Q 1 – The number of polynomials having zeroes as – 2 and 5 is:
(A) 1
(B) 2
(C) 3
(D) more than 3
Ans. Option (D) is correct.
Q 2 – If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is:
(A) b – a + 1
(B) b – a – 1
(C) a – b + 1
(D) a – b – 1
Ans. Option (A) is correct.
Q 3 – The zeroes of the quadratic polynomial x2 + 99x + 127 are:
(A) both positive
(B) both negative
(C) one positive and one negative
(D) both equal
Ans. Option (B) is correct.
Q 4 – The reroes of the quadratic polynomial x2 + kx + k, k ≠ 0,
(A) cannot both be positive
(B) cannot both be negative
(C) re always unequal
(D) are always equal
Ans. Option (A) is correct
Q 5 – If the zeroes of the quadratic polynomial ax2 + bx + c, α ≠ 0 are equal, then :
(A) c and a have opposite signs
(B) c and b have opposite signs
(C) c and a have the same sign
(D) c and b have the same sign
Ans. Option (C) is correct.
Q 6 – If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it
(A) has no linear term and the constant term is negative.
(B) has no linear term and the constant term is positive.
(C) can have a linear term but the constant term is negative.
(D) can have a linear term but the constant term is positive.
Ans. Option (A) is correct
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT .the correct explanation of A
(C) A is true but R is false
(D) A is false and R is True
Q 7 – Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Ans. Option (D) is correct.
Q 8 – Assertion (A): The value of k for which the quadratic polynomial kx2 + x + k has equal zeroes are ±
Reason (R): If all the three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
Ans. Option (C) is correct.
Q 9 – Assertion (A): If the zeroes of the quadratic polynomial (k – 1) x2 + kx + 1 is – 3, then the value of k is 
Reason (R): If -I is a zero of the polynomial p(x) = kx2 – 4x + k, then the value of k is -2.
Ans. Option (B) is correct.
Attempt any four sub-parts from each question.
Read the following text and answer the following questions on the basis of the same:
Each sub-part carries 1 mark.
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.
Q 10 – 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.
Ans. Option (C) is correct.
Q 11 – 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
Ans. Option (D) is correct.
Q 12 – The graph of X2 + 1 = 0
(A) Intersects x-axis at two distinct points.
(B)Touches x-axis at a point.
(C) Neither touches nor intersects x-axis.
(D) Either touches or intersects x-axis.
Ans. Option (C) is correct.
Read the following text and answer the following questions on the basis of the same:
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.
Q 13 – The shape of the poses shown is
(A) Spiral
(B) Ellipse
(C) Linear
(D) Parabola
Ans. Option (D) is correct.
Q 14 – The graph of parabola opens downwards, if
(A) a 0
(B) a = 0
(C) a < 0
(D) a > 0
Ans. Option (C) is correct.
Q 15 – In the graph, how many zeroes are there for the polynomial?
(A) 0
(B) 1
(C) 2
(D) 3
Ans. Option (C) is correct.
Q 16 – The two zeroes in the above shown graph are
(A) 2, 4
(B) – 2, 4
(C) – 8, 4
(D) 2, – 8
Ans. Option (B) is correct.
Read the following text and answer the following questions on the basis of the same:
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
Q 17 – The shape of the path traced shown is
(A) Spiral
(B) Ellipse
(C) Linear
(D) Parabola
Ans. Option (D) is correct
Q 18 – The graph of parabola opens upwards, if
(A) a = 0
(B) a < 0
(C) a > 0
(D) a . 0
Ans. Option (C) is correct.
Q 19 –Observe the following graph and answer the above graph, how many zeroes are there for the polynomial?
(A) 0
(B) 1
(C) 2
(D) 3
Ans. Option (D) is correct.
Q 20 – The three zeroes in the above shown graph are
(A) 2, 3, -1
(B) -2, 3, 1
(C) -3, -1, 2
(D) -2, -3, -1
Ans. Option (C) is correct.
Q 21 – What will be the expression of the polynomial?
(A) .r3 + 2x2 – 5x – 6
(B) x3 + 2x2 – 5x – 6
(C) x3 + 2x2 + 5x – 6
(D) .r3 + 2,x2 + 5x + 6
Ans. Option (A) is correct.
Read the following text and answer the following questions on the basis of the same:
Applications of Parabolas: Highway Overpasses
A highway underpass is parabolic in shape.
Parabola
A parabola is the graph that results from
p(x) = ax2 + bx + c.
Parabolas are symmetric about a vertical line known as the Axis of Symmetry.
The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the Vertex.
Q 22 – If the highway overpass is represented by x2– 2x – 8. Then its zeroes are
(A) (2, – 4)
(B) (4, – 2)
(C) (- 2, – 2)
(D) (- 4, – 4)
Ans. Option (B) is Correct .
Q 23 – The highway overpass is represented graphically. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial:
(A) Intersects X-axis
(B) Intersects Y-axis
(C) Intersects Y-axis or X-axis
(D) None of the above
Ans. Option (A) is correct.
Q 24 – Graph of a quadratic polynomial is a:
(A) straight line
(B) circle
(C) parabola
(D) ellipse
Ans. Option (C) is correct.
Q 25 – The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is
(A) x2 – 6x + 2
(B) x2 – 36
(C) x2 – 6
(D) x2 – 3
Ans. Option (B) is correct
Q 26 – The number of zeroes that polynomial f(x) = (x – 2)2 + 4 can have is:
(A) 1
(B) 2
(C) 0
(D) 3
Ans. Option (C) is correct.
Q 27 –The graf of y=p(x) is Given in figure below for some polynomial p(x). the number of zero /zeros of p(x) /are:
(A) 1
(B) 2
(C) 3
(D) 0
Ans. Option (D) is Correct.
Q 28 – If a and β are the zeroes of the quadratic polynomial x2 – 5x + k such that a – β= 1, then the value of k is.
(A) 4
(C) 6
(B) 5
(D) 3
Ans. option (C) is Correct.
Q 29– If the product of the zeroes of the quadratic polynomial p(x) = axe – 6x – 6 is 4, then the value of a is:
(A) 
(B) 
(C) 
(D) 
Ans. Option (A) is Correct.
Q 30 –Which of the Following is not the Graf of a quadratic Polynomial?
Ans. Option (D) is Correct.
Q 31 –Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is:
(A) 
(B) 
(C) 0
(D) 
Ans. Option (B) is Correct.