## 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. If 2a = 3b = 6-c then  $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$ reduces to
a) 0
b) 2
c) 3
d) 1

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. $\frac{4}{x} - \frac{5}{y} = \frac{x+y}{xy} +\frac{3}{10}\, \, \, \, 3xy = 10 (y-x)$
a) (2, 5)
b) (5, 2)
c) (2, 7)
d) (3, 4)

2. Points (p, 0) (0, q) and (1,1) are collinear if
a) 1/p+1/q=1
b) 1/p-1/q=1
c) 1/p+1/q=0
d) 1/p-1/q=0

• 3. Inequalities - Quiz

1. The solution of the inequality 8x + 6 < 12x + 14 is
a) (-2,2)
b) (0,-2)
c) (2, ∞)
d) (-2,∞)

2. On solving the inequalities 2x + 5y ≤ 20, 3x+2y ≤ 12, x≥ 0 , y ≥ 0, we get following situation
a) (0,0), (0,4), (4,0) and (20/11, 36/11)
b) (0,0), (10,0),(0,6) and (20/11, 36/11)
c) (0,0), (0,4), (4,0) and (2,3)
d) (0,0), (10,0), (0,6) and (2,3)

• 4. Simple and Compound Interest - Quiz

1. The effective annual rate of interest corresponding to nominal rate 6% p.a. payable half yearly is
a) 6.06%
b) 6.07%
c) 6.08%
d) 6.09%

2. If Rs. 1,000 be invested at interest rate of 5% and the interest be added to the principal every 10 years, then the number of years in which it will amount to Rs. 2,000 is:
a) $16\frac{2}{3}years$
b) $6\frac{1}{4}years$
c) 16 years
d) $6\frac{2}{3}years$

• 5. Permutations and Combinations - Quiz

1. If you have 5 cpoies of one book, 4 copies of each of two books, 6 copies each of three books and single copy of 8 books you may arrange it in ___________number of ways.
a) $\frac{39!}{5! \times (4!)^{2} \times (6!)^{3}}$
b) $\frac{39!}{5! \times 8! \times (4!)^{2} \times (6!)^{3}}$
c) $\frac{39!}{5! \times 8! \times 4! \times (6!)^{2}}$
d) $\frac{39!}{5! \times 8! \times 4! \times 6!}$

2. In how many ways can the word “strange” be arranged so that the vowels are never separated?
a) 6! X 2!
b) 7!
c) 7! ÷ 2!
d) None

• 6. Sets, Functions and Relations - Quiz

1. If f(x) = x+3, g(x) = x2, then gof(x) is
a) (x+3)2
b) x2+3
c) x2(x+3),
d) None of these

2. On a survey of 100 boys it was found that 50 used white that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. If 10 boys did not use any of the white red or blue colours and 20 boys used all the colours offer your comments.
a) Inconsistent since 50+40+30-20-15-10+20≠100
b) Consistent
c) Cannot determine due to data insufficiency
d) None

• 7. Limits and Continuity - Quiz

1. $\lim_{x\rightarrow 0}$ $\frac{1}{x}$ is
a) + ∞
b) - ∞
c) 0
d) Does not exist

2. $\lim_{x\rightarrow 2}$ (3x +2) is equal to
a) 6
b) 4
c) 8
d) None of these

• 8. Differential and Integral Calculas - Quiz

1. If y=log[ex{x-2)/(x+3)}3/4  then dy/dx
a) 1+(3/4)(x-2)-1-(3/4)(x+3)-1
b) 1-(3/4)(x-2)-1+(3/4)(x+3)-1
c) 1+(3/4)(x-2)-1+(3/4)(x+3)-1
d) None

2. The slope of the tangent at the point (2 - 2) to the curve x2+xy+y2-4=0 is given by
a) 0
b) 1
c) -1
d) None

• 9. Statistical Description of Data - Quiz

1. In order to compare two or more related series, we consider:
a) Multiple Bar chart
b) Grouped Bar Chart
c) (a) or (b)
d) (a) and (b)

2. Relative frequency for a particular class lies between:
a) 0 and 1
b) 0 and 1, both inclusive
c) -1 and 0
d) -1 and 1

• 10. Measures of Central tendency and Dispersion - Quiz

1. A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is:
a) 5
b) 6
c) 3
d) 7

2. Pooled Mean is also called
a) Mean
b) Geometric Mean
c) Grouped Mean
d) None

• 11. Correlation and Regression - Quiz

1. Take 200 and 150 respectively as the assumed mean for X and Y series of 11 values, then dx=X-200, dy=Y-150,   ∑dx = 13,  ∑dx= 2667, ∑dy=42, ∑dy2 = 6964, ∑dx dy = 3943. The value of r is:
a) 0.77
b) 0.98
c) 0.92
d) 0.82

2. If the correlation coefficient between x and y is r, then between U=$\frac{y}{2}$ and V=$\frac{y-7}{2}$ is
a) r
b) –r
c) (r-5)/2
d) (r-7)/10

• 12. Probablilty - Quiz

1. There are 10 balls numbered from 1 to 10 in a box. If one of them is selected at random what is the probability that the number printed on the ball would be an odd number greater that 4?
a) 0.50
b) 0.40
c) 0.60
d) 0.30

2. Probability of occurrence of at least one of the events A and B is denoted by
a) P(AB)
b) P(A+B)
c) P(A/B)
d) None

• 13. Theoretical Distributions - Quiz

1. If for a Binomial distribution B (n,p,) the mean =6 and Variance =2 then ‘p’ is
a) 2/3
b) 1/3
c) 3/5
d) 1/4

2. The mean of a binomial distribution with parameter n and p is
a) n(1-p).
b) np(1-p).
c) np
d) $\sqrt{np(1-p)}$

• 14. Sampling Theory - Quiz

1. A unbiased estimator:
a) Has the smallest variance among all estimator:
b) Is always the best estimator.
c) Has an expected value equal to the true parameter value.
d) Always generates the true value of the parameter.

2. The permissible sampling error is required to determine sample size for
a) Estimating a mean
b) Estimating a proportion
c) Both
d) None

• 15. Index Numbers - Quiz

1. Bowley index number is 150. Fisher index number is 149.95. Paasche index number is
a) 158
b) 154
c) 148
d) 156

2. The ___________makes index nos. time-reversible.
a) A.M.
b) G.M.
c) H.M.
d) None

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

1. The sum of n terms of the series 1/(4.9)+1/(9.14)+1/(19.24)+………is
a) (n/4)(5n+4)-1
b) (n/4)(5n+4)
c) (n/4)(5n-4)-1
d) None

2. The population of a country was 55 crore in 2005 and is growing at 2% p.a. C.I. the population is the year 2015 is estimated as
a) 5705
b) 6005
c) 6700
d) None of these