Board Paper of Class 12-Commerce Term-I 2021 Applied Math Delhi(Set 4) - Solutions

• Question 1
  If $100 \equiv x (\mathrm{mod} 7)$, then the least positive value of x is :
  (a) 2
  (b) 3
  (c) 6
  (d) 4 VIEW SOLUTION

• Question 2
  If $\tau \left(n\right)$ denotes the number of divisors of n, then the value of $\tau \left(15\right)$ is :
  (a) 3
  (b) 4
  (c) 5
  (d) 7
  
    VIEW SOLUTION

• Question 3
  If a man rows 32 km downstream and 14 km upstream in 6 hours each, then the speed of the stream is:
  (a) 2 km/h
  (b) 1.5 km/h
  (c) 2.5 km/h
  (d) 2.25 km/h VIEW SOLUTION

• Question 4
  In a 2 km race, P can give Q a start of 200 m and R a start of 560 m. Then, in the same race, Q can give R a start of :
  (a) 360 m
  (b) 380 m
  (c) 400 m
  (d) 430 m VIEW SOLUTION

• Question 5
  Pipe A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the time taken to fill the tank is :
  (a) 2 hours
  
  (b) $2\frac{3}{4}$ hours
  
  (c) 3 hours
  
  (d) $3\frac{9}{17}$ hours VIEW SOLUTION

• Question 6
  The solution of $\frac{x-3}{x+5}>0, x\ne -5, x\in \mathrm{R}$ is
  (a) x > 3
  (b) x < –5
  (c) x < –5 or x > 3
  (d) no solution VIEW SOLUTION

• Question 7
  If matrix A is given by A = [a_ij]_2×2, where a_ij = i + j, then A is equal to:
  
  (a) $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$
  
  (b) $\left[\begin{array}{cc}2& 3\\ 3& 4\end{array}\right]$
  
  (c) $\left[\begin{array}{cc}1& 1\\ 2& 2\end{array}\right]$
  
  (d) $\left[\begin{array}{cc}1& 2\\ 1& 2\end{array}\right]$ VIEW SOLUTION

• Question 8
  If A is a square matrix such that A² = A, then (I + A)² – 3A is equal to:
  (a) I
  (b) 2A
  (c) 3I
  (d) A VIEW SOLUTION

• Question 9
  If A is a square matrix of order 3 × 3 such that |A| = 4, then |3A | is equal to:
  (a) 27 
  (b) 81
  (c) 108
  (d) 256 VIEW SOLUTION

• Question 10
  The function f(x) = a^x is increasing on R, if:
  (a) a > 0
  (b) a < 0
  (c) 0 < a < 1
  (d) a > 1 VIEW SOLUTION

• Question 11
  If C(x) and R(x) are respectively Cost function and Revenue function, then the Profit function P(x) is given by :
  (a) P(x) = R(x) 
  (b) P(x) = C(x) + R(x)
  (c) P(x) = R(x) – C(x)
  (d) P(x) = R(x) . C(x) VIEW SOLUTION

• Question 12
  If 'm' is the mean of Poisson distribution, then its standard deviation is given by:
  (a) $\sqrt{m}$
  (b) m²
  (c) m
  (d) $\frac{m}{2}$  VIEW SOLUTION

• Question 13
  The normal distribution curve is symmetrical about :
  (a) X = μ
  (b) X = σ
  (c) X = $\frac{\mathrm{\mu }}{\mathrm{\sigma }}$
  (d) X = $\frac{\mathrm{\sigma }}{\mathrm{\mu }}$ VIEW SOLUTION

• Question 14
  Let X be a discrete random variable whose probability distribution is given below:

  X = xi :	0	1	2	3	4	5	6	7
  P(X = xi) :	0	2K	2K	3K	K2	2K2	7K2	2K

  ​​The value of K is :
  (a) $\frac{1}{10}$

  (b) –1
  (c) –$\frac{1}{10}$
  (d) $\frac{1}{5}$

  ​​ VIEW SOLUTION

• Question 15
  In a box of 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
  (a) ${\left(\frac{9}{10}\right)}^5$
  (b) $\frac{9}{10}$
  (c) 10^–5
  (d) ${\left(\frac{1}{2}\right)}^2$ VIEW SOLUTION

• Question 16
  If X is a normal variate with mean $\mathrm{\mu }$ and standard deviation $\mathrm{\sigma }>0,$ then the new random variate Z = $\frac{\mathrm{X}-\mathrm{\mu }}{\mathrm{\sigma }}$ is a variate with : 
  (a) Mean = 1, Standard deviation = 0.
  (b) Mean = 1, Standard deviation = 1.
  (c) Mean = 2, Standard deviation = 1.
  (d) Mean = 0, Standard deviation = 1. VIEW SOLUTION

• Question 17
  The mean E(x) of the number obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is :
  (a) 1
  (b) 2
  (c) 5
  (d) $\frac{8}{3}$ VIEW SOLUTION

• Question 18
  Which of the following index number satisfies the "time reversal test"?
  (a) Fisher's ideal index number
  (b) Laspeyres' index number 
  (c) Paasche's index number
  (d) None of these VIEW SOLUTION

• Question 19
  To calculate Paasche's price index, the weights are taken as : 
  (a) p₀
  (b) p₁
  (c) q₀
  (d) q₁ VIEW SOLUTION

• Question 20
  Given that $\sum {\mathrm{p}}_1{\mathrm{q}}_1=860,\sum {\mathrm{p}}_0{\mathrm{q}}_0=520,\sum {\mathrm{p}}_1{\mathrm{q}}_0=630 \mathrm{and}\sum {\mathrm{p}}_0{\mathrm{q}}_1=730,$ where subscript 0 and 1 are used for base year and current year respectively. The Laspeyres' index number is : 
  (a) 117.81
  (b) 119.5
  (c) 121.15
  (d) 123.35 VIEW SOLUTION