SSC (English Medium)
Academic Year: 2023-2024
Date & Time: 13th March 2024, 11:00 am
Duration: 2h
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Notes -
- All questions are compulsory.
- Use of a calculator is not allowed.
- The numbers to the right of the questions indicate full marks.
- In case of MCQs [Q. No. 1 (A)] only the first attempt will be evaluated and will be given credit.
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
1
−1
3
−3
Chapter: [0.02] Quadratic Equations
To draw the graph of x + 2y = 4, find x when y = 1:
1
2
−2
6
Chapter:
For an given A.P., t7 = 4, d = −4, then a = ______.
6
7
20
28
Chapter: [0.03] Arithmetic Progression
In the format of GSTIN, there are ______ alpha-numerals.
15
10
16
9
Chapter: [0.04] Financial Planning
If 17x + 15y = 11 and 15x + 17y = 21, then find the value of x − y.
Chapter: [0.01] Linear equations in two variables
Find first term of the sequence tn = 3n − 2.
Chapter: [0.03] Arithmetic Progression
If the face value of a share is ₹ 100 and the market value is ₹ 150. If rate of brokerage is 2%, find brokerage paid on one share.
Chapter: [0.04] Financial Planning
For the following experiment write sample space ‘S’ and number of sample points n(S).
Two-digit numbers are formed using digits 2, 3 and 5 without repeating a digit.
Chapter: [0.05] Probability
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Activity:
(0, 2) is the solution of the equation 2x + 3y = k.
Put `x = square and y = square` in the given equation;
∴ `2 xx square + 3 xx 2 = k`
∴ 0 + 6 = k
∴ `k = square`
Chapter:
If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation:
Activity:
Let α = 2 and β = 5 are the roots of the quadratic equation.
Then quadratic equation is:
x2 − (α + β)x + αβ = 0
∴ `x^2 - (2 + square)x + square xx 5 = 0`
∴ `x^2 - square x + square = 0`
Chapter: [0.02] Quadratic Equations
Two coins are tossed simultaneously. Complete the following activity to write the sample space and the given events A and B in the set form:
Event A: To get at least one head.
Event B: To get no head.
Activity:
Two coins are tossed simultaneously.
∴ Sample space is
S = `{square, HT, TH, square}`
Event A: To get at least one head.
∴ A = `{square, HT, TH}`
Event B: To get no head.
∴ B = `{square}`
Chapter: [0.05] Probability
`square`ABCD is a rectangle. Write two simultaneous equations using information given below in the diagram, in the form of ax + by = c:
Chapter:
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
Chapter: [0.02] Quadratic Equations
Find the 19th term of the following A.P.:
7, 13, 19, 25, ...
Chapter: [0.03] Arithmetic Progression
A card is drawn from well shuffled pack of 52 playing cards. Find the probability that the card drawn is a face card.
Chapter: [0.05] Probability
The following table shows classification of number of workers and number of hours they work in software company. Prepare less than upper limit type cumulative frequency distribution table:
| Number of hours daily | Number of workers |
| 8 - 10 | 150 |
| 10 - 12 | 500 |
| 12 - 14 | 300 |
| 14 - 16 | 50 |
Chapter: [0.06] Statistics
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The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity:
| Class (Petrol filled in Liters) |
Frequency (Number of Vehicles) |
| 0.5 - 3.5 | 33 |
| 3.5 - 6.5 | 40 |
| 6.5 - 9.5 | 27 |
| 9.5 - 12.5 | 18 |
| 12.5 - 15.5 | 12 |
Activity:
From the given table,
Modal class = `square`
∴ Mode = `square + [(f_1 - f_0)/(2f_1 -f_0 - square)] xx h`
∴ Mode = `3.5 + [(40 - 33)/(2(40) - 33 - 27)] xx square`
∴ Mode = `3.5 +[7/(80 - 60)] xx 3`
∴ Mode = `square`
∴ The mode of the volume of petrol filled is `square`.
Chapter: [0.06] Statistics
The total value (with GST) of remote controlled toy car is ₹ 2360. Rate of GST is 18% on toys. Complete the following activity to find the taxable value for the toy car.
Activity:
Total value for toy car with GST = ₹ 2360
Rate of GST = 18%
Let taxable value for toy car be ₹ x
∴ GST = `18/100 xx x`
∴ Total value for toy car = (taxable value for toy car) + `square` .....Formula
∴ 2360 = `square + square/100 xx x`
∴ 2360 = `square/100 xx x`
∴ 2360 x 100 = 118x
∴ `x = (2360 xx 100)/square`
∴ Taxable value for toy car is ₹ `square`
Chapter: [0.04] Financial Planning
Solve the following quadratic equation by formula method:
3m2 − m − 10 = 0
Chapter: [0.02] Quadratic Equations
Solve the following simultaneous equations using Cramer’s rule.
3x – 4y = 10 ; 4x + 3y = 5
Chapter:
50 shares of face value ₹ 10 were purchased for market value of ₹ 25. Company declared 30% dividend on the shares, then find:
- Sum invested
- Dividend received
- Rate of return.
Chapter: [0.04] Financial Planning
One coin and a die are thrown simultaneously. Find the probability of the following event:
Event A: To get a head and a prime number.
Chapter: [0.05] Probability
One coin and a die are thrown simultaneously. Find the probability of the following event:
Event B: To get a tail and an odd number.
Chapter: [0.05] Probability
A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.
Chapter: [0.02] Quadratic Equations
The following table shows the classification of percentage of marks of students and the number of students. Draw frequency polygon from the table without drawing histogram:
| Result (Percentage) | Number of Students |
| 20 - 40 | 25 |
| 40 - 60 | 65 |
| 60 - 80 | 80 |
| 80 - 100 | 15 |
Chapter: [0.06] Statistics
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
Chapter: [0.03] Arithmetic Progression
In the given figure, the pie diagram represents the amount spent on different sports by a school administration in a year. If the money spent on football is ₹ 9,000, answer the following questions:
- What is the total amount spent on sports?
- What is the amount spent on cricket?
Chapter: [0.06] Statistics
Draw the graph of the equation x + y = 4 and answer the following questions:
- Which type of triangle is formed by the line with X and Y-axes based on its sides.
- Find the area of that triangle.
Chapter:
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