SSC (English Medium)
Academic Year: 2023-2024
Date & Time: 23rd July 2024, 11:00 am
Duration: 2h
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Note:
- All questions are compulsory.
- Use of 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.
- For every MCQ, four alternatives (A), (B), (C), or (D) of answers are given. Alternative of correct answer is to be written in front of the subquestion number.
For simultaneous equations in variables x and y, Dx = 49, Dy = –63, D = 7 then what is x?
7
–7
`1/7`
`(-1)/7`
`-1/7`
Chapter:
Which one is the quadratic equation?
`5/x - 3 = x^2`
x(x + 5) = 2
n – 1 = 2n
`1/x^2(x + 2)` = x
Chapter:
The sequence −10, −6, −2, 2, ... is ______.
an A.P., Reason d = −16
an A.P Reason d = 4
an A.P., Reason d = −4
is not an A.P.
Chapter:
Which number cannot represent a probability?
`2/3`
1.5
15%
0.7
`15/10`
Chapter:
Find the value of the following determinant.
`|(5, -2), (-3, 1)|`
Chapter:
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Chapter:
Face value of a share is ₹ 100 and premium is ₹ 65, then what is the market value of that share?
Chapter:
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Complete the following table for drawing the graph of the equation x + 2y = 4.
| x | −2 | 0 | `square` |
| y | `square` | 2 | 1 |
| (x, y) | `square` | (0, 2) | `square` |
Chapter:
Determine the nature of roots of the quadratic equation m2 + 2m + 9 = 0.
Activity:
m2 + 2m + 9 = 0
a = `square`, b = 2, c = 9
b2 − 4ac = 22 − 4 × 1 × `square`
= `square` − 36
∴ b2 − 4ac = `square`
∴ b2 − 4ac < 0
∴ The roots of the quadratic equation are not real.
Chapter:
Smita has invested ₹12,000 and purchased shares of FV ₹10 at a premium of ₹2. Find the number of shares she purchased. Complete the given activity to get the answer.
Activity:
FV = ₹10, Premium = ₹2
∴ MV = FV + `square`
= `square` + 2
= ₹12
∴ Number of shares = `"Total investment"/"MV" = 12000/square`
= `square` shares.
Chapter:
Solve the following simultaneous equations:
x + y = 5; x − y = 3.
Chapter:
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Chapter:
Find the 19th term of the following A.P.:
7, 13, 19, 25, ...
Chapter:
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 ?
Chapter:
The annual investments of a family are shown in the adjacent pie diagram. Answer the following questions based on it.
- If the investment in shares is ₹ 2000, find the total investment.
- How much amount is deposited in the bank?
- How much more money is invested in immovable property than in mutual fund?
- How much amount is invested in post?
Chapter:
A share is sold for the market value of ₹ 1000. Brokerage is paid at the rate of 0.1%. Find the amount received after sale by completing the activity.
Activity:
Brokerage = `square` × the rate of brokerage.
= `1000 xx 0.1/square`
= 10 × 0.1
= `square`
Amount received after sale = MV − `square`
= `square` − 1
= ₹ `square`
Chapter:
The numbers 2, 4, 6, 8, 10, 12 are on the surface of one die. If this die is rolled once, then complete the activity to find probability of getting a perfect square number on upper face.
Activity:
S = `{square}` ∴ n(S) = `square`
Condition for event B: getting a perfect square number on the upper surface of that die.
B = `{square}` ∴ n(B) = `square`
P(B) = `"n(B)"/"n(S)" = square/6`
= `square`.
Chapter:
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Solve the following equation by Cramer’s method.
4m − 2n = –4 ; 4m + 3n = 16
Chapter:
Solve the following quadratic equation by the formula method:
`y^2 + 1/3y = 2`
Chapter:
Two dice are rolled. Write the sample space S and number of sample points n(S). Also write the events in the set form and number of sample points in the event according to the given condition.
Condition for event A: The sum of the digits on upper face is a multiple of 5.
Chapter:
Two dice are rolled. Write the sample space S and number of sample points n(S). Also write the events in the set form and number of sample points in the event according to the given condition.
Condition for event B: The sum of the digits on upper face is 25.
Chapter:
In the following table, the toll (in ₹) paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.
| Toll (Rupees) | 300 - 400 | 400 - 500 | 500 - 600 | 600 - 700 | 700 - 800 |
| No. of vehicles | 80 | 110 | 120 | 70 | 40 |
Chapter:
Ranjana wants to distribute 540 oranges among some students. If 30 students were more, each would get 3 oranges less. Find the number of students.
Chapter:
₹ 2000 is invested at 10 p.c.p.a. simple interest. Check at the end of the every year whether the interest amount is in A.P. or not. If this is an A.P., then find interest amount after 10 years.
Chapter:
In one group of students; 10% students got 0 to 20 marks; 20% students got 20 to 40 marks; 35% students got 40 to 60 marks; 20% students got 60 to 80 marks and remaining 30 students got 80 to 100 marks, then:
- Prepare a grouped frequency distribution table.
- Find the mode of the marks scored.
Chapter:
Draw a histogram of the following data:
| Students I.Q. | Number of Students |
| 60-80 | 4 |
| 80-100 | 12 |
| 100-120 | 16 |
| 120-140 | 8 |
Chapter:
Using information given in the following figure, find the length and breadth of this rectangle in cm.
Chapter:
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