## Class/Course - CA - CPC

### Subject - Quantitative Aptitude

#### Total Number of Question/s - 6262

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• 1. Ratio and Proportion, Indices and Logarithm - Quiz

1. Show that  $\left ( x^{\frac{1}{a-b}} \right )^{\frac{1}{a-c}}\times \left ( x^{\frac{1}{b-c}} \right )^{\frac{1}{b-a}}\times\left ( x^{\frac{1}{c-a}} \right )^{\frac{1}{c-b}}$ is given by
a) 0
b) 1
c) -1
d) None

2. On solving the equation log3[log2(log3t)] = 1 we get the value of t as
a) 8
b) 18
c) 81
d) 6561

• 2. Equations - Quiz

1. If $\frac{x-a}{b}+ \frac{x-b}{a} = \frac{b}{x-a} +\frac{a}{x-b}$ then the values of x are
a) 0, (a+b) , (a-b)
b) 0, (a+b), $\frac{a^{2}+b^{2}}{a+b}$
c) 0, (a-b), $\frac{a^{2}+b^{2}}{a+b}$
d) $\frac{a^{2}+b^{2}}{a+b}$

2. Solving equation  $6\left [ \sqrt{\frac{x}{1-x}} + \sqrt{\frac{1-x}{x}}\right ] = 13$ following roots are obtained
a) $\frac{4}{13}, \frac{9}{13}$
b) $\frac{-4}{13}, \frac{-4}{13}$
c) $\frac{4}{13}, \frac{5}{13}$
d) $\frac{6}{13}, \frac{7}{13}$

• 3. Inequalities - Quiz

1. Graph of the inequations are below:

L1 : 2x + y = 9 L2 : x + y = 7 L3 : x + 2y = 10 L4: x + 3y = 12
The coomon region (shaded part) indicated on the diagram is expressed by the set of inequalities
a) 2x + y ≤ 9
x + y ≥ 7
x + 2y ≥ 10
x + 3 y ≥ 12
b) 2x + y ≥ 9
x + y ≤ 7
x + 2y ≥ 10
x + 3y ≥ 12
c) 2x + y ≥ 9
x + y ≥ 7
x + 2y ≥ 10
x + 3 y ≥ 12
x ≥ 0, y ≥ 0
d) none of these

2. A car manufacturing company manufactures cars of two types A and B. Model A requires 150 man-hours for assembling, 50 man-hours for painting and 10 man-hours for checking and testing. Model B requires 60 man-hours for assembling, 40 man-hours for painting and 20 man-hours for checking and testing. There are available 30 thousand man-hours for assembling, 13 thousand man-hours for checking and testing. Express the above situation using linear inequalities. Let the company manufacture x units of type A model of car and y units type B model of car. Then, the inequalities are:
a) 5x+2y ≥ 1000; 5x + 4y ≥ 1300,
x+2y ≤ 500; x ≥ 0, y ≥ 0,
b) 5x + 2y ≤ 1000, 5x+4y ≤ 13000,
x+2y ≥ 500; x ≥ 0, y ≥ 0.
c) 5x+2y ≤ 1,000, 5x+4y ≤ 1300,
x+2y ≤ 500; x≥ 0, y≥ 0.
d) 5x + 2y = 1000, 5x+4y ≥ 1300,
x+2y = 500; x≥ 0, y ≥ 0.

• 4. Simple and Compound Interest - Quiz

1. Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. If his expectation of life is another 30 years and he starts making equal annual investments commencing now at 3% compound interest p.a. How much should he invest annually?
a) Rs. 84.077
b) Rs. 81.628
c) Rs. 84.449
d) Rs. 84.247

2. A loan of Rs. 10.000 is to be paid back in 30 equal instalments. The amount of each installment to cover the principal and at 4% p.a. CI is
a) Rs. 587.87
b) Rs. 587
c) Rs. 578.87
d) None of these

• 5. Permutations and Combinations - Quiz

1. 51c31 is equal to
a) 51c20
b) 2.50c20
c) 2.45c15
d) None of these

2. Find  the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included.
a) 39,000
b) 37,600
c) 39,600
d) 36,000

• 6. Sets, Functions and Relations - Quiz

1. For a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming, further more 40 are interested in both music and photography, 30 in both music and swimming, 20 in photography and swimming and 10 in all the three. How many are interested in photography but not in music and swimming?
a) 30
b) 15
c) 25
d) 20

2. If A = {1, 2, 3, 4, }
B = {2, 4, 6, 8}
f(1) = 2, f(2) = 4, f(3) = 6 and
f(4) = 8, And f: →B then f-1 is:
a) {(2, 1), (4, 2), (6, 3), (8, 4)}
b) {(1, 2), (2, 4), (3, 6), (4, 8)}
c) {(1, 4), (2, 2), (3, 6), (4, 8)}
d) None

