Algebra Model set 4 by shaalaa.com 2024-2025 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

If FV = ₹ 460 and premium = ₹ 165, then what is the value of MV?

165

295

460

625

The coefficient of x² in x² + 2x + 9 = `3x(x/2 - 1)` is ______.

`1/2`

1

2

`3/2`

If the sum of the roots of the quadratic equation x² + kx + 6 = 0 is 6, then the value of k is ______.

– 12

6

12

– 6

For an A.P., if a = 7 and d = 2.5 then t₁₂ = ?

37.5

34.5

28.2

44.5

The monthly pocket money of ten friends is given below:

₹ 80, ₹ 65, ₹ 35, ₹ 65, ₹ 50, ₹ 30, ₹ 60, ₹ 35, ₹ 65, ₹ 30

What is the lowest pocket money?

The monthly pocket money of ten friends is given below :

₹ 80, ₹ 65, ₹ 35, ₹ 65, ₹ 50, ₹ 30, ₹ 60, ₹ 35, ₹ 65, ₹ 30

What is the highest pocket money?

Is (x – 5) a factor of the polynomial x³ – 5x – 30?

Find the value of x, if 3^{x – 7} × 4^{x – 4} = 768.

If x + y = 14 and 2x – y = 16 then x = ?

An urn contains 12 red balls, 15 yellow balls and 18 blue balls. A ball is choosen at random, then to find the probability of choosing a blue and red coloured balls, fill in the boxes.

Total number of balls = 12 + `square` + `square` = `square`

(1) Let E be the event that the choosen ball is blue.

Number of blue balls = `square`

Thus, 

P(E) = `"Number of blue balls"/"Total number of balls"`

= `square/square`

(2) Let F be the event that the choosen ball is red.

Number of red balls = `square`

Thus,

P(F) = `square/"Total number of balls"`

= `square/square`

Complete the following information:

In the adjoining figure, the arrow rests on any number, after the rotation of the disc. The probability that it will rest on any of the numbers on the disc is equal. Let A be any random event. To find the probability of A, fill in the boxes.

(1) S = `square`

(2) n(S) = `square`

(3) Let A be the event that arrow points at the number which is perfect cube.

A = `square` 

 ∴ n(A) = `square`

(4) ∴ P(A) = `(n(A))/(n(S)) = square/square = square`

If the roots of the quadratic equation x² + 12x + a = 0 are real and equal, then find the value of a.

Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax² + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.

If the difference between two numbers is 48 and one number is five times the other, then find the numbers.

How many terms are present in the sequence of A.P. 6, 11, 16, 21, ......... whose sum is 969?

Solve the quadratic equation 7x² + 9x + 2 = 0 by the quadratic formula.

The ratio of fruit trees and vegetable trees in an orchard is 3:4. If 6 more trees of each type are planted, the ratio of trees would be 6:7. Find the number of fruit trees and vegetable trees in the orchard.

The ratio of fruit trees and vegetable trees = 3:4

So, let the number of fruit trees= 3x and the number of vegetable trees = `square` 

From the given condition,

`(3x + square)/(square + square) = square/square`

`square (3x + square) = square (square + square)`

`square + square = square + square`

`square - square = square - square`

`- square = - square`

`square = square`

x = `square`

∴ Number of fruit trees in the orchard = 3x = 3 × `square` = `square` and number of vegetable trees in the orchard = 4x = 4 × `square` = `square`

Hence, the number of fruit trees and vegetable trees in the orchard are `square` and `square` respectively.

Roshan spends 80% of the money that he receives every month and saves ₹ 2500. How much money does he get monthly?

Let the total money be x.

Then, Amount spend = `square/100`

Amount saved = ₹ `square`

Now, `square/100 + square` = x

`x - square/100 = square`

`square/100 = square`

x = `(square xx 100)/square`

x = `square`

Hence, Roshan get ₹ `square` as monthly Salary.

Solve the given simultaneous equations using graphical method.

3x + 2y = 6, 5x + y = 10

The taxable value of a wall clock is ₹ 1092, rate of GST is 18%. Find the price of the wall clock for the customer.

Draw the graph of the linear equations x – 4y + 10 = 0 and x + 4y – 10 = 0. Find the coordinates of the vertices of the triangle formed by these lines along with the X-axis.

A handbag contained fifty ten rupees note, thirty-five fifty rupees note and fifteen hundred rupee note. One note is drawn from a handbag. What is the probability of getting:

Ten rupees note

A handbag contained fifty ten rupees note, thirty-five fifty rupees note and fifteen hundred rupees note. One note is drawn from a handbag. What is the probability of getting:

Fifty rupees note

A handbag contained fifty ten rupees note, thirty-five fifty rupees note and fifteen hundred rupees note. One note is drawn from a handbag. What is the probability of getting:

Hundred rupees note

Find the values of x and y if the mean and total frequency of the distribution are 25 and 50 respectively.

Solve the following simultaneous equations.

`2/(x + y) - 3/(x - y)` = 15; `8/(x + y) + 5/(x - y)` = 77

Find two consecutive positive even integers such that their product is 1520.

Solve x + 2y = 10 and 2x + y = 14 by substitution method and hence find the value of m for which y = mx + 8.

Find the mean, median and mode of the given data: