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Class 10 Math Chapter 2 Full Unit Test 2027 | Quadratic Equations and Inequalities | Board Paper Pattern 2027
Class 10 Chapter 2 Full Unit Test
Class 10 Mathematics Chapter 2 Full Chapter Test 2027 is prepared according to the expected board paper pattern 2027 for Quadratic Equations and Inequalities. This Class 10 Math Chapter 2 test includes objective and subjective questions covering quadratic equations, roots of quadratic equations, discriminant, factorization method, completing square method, quadratic formula, inequalities, graphs, and related problems. Students can use this Mathematics Model Paper 2027 for exam preparation, revision, self-assessment, and practice. This Class 10 Chapter 2 full chapter test is part of the 786Times Model Papers 2027 and is designed to provide practice according to the Class 10 board examination paper pattern.
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Full Unit Test
Unit 2: Quadratic Equations and Inequalities
T-6
Objective Type
Time Allowed: 20 Min.
Max. Marks: 15
Note: Four possible answers A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of that
question with Marker or ink pen in the answer book. Cutting filling two
or more circles will result in zero mark in that question.
(i) The type of the equation
2x2 − x + 1 = 0
is:
(ii) The solution set of
3x2 − 9 = 0
is:
(iii) What are the roots of
(x − 3)(x + 3) = 0
?
(iv) If
b2 − 4ac = 0
,
then the roots of
ax2 + bx + c = 0
are:
(v) A quadratic equation can be solved by using the method of:
(vi) Degree of the polynomial
3x2 + 5x3 − 2x + 1
is:
(vii) Solution of the equation
x2 + 2x + 1 = 0
is:
(viii) Subject “c” of
x − 2c = b
is:
(ix) Solution of a quadratic equation
ax2 + bx + c = 0
is x-coordinate of the point of intersection of the graph
of
f(x) = ax2 + bx + c
and:
(x) Graph of the function
f(x) = ax2 + bx + c
is of the form of ∪ if:
(xi) Intersection points of
y = x − 1
and
y = x + 1
is:
(xii) Product of roots of the quadratic equation
ax2 + bx + c = 0
is:
(xiii) Point of intersection of
y = 2x + 4
and y-axis is:
(xiv) Discriminant of the equation
x2 − 1 = 0
is:
(xv) Perimeter of a square is given by
P = 4ℓ
,
then we can write ℓ in terms of P as ℓ =
Here is Subjective Part of Paper. Solve it on Paper Carefully.
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Subjective Type
Time Allowed: 2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i)
Solve by factorization method:
x2 +
7
3
x = 2
(ii)
Solve by factorization method:
2x − 3
2
=
4x − 6
x
, x ≠ 0
(iii)
Solve by completing square method.
5x2 − 18 = 2x
(iv)
Solve by using quadratic formula:
3x2 + 7x − 6 = 0
(v)
Write the quadratic equation in standard form.
3x − 1 = 2x2
(vi)
Solve the following quadratic equations by
factorization method:
x2 − x − 6 = 0
(vii)
Solve the following quadratic equations by
completing square method:
2x2 + 5x + 2 = 0
(viii)
Use quadratic formula to solve the following equations:
2x2 − 5x + 3 = 0
(ix)
Find the sum and the product of the roots of the equation
3x2 + 5x − 12 = 0
without solving.
3. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i)
Form a quadratic equation whose roots are given below:
−4, 9
(ii)
Find the equation whose roots are double the roots of
x2 − px + q = 0.
(iii)
Define quadratic equation.
(iv)
Discuss relation between roots and quadratic equation.
(v)
Write the quadratic formula.
(vi)
Define discriminant.
(vii)
If α, β are the roots of the equation
x2 + 2x + 4 = 0,
then find the equation whose roots are:
1
α
,
1
β
(viii)
Find the value of k, given that one root of
x2 − (2k + 4)x + (7k + 1) = 0
is 3.
(ix)
Find the value of m in the equation
2x2 + 3x + m = 0
when sum of its roots is equal to double the product
of its roots.
4. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i)
Examine the nature of roots of the following quadratic
equations:
3x2 − 8x − 2 = 0
(ii)
Find the value of k if the equation
(k + 1)x2 + (2k − 1)x + (k − 1) = 0
has equal roots.
(iii)
If the quadratic equation
16x2 + 7px + 49 = 0
has equal roots, then find the values of p.
(iv)
The area of a circle is
A = πr2.
Make r the subject of the formula.
(v)
Make F the subject of the formula:
Co =
5
9
(Fo − 32).
(vi)
Make ‘a’ the subject of the formula:
S = 2a + (n − 1)d.
(vii)
A company models its profit P in thousands of rupees
by the equation:
P(x) = −5x2 + 150x − 1000,
where x is the price per item in rupees.
Find the price that gives maximum profit.
(viii)
Form a quadratic equation whose roots are:
6,
3
2
.
(ix)
Examine the nature of the roots of the following
equations:
(i) 15x2 + 11x + 2 = 0
(Part-II)
Note: Attempt any two (02) questions.
(2 × 8 = 16)
5:
(a)
Solve the following quadratic equations graphically:
x2 − 3x − 18 = 0
(b) Find the points of intersection of y = 2x + 4 with coordinate axes graphically.
(b) Find the points of intersection of y = 2x + 4 with coordinate axes graphically.
6:
(a)
Find the points of intersection of the following linear
equations with coordinate axes graphically:
x + y = 8
(b) If α, β are roots of the equation x2 − 7x + 10 = 0, then form an equation whose roots are 2α + 1 and 2β + 1.
(b) If α, β are roots of the equation x2 − 7x + 10 = 0, then form an equation whose roots are 2α + 1 and 2β + 1.
7:
(a)
If α, β are the roots of
x2 + ax + b = 0
and α2, β2 are the roots of
x2 + Ax + B = 0,
then prove that
A = 2b − a2,
B = b2.
(b) If the quadratic equation 4u2 + 8u + q = 0 has unequal and real roots, find the possible values for q.
(b) If the quadratic equation 4u2 + 8u + q = 0 has unequal and real roots, find the possible values for q.
(Part-III)
Note: Attempt any one (01) question.
(1 × 8 = 8)
8:
(a)
Solve the inequality:
2x2 − 5x + 2 ≤ 0
(b) A ball is thrown upward with an initial velocity of 20ms−1. Calculate the maximum height it reaches above ground level. Calculate time of return to the ground.
(b) A ball is thrown upward with an initial velocity of 20ms−1. Calculate the maximum height it reaches above ground level. Calculate time of return to the ground.
9:
(a)
If the equation
x2 + 2(1 + k)x + k2 = 0
has equal roots, then find the value of k.
(b) Solve the following quadratic equations by factorization method, by completing square method and by quadratic formula: 2x2 − x − 10 = 0
(b) Solve the following quadratic equations by factorization method, by completing square method and by quadratic formula: 2x2 − x − 10 = 0
