)}

Answer : b

A={1,2} B={3,4} C={3,4}

A × (B Ս C)

1. (B Ս C) = {3,4,5,6}

A × (B Ս C)

{1,2} × {3,4,5,6}

= {(1,3)(2,3)(1,4)(2,4)(1,5)(2,5)(1,6)(2,6)}

88. Calculate $\int\limits_1^3 {\left( {{e^x} - \frac{1}{{{x^2}}}} \right)} dx$

(a) ${e^3} - e - \frac{2}{3}$

(b) ${e^2} - e - \frac{1}{3}$

(d) ${e^3} - e + \frac{2}{3}$

Answer :

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89. In a family, there are six members A,B,C,D,E and F. A & B are married couple. A being the male member. D is only son of C and is brother of A. E is sister of D. daughter-in-law of F, whose husband is died. How C is related to B?

(a) Brother

(b) Nephew

(d) Sister-in-law

Answer :

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90. Pointing to a lady, Suresh said is “She mother of my son's wife's daughter". is Suresh related to lady?

(a) Uncle

(b) Cousin

(d) Father-in-law

Answer :

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91. Mr. X walks northwards. After a while, he turns to his right and a little further to his left. Finally, after walking 500 Meter, he turns to his left again. In which direction is he moving now.

(a) North

(b) South

(d) West

Answer :

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92. Pointing to a lady, a man said, “The son of her only brother is the brother of my wife ”. How is lady is related to man ?

(a) Mother-in-law

(b) Sister of father-in-law

(d) Cousin

Answer : b

93.The Median of the following frequency distribution is

x	0-10	10-20	20-30	30-40	40-50
f(x)	3	5	20	12	7

(a) 27.75

(b) 9.35

(d) 10.01

Answer :

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94. Frequency density corresponding to a class interval is ratio of:

(a) class frequency to class length

(b) class frequency to total frequency

(d) class length to class frequency

Answer :

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95. If two variable 'x' and 'y' are related as 2x-y=3, if the median of 'x' is 10. What is median of 'y' ?

(a) 4

(b) 7

(d) 6

Answer :

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96. If the mean and median of a modrately asymmetrical series are 26.8 and 27.9 respectively, then the most probable mode is :

(a) 35.4

(b) 30.1

(d)70.8

Answer : b

Mode = 3me - 2mean

=3 × 27.4 – 2 × 26.8

=83.7 - 53.6

=30.1

97. A Perpendicular drawn from the point of intersection of two Ogive on the horizontal axis gives the value of

(a) 2^nd Quartile

(b) 3^rd Quartile

(d) 1^st Quartile

Answer :

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98. A number is selected from the first 30 natural numbers. What is the probability that, it would be divisible by 3 or 8 ?

(a) 0.2

(b) 0.4

(d) 0.8

Answer : b

1^st 30 natural number

1. Divisible by 3 –

3,6,9 ….. 27,30

Total = 10

2. Divisible by 8 –

8,16,24

Total = 3

3. .Divivsible by both

Total = 1

4. P(divisible) by 3 or 8

=12/30

=0.4

99. P(AՈB) = 1/3, P(AՍB) =5/6,P()=1/2,then P() is :

(a) 2/3

(b) 1/3

(d) 3/4

Answer :

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100. A number is selected at random from the first 100 natural numbers. What is the probability that it would be a multiple of 3 or 7 ?

(a) 33/100

(b) 4/100

(d) 43/100

Answer : d

To find probability that it would be a multiple of 3 or 7:-

a) multiple of 3:

3,6,9,…….,99
total no = 33

b) multiple of 7:

7,14,21,….,98
Total no = 14

c) multiple of both:

21,42,63,84,….
total no =4

d) p(that it would be a multiple of 3 or 7)

CA Foundation Question Paper with Solution Dec 2023 - MATHS

Ca Foundation Question Paper with Solution | Maths Dec 23 Attempt

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