Class 10 Maths Chapter 2 MCQ based on Case Study with answers and explanation for the first term exams 2024-25. All the questions including CBSE MCQ set of questions are answered with complete explanation. Class 10 Maths Chapter 2 Case study based MCQ of Polynomials helps the students to understand the pattern of CBSE question papers and way of answering.
Class 10 Maths Chapter 2 MCQ – Case Study
10th Maths Chapter 2 Case Study – 1
During the skipping through skipping rope, its look like the in the form of parabola. It is a natural examples of parabolic shape which is represented by a quadratic polynomial. Similarly, we can observe in many other cases forming a in a variety of forms of different parabolas.
Q1
In the standard form of quadratic polynomial, ax² + bx + c, the condition between a, b and c are
[A]. a may be 0, but b and c must be non-zero.
[B]. a, b and c all may be zero.
[C]. ‘a’ is a non-zero real number and b and c are any real numbers.
[D]. All are integers.
Answer: Option C
Explanation:
Because if a = 0, the equation become linear. Then it is not a quadratic polynomial.
Hence, the correct option is (C).
If the roots of the quadratic polynomial are unequal, where the discriminant D = b² – 4ac, then
[A]. D > 0
[B]. D < 0
[C]. D ≥ 0
[D]. D = 0
Answer: Option A
Explanation:
We know that:
If D = b² – 4ac < 0, no real roots.
If D = b² – 4ac = 0, real and equal roots.
If D = b² – 4ac > 0, real and unequal roots.
Hence, the correct option is (A).
If α and -α are the zeroes of the quadratic polynomial 2x² – 3(k – 4)x – 8, then k is
[A]. 4
[B]. 1/4
[C]. -1/4
[D]. 2
Answer: Option A
Explanation:
From the quadratic polynomial 2x² – 3(k – 4)x – 8
Sum of zeros = 3(k – 4)/2 [Because sum of zeros = -b/a]
So, α + (- α) = 3(k – 4)/2, therefore, k – 4 = 0 or k = 4
Hence, the correct option is (A).
[D]. Either touches or intersects x‐ axis at one point.
Answer: Option A
Explanation:
The given equation: x² – 1 = 0 or 1.x² + 0.x – 1 = 0
Here, a = 1, b = 0 and c = – 1
D = b² – 4ac = 0² – 4 х 1 х(- 1) = 4, therefore, there is two real root.
So, the graph of the equation intersects x‐axis at two distinct points.
Hence, the correct option is (A).
If the sum of the roots is p and product of the roots is -p, then the quadratic polynomial is
[A]. k(px² + p + P)
[B]. k(px² – x/p – 1)
[C]. k(x² – px – p)
[D]. k(x² – px + p)
Answer: Option C
Explanation:
We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)]
Therefore, the equation = k(x² – (p)x + (-p)] = k(x² – px – p)
Hence, the correct option is (C).
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
Q6
In the standard form of quadratic polynomial, ax² + bx + c, a, b and c are
[A]. All are real numbers.
[B]. All are rational numbers.
[C]. ‘a’ is a non-zero real number and b and c are any real numbers.
[D]. All are integers.
Answer: Option C
Explanation:
Because if a = 0, the equation become linear. Then it is not a quadratic equation.
Hence, the correct option is (C).
If the roots of the quadratic polynomial are equal, where the discriminant D = b² – 4ac, then
[A]. D > 0
[B]. D < 0
[C]. D ≥ 0
[D]. D = 0
Answer: Option D
Explanation:
We know that:
If D = b² – 4ac < 0, no real roots.
If D = b² – 4ac = 0, real and equal roots.
If D = b² – 4ac > 0, real and unequal roots.
Hence, the correct option is (D).
If α and 1/ α are the zeroes of the quadratic polynomial 2x² – x + 8k, then k is
[A]. 4
[B]. 1/4
[C]. -1/4
[D]. 2
Answer: Option B
Explanation:
From the quadratic polynomial 2x² – x + 8k
Product of zeros = 8k/4 [Because product of zeros = c/a]
So, α x (1/α) = 8k/2
Therefore, 4k = 1
Hence, k = 1/4
Hence, the correct option is (B).
The given equation: x² + 1 = 0 or 1.x² + 0.x + 1 = 0
Here, a = 1, b = 0 and c = 1
D = b² – 4ac = 0² – 4 х 1 х 1 = – 4, therefore, there is no real root.
So, the graph of the equation neither touches nor intersects x‐axis.
Hence, the correct option is (C).
If the sum of the roots is –p and product of the roots is -1/p, then the quadratic polynomial is
[A]. k(-px² + x/p + 1)
[B]. k(px² – x/p – 1)
[C]. k(x² + px – 1/p)
[D]. k(x² – px + 1/p)
Answer: Option C
Explanation:
We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)]
Therefore, the equation = k(x² – (-p)x + (-1/p)] = k(x² + px – 1/p)
Hence, the correct option is (C).
Observe the position of the athlete taking long jump. He use to follow every time a particular shape of path. In the figure, a student can observe that the different positions can be related to representation of quadratic polynomial.
Q11
The path of the different positions form a
[A]. Spiral
[B]. Ellipse
[C]. Linear
[D]. Parabola
Answer: Option D
Explanation:
When we draw a dotted line following the different positions of athlete, it show a parabolic path. So, it is a parabola.
Hence, the correct option is (D).
If the sum of zeros of quadratic polynomial ax² + bx + c is equal to product of zero, then
[A]. b + c = 0
[B]. c + a = 0
[C]. a + b = 0
[D]. None of the above
Answer: Option C
Explanation:
Given polynomial: ax² + bx + c
Sum of zeros = -b/a,
Product of zeros = c/a,
According to question, -b/a = c/a
Therefore, – b = a or a + b = 0
Hence, the correct option is (C).
The graph of the polynomial cutting x-axis at (-4, 0), (-2, 0), (1, 0) and (3, 0). So, the zeros of polynomial are -4, -2, 1 and 3.
Hence, the correct option is (A).
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.
Q16
The shape of the poses shown is
[A]. Spiral
[B]. Ellipse
[C]. Linear
[D]. Parabola
Answer: Option D
Explanation:
The pose shown above are in the format of parabola.
Hence, the correct option is (D).
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
Q21
The shape of the path traced shown is
[A]. Spiral
[B]. Ellipse
[C]. Linear
[D]. Parabola
Answer: Option D
Explanation:
The pose shown above are in the format of parabola.
Hence, the correct option is (D).
The graph of the polynomial cutting x-axis at (-3, 0), (-1, 0) and (2, 0). So, the zeros of polynomial are -3, -1 and 2.
Hence, the correct option is (C).
