GSEB Std-10 Mathematics — Practice Paper
GSEB Std 10 · Mathematics
General instructions: Attempt all questions. Marks for each question are shown in the right margin. Internal choice, where given, is indicated by “OR”.
Section A
- 1.
Which of the following is a quadratic equation?
[1]- (a)2x + 3 = 0
- (b)x² + 2x + 1 = 0
- (c)x³ - 8 = 0
- (d)√x + 5 = 0
- 2.
The discriminant of the equation x² - 4x + 4 = 0 is:
[1]- (a)0
- (b)4
- (c)-4
- (d)16
- 3.
The common difference of the AP: 5, 2, -1, -4, ... is:
[1]- (a)5
- (b)3
- (c)-3
- (d)2
- 4.
If the roots of x² - 7x + 12 = 0 are α and β, then α + β equals:
[1]- (a)-7
- (b)7
- (c)12
- (d)-12
- 5.
The nth term of an AP with first term a and common difference d is:
[1]- (a)a + nd
- (b)a + (n - 1)d
- (c)a + (n + 1)d
- (d)nd
- 6.
If one root of the equation x² + 5x + k = 0 is -2, then k equals:
[1]- (a)6
- (b)-6
- (c)10
- (d)-10
- 7.
The sum of n terms of an AP is given by:
[1]- (a)Sₙ = (n/2)[2a + nd]
- (b)Sₙ = (n/2)[2a + (n-1)d]
- (c)Sₙ = a + (n-1)d
- (d)Sₙ = n[a + d]
- 8.
For the quadratic equation 3x² - 6x + 3 = 0, the roots are:
[1]- (a)real and distinct
- (b)real and equal
- (c)imaginary
- (d)irrational
Section B
- 9.
Solve: x² - 5x + 6 = 0 by factorization method.
[2] - 10.
Find the common difference of the AP: 12, 8, 4, 0, ...
[2] - 11.
Find the sum of the first 12 terms of the AP: 1, 4, 7, ...
[2] - 12.
Form a quadratic equation whose roots are 3 and -5.
[2] - 13.
Find the 8th term of the AP: 6, 10, 14, ...
[2]
Section C
- 14.
Solve the quadratic equation 2x² + 7x + 3 = 0 using the quadratic formula. Show all steps.
[3] - 15.
The sum of three consecutive terms of an AP is 24 and their product is 440. Find the three terms.
[3] - 16.
For what value(s) of m will the quadratic equation x² - 2x + m = 0 have real and unequal roots? Justify your answer.
[3] - 17.
An AP has 15 terms. If the first term is 4 and the last term is 46, find the common difference and the sum of all terms.
[3]
Section D
- 18.
The length of a rectangular hall is 4 meters more than its breadth. If the area of the hall is 96 square meters, find the length and breadth. (Form and solve a quadratic equation)
[4] - 19.
An AP has 20 terms. The sum of the first 10 terms is 145 and the sum of the last 10 terms is 425. Find the first term, common difference, and the 11th term.
[4] - 20.
A person buys a motorcycle for Rs. 40,000. Its value depreciates each year at a rate such that its value after n years is given by V(n) = 40,000(1 - n/50). In which year will the value become Rs. 32,000? (Hint: Form and solve a quadratic or linear equation)
[4]