SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2024-2025
Date: March 2025
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General Instructions :
- 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.
- For every MCQ, the correct alternative (A), (B), (C) or (D) with subquestion number is to be written as an answer.
Let E be an event and P(E) = `6/7`, then find the value of P(not E).
`1/7`
`6/7`
1
0
Chapter: [0.05] Probability
Which of the following sequence form an A.P.?
3, 6, 9, 15, ......
1, 8, 15, 22, 30, ....
2, 5, 9, 14, 20, ....
11, 22, 33, 44, 55, ....
Chapter: [0.03] Arithmetic Progression
28% GST was charged on the scooter having cost ₹ 50,000. Find the amount of CGST charged.
₹ 8,000
₹ 7,500
₹ 14,000
₹ 7,000
Chapter: [0.04] Financial Planning
If the terms 10, a, 40 are in A.P., then find the value of a.
35
20
25
30
Chapter: [0.03] Arithmetic Progression
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
Chapter: [0.02] Quadratic Equations
If `(5sqrt(2) + 3sqrt(3)) - (6sqrt(2) - 7sqrt(3)) = asqrt(2) + bsqrt(3)`, then find a and b.
Chapter: [0.02] Quadratic Equations
If the mean of 9, 8, 10, x, 14 is 11, find the value of x.
Chapter: [0.06] Statistics
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The table given below shows the months of birth of 36 students of a class:
| Month of birth |
Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. |
| No. of students |
4 | 3 | 5 | 0 | 1 | 6 | 1 | 3 | 4 | 3 | 4 | 2 |
A student is choosen at random. Fill in the boxes.
Total number of students = `square`
Let E be the event that the selected student is born in June.
Then,
Number of times event E occurs = `square`
So, P (selected student is born in June)
P(E) = `"Number of students born in June"/square`
= `square/square`
= `square`
Chapter: [0.05] Probability
Complete the following table.
| Face value | The share is at | Market value | |
| (i) | ₹ 100 | discount of ₹ 15 | ______ |
| (ii) | ₹ 25 | ______ | ₹ 360 |
Chapter: [0.04] Financial Planning
In the following frequency distribution, the heights of 90 students are recorded and the frequency polygon is drawn.
| Heights | 30 – 35 | 35 – 40 | 40 – 45 | 45 – 50 | 50 – 55 | 55 – 60 |
| No. of Students | 6 | 12 | 20 | 18 | 24 | 10 |
Chapter: [0.06] Statistics
Write the two points of the equation 4x – 5y = 10.
Chapter:
Solve the following simultaneous equations using Cramer’s rule.
4m + 6n = 54; 3m + 2n = 28
Chapter:
Check whether 422 is in the sequence 10, 13, 16, 19, 22, ....
Chapter: [0.03] Arithmetic Progression
Find the value of determinant.
`|(5/2, 11/3),(3/8, 17/12)|`
Chapter: [0.01] Linear equations in two variables
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.
Chapter: [0.02] Quadratic Equations
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If a, b, care in continued proportion, then show that `(a + b)^2/(ab) = (b + c)^2/(bc)`.
Since a, b, c are in continued proportion
∴ `a/b = square/square` = k(say)
⇒ b = `square`, a = `square` = `square`.k = `square`.k2
Now, L.H.S. = `(a + b)^2/(a.square) = (square + square)^2/(square*square)`
= `(squarek^2(k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
R.H.S. = `(b + c)^2/(b.square) = (square + square)^2/(square*square) = (square (k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
L.H.S. = `square`
Chapter: [0.02] Quadratic Equations
Determine whether (x – 3) is a factor of polynomial x3 – 19x + 30.
Let P(x) = x3 – 19x + 30
By remainder theorem, `square` will be a factor of P(x), if P(3) = 0
Now, P(3) = `square` – 19 `square` + 30
= `square – square` + 30
= `square – square`
= 0
∵ P(3) = 0
Hence, `square` is a factor of polynomial x3 – 19x + 30.
Chapter: [0.02] Quadratic Equations
Sudesh choose a card from a well-shuffled deck of 52 cards. Calculate the probability of getting a queen
Chapter: [0.05] Probability
Sudesh choose a card from a well-shuffled deck of 52 cards. Calculate the probability of getting the nine of the spade
Chapter: [0.05] Probability
Sudesh choose a card from a well-shuffled deck of 52 cards. Calculate the probability of getting an ace
Chapter: [0.05] Probability
Himanshu invested ₹ 1,55,91,490 in the shares of FV ₹ 100 when MV is ₹ 1,550. Also, the rate of brokerage is 0.5% and GST is 18%. Then find how many shares were buy. Also find the amount of brokerage paid and GST paid for the trading.
Chapter: [0.04] Financial Planning
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Chapter: [0.03] Arithmetic Progression
Using the digits 0, 2, 3, 5 the two-digit numbers are constructed without repetition of digits. Find the probability of the following events:
Condition for event A: The number formed is even.
Chapter: [0.05] Probability
Using the digits 0, 2, 3, 5 the two-digit numbers are constructed without repetition of digits. Find the probability of the following events:
Condition for event B: The number formed is prime number.
Chapter: [0.05] Probability
An electric company producing electric bulb, has packed 100 bulbs in each box. Some bulbs from 16 such boxes are tested defective. The information of number of defective bulbs in 16 boxes is given below.
| No. of defective bulbs | No. of boxes |
| 0 – 2 | 3 |
| 2 – 4 | 4 |
| 4 – 6 | 5 |
| 6 – 8 | 3 |
| 8 – 10 | 1 |
- How many boxes contains maximum number of defective bulbs ?
- Find the mean of defective bulbs.
- The box is selected at random. What is the probability that it will contain average 2 to 4 defective bulbs?
- Find the probability of getting highest number of defective bulbs.
Chapter: [0.06] Statistics
The ratio of two numbers is 3:2 and the difference of their square is 500. Find the numbers.
Chapter: [0.02] Quadratic Equations
Sum of 1 to n natural number is 45, then find the value of n.
Chapter: [0.03] Arithmetic Progression
Calculate the median of marks of students for the following distribution:
| Marks | Number of students |
| More than or equal to 0 | 100 |
| More than or equal to 10 | 93 |
| More than or equal to 20 | 88 |
| More than or equal to 30 | 70 |
| More than or equal to 40 | 59 |
| More than or equal to 50 | 42 |
| More than or equal to 60 | 34 |
| More than or equal to 70 | 20 |
| More than or equal to 80 | 11 |
| More than or equal to 90 | 4 |
Chapter: [0.06] Statistics
The following determinants are obtained from the simultaneous equations in variable x and y.
If Dx = `|(24, a),(16, -1)|`, Dy = `|(5, 24),(b, 16)|`, D = `|(5, 1),(3, -1)|` the solution for this equations are x = 5 and y = – 1. Find the value of' a' and 'b'. Also form the original simultaneous equations having this solution.
Chapter:
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