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If the coefficient of variation and standard deviation are 60 and 21 respectively, then the arithmetic mean of the distribution is

1) 60 2) 30 3) 35 4) 21 Solution: (3) 35 Coefficient of variation = [𝜎 / ] * 100 60 = [21 / ] * 100 = 35... View Article

The variance of first n natural numbers

1) [n (n + 1)] / 2 2) [(n + 1) (n + 5)] / 12 3) [(n + 1) (n - 5)] / 12 4) (n2 - 1) / 12 Solution: (4) (n2 - 1) / 12 Variance = [∑n2 / n] -... View Article

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

1) 24.0 2) 25.5 3) 20.5 4) 22.0 Solution: (1) 24.0 Given that mean = 21 and median = 22 Mode = 3 Median - 2 Mean Mode = 3 (22) - 2 (21) = 66... View Article

In a class of 100 students, there are 70 boys, whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls?

1) 73 2) 65 3) 68 4) 74 Solution: (2) 65 Since, total number of students = 100 and number of boys = 70 Number of girls = (100 - 70)= 30 The... View Article

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined are 50. The percentage of boys in the class is

1) 40% 2) 20% 3) 80% 4) 60% Solution: (3) 80% 52x + 42y = 50 (x + y) 2x = 8y (x / y) = 4 / 1 and x / (x + y) = 4 / 5 Percentage of boys = 80%... View Article

The values of mean, median and mode coincide, then the distribution is

1) positive skewness 2) symmetric distribution 3) negative skewness 4) All of these Solution: (2) symmetric distribution If the mean, median... View Article

The median of ²ⁿC₀, ²ⁿC₁, ²ⁿC₂, ²ⁿC₃…… ²ⁿC_n (where n is even)

1) 2nCn/2 2) 2nC[n+1]/2 3) 2nC[n-1]/2 4) None of these Solution: (1) 2nCn/2 The given observations are 2nC0, 2nC1, 2nC2, 2nC3…… 2nCn. The... View Article

The average of the four-digit numbers that can be formed using each of the digits 3, 5, 7 and 9 exactly once in each number, is

1) 4444 2) 5555 3) 6666 4) 7777 5) 8888 Solution: (3) 6666 The average of a list of numbers is equal to the ratio of the sum of all the... View Article

The mean age of a combined group of men and women is 25 yr. If the mean age of the group of the mean is 26 and that of the group of women is 21, then the percentage of men and women in the group is

1) 46, 60 2) 80, 20 3) 20, 80 4) 60, 40 Solution: (2) 80, 20 Let the total number of people in the group be 100 and out of them, “x” is men... View Article

The mean of the values 0, 1, 2, 3 ….. n with the corresponding weights ⁿC₀, ⁿC₁, ….. ⁿC_n respectively, is

1) [n + 1] / 2 2) [n - 1] / 2 3) [2n - 1] / 2 4) [2n + 1] / 2 5) n / 2 Solution: (5) n / 2 Mean = [0 * nC0 + 1 * nC1 + 2 * nC2 + …. + n *... View Article

The median of (x / 5), (x / 4), (x / 3), (x / 2), x (x > 0) is 8, then the value of x is

1) 24 2) 32 3) 8 4) 16 5) 40 Solution: (1) 24 The given observations are arranged in ascending order. (x / 5), (x / 4), (x / 3), (x / 2), x... View Article

The AM of 9 terms is 15. If one more term is added to this series, then AM becomes 16. The value of the added term is

1) 30 2) 27 3) 25 4) 23 5) 20 Solution: (3) 25 The arithmetic mean of 9 terms is 15. ⇒ 15 × 9 = 135 is the sum of the first 9 terms. The... View Article

In a moderately asymmetrical distribution, if the mean and median are 36 and 34 respectively, then find out the value of empirical mode.

1) 30 2) 32 3) 42 4) 22 Solution: (1) 30 Mean = 36 Median = 34 Mode = 3 median - 2 mean = 3 * 34 - 2 * 36 = 102 - 72 = 30... View Article

The mean of n terms is [latex]bar{x}[/latex]. If the first term is increased by 1, second by 2 and so on, then the new mean is

1) + n 2) + (n / 2) 3) + [n + 1] / 2 4) None of these Solution: (3) + [n + 1] / 2 I term + 1 II term + 2 III term + 3 n term + n The... View Article

Read the following information carefully and answer the following request. Let p be an odd prime number and T_p be the following set of 2 x 2 matrices . The number of A in T_p such that A is either symmetric or skew-symmetric or both and det (A) is divisible by p is

1) (p - 1)2 2) 2(p - 1) 3) (p - 1)2/ 4) 2p - 1 Solution: (4) 2p - 1 Tr (A) is not divisible by P. Let (A) be divisible by P. If A is... View Article

If 𝛚 is an imaginary cube root of unity and if [latex]\begin{vmatrix} x+\omega^{2} &\omega &1 \\ \omega& \omega^{2} &1+x \\ 1&x+\omega &\omega^{2} \end{vmatrix}=0[/latex] then one of the value of x is

1) 1 2) 0 3) - 1 4) 2 Solution: (2) 0... View Article