Algebra Model set 3 by shaalaa.com 2021-2022 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Find the correct answer from the alternatives given.

The persons of O - blood group are 40%. The classification of persons based on blood groups is to be shown by a pie diagram. What should be the measures of angle for the persons of O - blood group?

114°

140°

104°

144°

Write the correct alternative for the following questions.

To find the cost of one share at the time of buying the amount of Brokerage and GST is to be ______ the MV of share.

added to 

substracted from

 Multiplied with

 divided by

Which of the following options shows the highest probability?

`4/5`

0.83

58%

`1/2`

The solution of the equation x − y = 10 and x + y = 70 is ______

(40, 30)

(30, 40)

(10, 60)

(50, 20)

Find t₅ if a = 3 आणि d = −3

Show the condition using variables x and y: Two numbers differ by 3

If x + 2y = 5 and 2x + y = 7, then find the value of x + y

In Adarsh High School, out of 30 students in a class 3 students wear glasses (spectacles). If a student in the class is randomly selected, find the probability that he or she wears glasses (spectacles) by completing the following activity

Activity: There are a total of 30 students in the class.

∴ n(S) = `square`

Event: A selected student wears glasses (spectacles).

∴ n(A) = `square`

P(A) = `square/("n"("S"))`     ......[Formula]

P(A) = `square`

If (2, 0) is the solution of 2x + 3y = k then finds the value of k by completing the activity

Solution: (2, 0) is solution of the equation 2x + 3y = k

Putting x = `square` and y = `square`

∴ `2(square) + 3 xx 0` = k

∴ 4 + 0 = k

∴ k = `square`

t₁₉ = ? for the given A.P., 9, 4, −1, −6 ........

Activity :- Here a = 9, d = `square`

t_n = a + (n − 1)d

t₁₉ = 9 + (19 − 1) `square`

= 9 + `square`

= `square`

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.

There are 30 cards in a box, each bearing one of the numbers from 1 to 30. One card is drawn at random from the box. Find the probability of event that the card drawn shows a number which is a multiple of 5

Roots of a quadratic equation are 5 and – 4, then form the quadratic equation

Find the mode from the following information: 

L = 10, h = 2, f₀ = 58, f₁ = 70, f₂ = 42. 

If a = 6 and d = 10, then find S₁₀ 

Complete the following activity to solve the given quadratic equation by formula method.

2x² + 13x + 15 = 0

Activity: 2x² + 13x + 15 = 0

a = (______), b = 13, c = 15

b² – 4ac = (13)² – 4 × 2 × (______)

= 169 – 120

b² – 4ac = 49

x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`

x = `(- ("______") +- sqrt(49))/4` 

x = `(-13 +- ("______"))/4`

x = `(-6)/4` or x = `(-20)/4`

x = (______) or x = (______)

Complete the following table.

The age group and number of persons, who donated blood in a blood donation camp is given below. Draw a pie diagram from it.

Solve by Cramer’s rule, 3x – 4y = 10, 4x + 3y = 5

Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`

The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distance.

Solve the following quadratic equation.

`1/(4 - "p") - 1/(2 + "p") = 1/4`

Smt. Aruna Thakkar purchased 100 shares of FV 100 when the MV is Rs 1200. She paid brokerage at the rate of 0.3% and 18% GST on brokerage. Find the following – 
(1) Net amount paid for 100 shares. 
(2) Brokerage paid on sum invested. 
(3) GST paid on brokerage. 
(4) Total amount paid for 100 shares.

Form the pair of linear equations for the following problems and find their solution by substitution method.

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Find the first terms and common difference of an A.P. whose t₈ = 3 and t₁₂ = 52.

A company provided Z-security services for the taxable value of Rs 64,500. Rate of GST is 18%. Company had paid GST of Rs 1550 for laundry services and uniforms etc. What is the amount of ITC (input Tax Credit) ? Find the amount of CGST and SGST payable by the company.