2018-2019 March

Solve any four of the following.

Write the set Q of rational numbers in the property form.

Concept: Introduction to Sequence

Solve any four of the following.

`|8|+|-3|=?`

Concept: Introduction to Sequence

Solve any four of the following.

Find the value of `x^4-x^3+5` When `x=-1`

Concept: Introduction to Sequence

Solve any four of the following.

If x is the geometric mean of 16 and 9, find x.

Concept: Arithmetic Progression Examples and Solutions

Solve any four of the following.

Find the value of y in the equation x + y = 12, when x = 5

Concept: Quadratic Equations Examples and Solutions

Solve any four of the following.

Write the dates of start and end of a financial year in our country.

Concept: GST - Introduction

Solve any two of the following.

In some families in a colony the daily purchase of milk in litre is 1, 3, 2, 2, 4, 1, 2, 2, 1. Find the mean, median and mode of daily purchase of milk.

Concept: Arithmetic Mean

Solve any two of the following.

If a : b = 7 : 2, find the ratios (i)` b : a` (ii) `(a+b)/b`

Concept: Introduction to Sequence

Solve any two of the following.

Solve : `3x+y=14 ; x-y=2`

Concept: Quadratic Equations Examples and Solutions

Select the correct alternative and write it.

What is the solution of the quadratic equation` 2x^2-7x+6=0`

(A) `-3/2,2`

(B)` 3/2,2`

(C) `-2,3/2`

(d)` 2,2/3`

Concept: Quadratic Equations Examples and Solutions

Select the correct alternative and write it.

What is the sum of first n natural numbers ?

(A)` (n(n-1))/2`

(B)`n/2(n-2)`

(c)` n(n+1)/2`

(D) `(n(n+2))/2`

Concept: General Term of an Arithmetic Progression

Select the correct alternative and write it.

If a share is at premium, then -

(A) Market value > Face value

(B) Market value = Face value

(C) Market value < Face value

(D) Market value ≤ Face value

Concept: General Term of an Arithmetic Progression

Select the correct alternative and write it.

What is the degree of the determinant `|[a ,b],[c,d]|`

(A) 1

(B) 3

(C) 4

(D) 2

Concept: Determinant of Order Two

Solve any two of the following.

If two coins are tossed simultaneously, find the probability of getting a head on both the coins.

Concept: Probability Examples and Solutions

Solve any two of the following.

Find the mean of the data given in the following table.

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency | 6 | 4 | 5 | 7 | 3 |

Concept: Arithmetic Mean

Solve any two of the following.

Form a quadratic equation whose roots are 4 and -12.

Concept: Quadratic Equations

The following table shows the blood-groups of employees in a bank.

Event C is : ‘the blood-group of an employee is AB.’

Blood - group | A | B | AB | 0 |

No. of employees | 20 | 40 | 15 | 25 |

If an employee is chosen at random, what is the probability that his blood-group is AB ?

Fill in the following boxes and find the answer

n(S)= ______

n(C)= ______

p(C)=________=_________

Concept: Probability Examples and Solutions

The first term and the common difference of an A.P. is 10 and 5 respectively. Complete the following activity to find the sum of first 30 terms of the A. P.

`S_n=n/2[ ____+(n-1)d ]`

`∴ s_30=30/2[20+(30-1)xx _____ ]`

=`15[20+________]`

=`15xx165`

=_________

Concept: Sum of the First 'N' Terms of an Geometric Progression

Complete the following table to draw the graph of 3x - y = 2

x | ________ | -1 |

y | 1 | _______ |

(x,y) | ________ | _______ |

Concept: Graphical Method of Solution of a Pair of Linear Equations

Prasad purchased a share of face value Rs. 100 when its market price was Rs. 150. Company declared a dividend of 12% on the share. What was the rate of return on the investment Prasad made ?

Concept: Shares

The` "n"^(th)` term of the A. P. 3, 8, 13, 18, ............ is 148. Find n

Concept: Arithmetic Mean

Solve the following simultaneous equations by Cramer's method.

`x+y=7,2x-3y=9`

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find the values of (i) `α^2+β^2` (ii) `α^3+β^3`

Concept: Roots of a Quadratic Equation

The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.

Concept: Sum of First n Terms of an AP

A survey was conducted in Aadarsh Vidyalaya to know the inclication of students towards different subjects. The data obtained is presented by the adjacent pie diagram. If the total number of students was 500, answer the following questions.

(i) How many students show inclination towards mathematics ?

(ii) How many students are inclined towards social sciences ?

(iii) How many more students are inclined towards languages than

science ?

Concept: Sum of the First 'N' Terms of an Geometric Progression

The sum of a two digit number and the number obtained by reversing its digits is 121. Find the number if its units place digit is greater than the tens place digit by 7.

Concept: Simple Situational Problems

The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.

Concept: Solutions of Quadratic Equations by Factorization

The following table is based on the marks of the first term examination of 10th class students. Show the information by a histogram. Also, draw a frequency polygon with the help of the histogram.

Class-mark of marks | 325 | 375 | 425 | 475 | 525 | 575 |

No. of students | 25 | 35 | 45 | 40 | 32 | 20 |

Concept: Histograms

A bag contains in all 50 balls. Some of them are white, some are blue and some are red. The number of white balls is 11 times the number of blue balls. The number of red balls is less than the number of white balls. Also, the number of red balls is more than the number of blue balls. If one of the balls is selected at random from the bag, what is the probability that it is red ?

Concept: Random Experiments

There are three dealers A, B and C in Maharashtra. Suppose, the trade of each of them in september 2018 was as shown in the following table.

The rate of GST on each transaction was 5%.

Read the table and answer the questions below it.

Dealer |
GSTcollectedon the sale |
GST paid at the time ofpurchase |
ITC |
Tax paidto theGovt. |
Taxbalancewith theGovt. |

A | Rs.5000 | Rs. 6000 | Rs. 5000 | Rs. 0 | Rs. 1000 |

B | Rs 5000 | Rs. 4000 | Rs. 4000 | Rs. 1000 | Rs. 0 |

C | Rs.5000 | Rs. 5000 | Rs. 5000 | Rs. 0 | Rs. 0 |

(i) How much amount did the dealer A get by sale ?

(ii) For how much amount did the dealer B buy the articles ?

(iii) How much is the balance of CGST and SGST left with the government that was paid by A ?

Concept: Mean of Grouped Data

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