Algebra Model set 1 by shaalaa.com 2021-2022 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Choose the correct alternative answer for the following sub question

For an A.P. 5, 12, 19, 26, … a = ?

12

26

19

5

If 49x – 57y = 172 and 57x – 49y = 252 then x + y = ?

80

0

10

8

If n(A) = 5 , P(A) = `1/2` then n(S) = ?

10

`3/5`

`4/5`

`1/3`

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

Which of the following is not a quadratic equation?

2X² – X + 3 = 0

4X² – 3X = 0

X³ – 5X + 3 = 0

4X² = 0

When we toss a coin, there are two possible outcomes - Head or Tail. Therefore, the probability of each outcome is `1/2`. Justify your answer.

Write the given quadratic equation in standard form and also write the values of a, b and c

4y² – 3y = – 7

‘Pawan Medical’ supplies medicines. On some medicines the rate of GST is 12%, then what is the rate of CGST and SGST?

Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

Complete the table to draw the graph of 2x – 3y = 3,

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

Activity: x² + 8x – 20 = 0

x² + ( __ ) – 2x – 20 = 0

x (x + 10) – ( __ ) (x + 10) = 0

(x + 10) ( ____ ) = 0

x = ___ or x = 2

Complete the following table by writting suitable numbers and words.

Find the mean of the distribution:

Using variables a and b write any two equations whose solution is (0, 2).

If one of the roots of quadratic equation x² – kx – 15 = 0 is – 3, then find the value of ‘k’

Nazama is a proprietor of a firm, registered under GST. She has paid GST of Rs 12,500 on purchase and collected Rs 14,750 on sale. What is the amount of ITC to be claimed ? What is the amount of GST payable ?

Two dice are thrown at the same time. Find the probability of getting same number on both dice.

Kalpana saves some amount every month. In the first three months, she saves ₹ 100, ₹ 150, and ₹ 200 respectively. In how many months will she save ₹ 1200?

Activity :- Kalpana’s monthly saving is ₹ 100, ₹ 150, ₹ 200, ......, ₹ 1200

Here, d = 50. Therefore this sequence is an A.P.

a = 100, d = 50, t_n = `square`, n = ?

t_n = a + (n – 1) `square`

`square` = 100 + (n – 1) × 50

`square/50` = n – 1

n = `square`

Therefore, she saves ₹ 1200 in `square` months.

Complete the following table to draw the graph of 3x − 2y = 18

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the second player wins a prize, if the first has won?

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

In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she just gets her entry fee.

Joseph purchased following shares, Find his total investment.

Form the simultaneous linear equations using the determinants

D = `|(4, -3),(2, 5)|`, D_x = `|(5, -3),(9, 5)|`, D_y = `|(4, 5),(2, 9)|`

If the ratio of sum of the first m and n terms of an AP is m² : n², show that the ratio of its  m^th and n^th terms is (2m − 1) : (2n − 1) ?

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on

1. the same day?
2. consecutive days?
3. different days?

Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. (For the formation of word problems you can use quantities like age, rupees, or natural numbers.) (Sample solution for the above example is given below students can take another number to form another example)
Solution:
We need one of the solutions of the quadratic equation as 5.
Then we can take another root as any number like a positive or negative number or zero. Here I am taking another root of the quadratic equation as 2.
Then we can form a word problem as below,
Smita is younger than her sister Mita by 3 years (5 – 2 = 3). If the product of their ages is (5 × 2 = 10). Then find their present ages. 
Let the age of Mita be x.
Therefore age of Smita = x – 3 
By the given condition,
x(x – 3) = 10
x² – 3x – 10 = 0

A missing helicopter is reported to have crashed somewhere in the rectangular region shown in the figure. What is the probability that it crashed inside the lake shown in the figure?