Observe the adjacent Venn diagram and write the complement of A.

Concept: Arithmetic Progression Examples and Solutions

Multiply : 2`sqrt(12) × sqrt(3)`

Concept: Arithmetic Progression Examples and Solutions

Find the geometric mean of 4 and 25.

Concept: Geometric Mean

Find x if x + y = 5, and x - y = 7

Concept: Arithmetic Progression Examples and Solutions

The estimated tax on the income of Shreemati Hinduja is Rs. 8000. How much education cess has she to pay at 3% ?

Concept: Arithmetic Progression Examples and Solutions

Find the class-mark of 80-90.

Concept: Arithmetic Progression Examples and Solutions

Factorise : m2 + 5x + 6.

Concept: Solutions of Quadratic Equations by Factorization

The sum of two natural numbers is 20 while their difference is 4. Find the numbers.

Concept: Solutions of Quadratic Equations by Factorization

In PQRS, ∠ R = 60°. Find the ratio ∠ R : ∠ Q

Concept: Linear Equations in Two Variables Applications

(1) For a simultaneous equation in x and y, if Dx = 25, Dy = 50 and

D = 5, What is the value of x ?

(A) -5

(B) `1/ 5`

(C) 10

(D) 5

Concept: Linear Equations in Two Variables Applications

Which of the following is a quadratic equation ?

(A) 6x^{2} = 20 - x^{3}

(B) `x^2(1/x-2) = 72`

(C)` 3/x - 3 = 4x^2`

(D) 5x + 7 = 3x

Concept: Quadratic Equations Examples and Solutions

If in an A. P., d = 10, find t_{6} - t_{2}.

(A) 10

(B) 20

(c) 30

(D) 40

Concept: Quadratic Equations Examples and Solutions

The rate of GST on stainless steel is 18%, of which the share of a state government is ...............

(A) 18%

(B) 9%

(C) 36%

Concept: Shares

Two coins are tossed simultaneously. Find the probability of getting at least one head.

Concept: Probability Examples and Solutions

If the roots of 2x2 - 6x + k = 0 are real and equal, find k.

Concept: Roots of a Quadratic Equation

Solve the following simultaneous equations.

101x + 99y = 501, 99x + 101y = 499

Concept: Introduction of System of Linear Equations in Two Variables

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?

`s_n = n/2 [ square ]`

`s_12 = 12/2 [10 +square]`

`= 6 × square `

` =square`

Concept: Sum of First n Terms of an AP

Complete the following activity to solve the simultaneous equations

3x + 2y = 6 and 2x + 4y = 12 by cramer's method.

`D = [[ 3,2] ,[2, 4 ]] = 8 Dx = [[6,2],[12,4]] = square , Dy = [[3,6],[2,12]] = square x= square y = square`

Concept: Cramer'S Rule

The six faces of a die are marked

The event M is getting a vowel on the upper face of the die when it is tossed. Complete the following activity and find the probability of the event.

` S = {square}`

`n(S) =square`

` M = {square}`

`n(M) =square`

`P(M) = square/square=square`

Concept: Probability of an Event

The following table shows the percentages of vehicles passing a signal. Find out the measures of central angle to show the information by a pie diagram and hence draw the pie diagram.

Type of Vehicle | Bicycle | Two wheeler | Car | Bus | Rickshaw |

Percentage | 10 | 30 | 20 | 20 | 20 |

Concept: Pie Diagram

Mr. Mahajan purchased 100 shares, each of face value Rs. 100, when the market price was Rs. 45 per share, paying 2% brokerage. If the rate of GST on the brokerage is 18%, find the total amount he spent.

Concept: Brokerage and taxes on share tradin

There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?

Concept: Sum of First n Terms of an AP

Solve : 7y = -3y^{2} - 4

Concept: Roots of a Quadratic Equation

In a game of chance, the spinning arrow rests at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probabilities of the following events.

(A) The arrow rests at an odd number.

(B) It rests at a prime

number.

(C) It rests at a multiple

of 2.

Concept: Equally Likely Outcomes

Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.

Concept: Sum of First n Terms of an AP

The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.

Class (No. of mangoes) |
Frequency (No. of trees) |
Cumulative frequency (less than) |

50-100 | 33 | 33 |

100-150 | 30 | 63 |

150-200 | 90 | 153 |

200-250 | 80 | 233 |

250-300 | 17 | 250 |

Concept: Median of Grouped Data

Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.

Concept: General Term of an Arithmetic Progression

Draw a frequency polygon from the information given in the following table.

Age of blood donar (Years) | No. of blood donars |

Less than 20 | 0 |

Less than 25 | 30 |

75Less than 30 | 75 |

165Less than 35 | 127 |

Less than 40 | 165 |

Less than 45 | 185 |

Less than 50 | 197 |

Concept: Frequency Polygon

Draw the graph of x + y = 6 which intersects the X-axis and the Y-axis at A and B respectively. Find the length of seg AB. Also, find the area of Δ AOB where point O is the origin.

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

The market value of a mutual fund is 400 crore rupees. Which is divided into 8 crore units.

(a) Suppose you invest Rs. 10,000 in the units, how many units will you

get ?

(b) While selling the units if their market value is increased by 10%,

how much amount will you get by selling them ?

Concept: Mutual Fund - MF

## Maharashtra State Board previous year question papers Class 10th Board Exam Algebra with solutions 2018 - 2019

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