Algebra Model set 2 by shaalaa.com 2021-2022 SSC (English Medium) 10th Standard Question Paper Solution

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

What is the value of discriminant for the quadratic equation X² – 2X – 3 = 0?

– 16

16

8

4

Find the correct answer from the alternatives given.

Cumulative frequencies in a grouped frequency table are useful to find ______.

Mean

Median

Mode

All of these

Write the correct alternative for each of the following.

GST system was introduced in our country from ...

 31^st March 2017

1^st April 2017

 1^st January 2017

 1^st July 2017

Choose the correct alternative answer for the following sub questions

A set of numbers where the numbers are arranged in a definite order, like the natural numbers, is called a ______

index

numbers

line

sequence

Write the roots of following quadratic equation.

(p – 5) (p + 3) = 0

Courier service agent charged a total ₹ 590 to courier a parcel from Nashik to Nagpur. In the tax invoice taxable value is ₹ 500 on which CGST is ₹ 45 and SGST is ₹ 45. Find the rate of GST charged for this service.

Write a sample space when a die is thrown.

To decide whether 1 is a root of quadratic equation x² + 4x – 5 = 0 or not, complete the following activity.

Activity: When x = (______)
L.H.S. = 1² + 4(______) – 5
= 1 + 4 – 5
= (______) – 5
= ______
= R.H.S
Therefore x = 1 is a root of quadratic equation x² + 4x – 5 = 0

If one die is rolled, then find the probability of the following event by completing the activity.

Event A: The number on the upper face is prime.

Activity: Let ‘S’ be the sample space.

S = {1, 2, 3, 4, 5, 6}  

∴ n(S) = 6

Event A: Prime number on the upper face.

A = {`square`}            

∴ n(A) = 3

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

= `square/6`

∴ P(A) = `1/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`

The following table shows the income of farmers in a grape season. Find the mean of their income. 

The taxable value of a wristwatch belt is Rs 586. The rate of GST is 18%. Then what is the price of the belt for the customer ?

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.

If roots of a quadratic equation 3y² + ky + 12 = 0 are real and equal, then find the value of ‘k’

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

How many two-digit numbers are divisible by 5?

Activity :-  Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, t_n = 95, n = ?

t_n = a + (n − 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5

Complete the activity.

Solve the following quadratic equation by the formula method:

`y^2 + 1/3y = 2`

Mr.Amol purchased 50 shares of Face Value Rs100 when the Market value of the share was Rs 80. Company had given 20% dividend. Find the rate of return on investment.

Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay

Solve the following quadratic equations by formula method.

5m² – 4m – 2 = 0

From the railway station I took a rickshaw to go home. It is decided that I have to pay ₹ X for the first kilometre and for each kilometre ₹ Y for the next. For 10 kilometres the fare is ₹ 40 and for 16 kilometres fare is ₹ 58. Find the fare for the first kilometre

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table:

A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment

The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.