• 7. Limits and Continuity - Quiz

1. $\lim_{x\rightarrow 1}$ $\frac{x^{3}-1}{x-1}$ is equal to
a) 3
b) -1/3
c) -3
d) None of these

2.  $\lim_{y\rightarrow 0}$ $\frac{3y+|y|}{7y-5|y|}$ =
a) 2
b) 1/6
c) 3/7
d) Does not exit

• 8. Differential and Integral Calculas - Quiz

1. Given exy - 4xy = 0,$\frac{dy}{dx}$ can be proved to be
a) -y/x
b) y/x
c) x/y
d) None of these

2. Integrate w.r.t x, (3x-1+ 4x2 -3x +8)
a) 3log x - (4/3)x3 + (3/2)x2 - 8x
b) 3log x + (4/3)x3 - (3/2)x2 + 8x
c) 3log x + (4/3)x3 + (3/2)x2 + 8x
d) None

• 9. Statistical Description of Data - Quiz

1. The quickest method to collect primary data is:
a) Personal interview
b) Indirect interview
c) Mailed Questionnaire Method
d) Telephonic interview

2. In a study about the male and female students of commerce and science departments of a college in 5 years, the following dates were obtained:
 1995 2000 70% male students 65% read commerce 20% of female students read science  3000 total no. of students 75% male students  40% read science  50% of male students read commerce   3600 total no. of students

After combining 1995 and 2000 if x denotes the ratio of female commerce students to female Science student and y denotes the ratio of male commerce student to male Science student, then

a) x = y
b) x > y
c) x < y
d) x ≥ y

• 10. Measures of Central tendency and Dispersion - Quiz

1. If A be the A.M. of two positive unequal quantities X and Y and G be heir G.M. the;
a) A<G
b) A>G
c) A≤G
d) A≥G

2. What is the coefficient of range for the following distribution?
 Class Interval 10-19 20-29 30-39 40-49 50-59 Frequency 11 25 16 7 3

a) 22
b) 50
c) 75.82
d) 72.46

• 11. Correlation and Regression - Quiz

1. If the values of y are not affected by changes in the values of x, the variables are said to be
a) Correlated
b) Uncorrelated
c) Both
d) Zero

2. Two regression lines always intersect at the means.
a) True
b) False
c) Both
d) None

• 12. Probablilty - Quiz

1. Two balls are drawn from a bag containing 5 white and 7 black balls at random. What is the probability that they would be of different colours?
a) 35/66
b) 30/66
c) 12/66
d) None of these

2. If P(A)=3/8, P(B)=1/3 then P(B) is equal to
a) 1
b) 1/3
c) 2/3
d) None

• 13. Theoretical Distributions - Quiz

1. An unbiased die is tossed 500 times.The mean of the number of 'Sixes' in these 500 tosses is
a) 50/6
b) 500/6
c) 5/6
d) None

2. Which of the following is not a characteristic of a normal probability distribution?
a) Mean of the normally distributed population lies at the centre of its normal curve.
b) It is multi-modal
c) The mean, median and mode are equal
d) It is a symmetric curve

• 14. Sampling Theory - Quiz

1. Sampling is the process of obtaining a
a) Population
b) Sample
c) Frequency
d) None

2. The sampling is said to be large sampling if the size of the sample is
a) Greater than or equal to 30
b) less than 30
c) less than or equal to 35
d) less than 25

• 15. Index Numbers - Quiz

1. If ∑Poqo = 3500, ∑Pnqo = 3850, then the cost of living Index (C.L.T) for 1950 w.r. to base 1960 is
a) 110
b) 90
c) 100
d) None of these

2. Given below are the data on prices of some consumer goods and the weights attached to the various items Compute price index number for the year 1985 (Base 1984 = 100)
 Items Unit 1984 1985 Weight Wheat        Milk        Egg        Sugar       Shoes Kg.       Litre       Dozen       Kg.       Pair 0.50         0.60         2.00         1.80          8.00 0.75     0.75     2.40     2.10     10.00 2       5       4       8       1

Then weighted average of price Relative Index is:
a) 125.43
b) 123.3
c) 124.53
d) 124.52

• 16. Sequence and Series, Arithmetic and Geometric Progression - Quiz

1. Sum of n terms of the series 4+44+444+……is
a) 4/9 {10/9(10- 1) -n}
b) 10/9 (10n- 1) -n
c) 4/9 (10-1 ) -n
d) None of these

2. The sum of n terms of the series whose nth terms n.2n is given by
a) (n-1)2n+1+2
b) (n+1)2n+1+2
c) (n/2)2n+2
d) None