# Sample Paper Applied Maths Class XII

In this post, you will find 15 questions based on the class XII Applied Maths curriculum. It includes topics such as number and quantification, algebra, probability distribution, index numbers.

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## 1. The value of 5 ʘ_{8} 11, where ⨀ is multiplication modulo is

## (a) -1 (b) 0 (c) 7 (d) 9

Solution. For such questions, use the following steps and find the remainder.

(5 x 11) mod 8 = 55 mod 8

Now divide 55 by 8

The remainder is 7. So, option c.

## 2. If a random variable X has the following probability distribution:

X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

P(X) | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |

**then the value of a is **

## (a) 7/81 (b) 5/81 (c) 2/81 (d) 1/81

Solution.

P(X) = Summation of all probabilities = 1

a+3a+5a+7a+9a+11a+13a+15a+17a = 1

81a=1

a= 1/81

So, option is (d)

## 3. A person can row in still water at the rate of 8 km/h. If it takes him thrice as long to row upstream as to row downstream then the speed of the stream is:

## (a) 2 km/h (b) 3 km/h (c) 4 km/h (d) 6 km/h

Solution. Speed of boat in still water = xkm/h

Speed of the stream = y km/h

x = 8 (given)

Upstream is v = (x-y)

Downstream is u = x+y

x+y = 3(x-y) [ATQ]

8 + y = 3(8- y)

8 + y = 24 – 3y

4y = 16

y = 4

**So, correct option is (c) 4km/h**

## 4.

Solution.

x + 4 = 0(mod3)

So, the number should be fully divisible by 3

35 + 4 is 39 which is fully divisible by 3.

Hence, option d

## 5.

Solution: In the case of a square matrix, then the determinant value of A and its adj(A) is the same.

Option (b) -2.

## 6.

Solution. (a) 0

## 7. If two square matrices A and B are such that |AB| = 12 and |B| = −4, then value of |A| is:

## (a) 8 (b) -8 (c) -3 (d)16

Solution:

|AB| = 12

|A||B| = 12 (since its a square matrix)

|A| (-4) = 12

|A| = -3

Hence, option (c)

## 8.

Solution. (a) no solution

## 9. To calculate Laspeyres price index the weights are taken as

## (a) Base year prices (b) Current year prices(c)Base year quantities (d) Current year quantities

Solution.

So, its option (c)

## 10.

Solution.

Using the Paasche formula.

P01 = (506 x 100)/ 451

= 112.19

Hence, option (a)

## 11. Two athletes Vijay and Samuel finish 100 meters race in 12 secs and 16 secs respectively. By how many meters does Vijay defeat Samuel?

## (a) 10.2 meters (b) 15 meters (c) 25 meters (d) 33.3 meters

Solution.

Hence, option c

## 12.

Solution.

Let’s define each event.

P(E) = { 2, 3, 5, 7}

P(F) = {1,2,3)

P(E U F) = P(E) + P(F) – P (E intersection F)

P (E intersection F) = {2,3}

P (E U F) = {2,3,5,7} + {1,2,3} – {2,3}

P (E U F) = {2} + {3} + {5} + {7} + {1}

All these probabilities from the table

P (EUF) = .77

Hence, option (b)

## 13. A, B and C enter into a partnership. B contributes 1/3rd of the capital, while A contributes as much as B and C together contribute. The ratio of their capitals is:

## (a) 1:2:3 (b) 3:2:1 (c) 3:1:1 (d)2:1:1

Solution.

Let the total capital be x

Let’s C contribution be y

Then, B’s contribution = 1/3 of x

A = y + x/3

A + B + C = y + x/3 + x/3 + y = x

2y + 2x/3 = x

2y = x – 2x/3

2y = (3x – 2x) / 3

2y = x/3

y = x /6

x = 6y

Now, each partner contribution

A = y + x/3 = y + 6y/3 = y + 2y = 3y

B = x/3 = 6y/3 = 2y

C = y

Hence, the ratio is 3:2:1

Option (b)

## 14.

Solution. (d) an equivalence relation

## 15. Three friends X, Y and Z agrees to invest for time periods in the ratio 2:3:4. If their profit sharing ratio is 6:7:8 then the ratio of their investments is

## (a) 4:5:6 (b) 9:7:6 (c) 8:7:6 (d) 12:21:32

Solution.

Investment ratio = Profit / Time

Investment Ratio = 6/2 : 7/3 : 8/4

Take LCM which will be 12

then ratio will become 36 : 28: 24

Reduce it, by dividing it be common factor 4

9 : 7 : 6

Hence, option (b)

You can check the following posts related to applied mathematics:

*Logical Reasoning – Basics*- What are functions?
- What is probability?
- Relations and functions
- Sets and Venn diagram
- What are the different types of sets?
- Set theory

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