Class 10: Question Bank & Solution (CBSE)

$\displaystyle \text{REAL NUMBERS}$

$\displaystyle \textbf{Case Study - 1}$

$\displaystyle \text{To enhance the reading skills of Grade X students, the school nominates you and two of your}$
$\displaystyle \text{friends to set up a class library. There are two sections, Section A and Section B, in Grade X.}$
$\displaystyle \text{There are }32\text{ students in Section A and }36\text{ students in Section B.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{What is the minimum number of books you will acquire for the class library, so}$
$\displaystyle \text{that they can be distributed equally among students of Section A or Section B?}$
$\displaystyle \text{(a) }144\qquad\text{(b) }128\qquad\text{(c) }288\qquad\text{(d) }272$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Number of students in Section A}=32$
$\displaystyle \text{Number of students in Section B}=36$
$\displaystyle \text{The required number of books must be exactly divisible by both }32\text{ and }36.$
$\displaystyle \therefore \text{Required number of books}=\mathrm{LCM}(32,36)$
$\displaystyle 32=2^5,\qquad 36=2^2\times3^2$
$\displaystyle \mathrm{LCM}(32,36)=2^5\times3^2=32\times9=288$
$\displaystyle \therefore \text{The minimum number of books required is }288.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{If the product of two positive integers is equal to the product of their HCF}$
$\displaystyle \text{and LCM, then the HCF of }32\text{ and }36\text{ is:}$
$\displaystyle \text{(a) }2\qquad\text{(b) }4\qquad\text{(c) }6\qquad\text{(d) }8$
$\displaystyle \text{Answer:}$
$\displaystyle 32=2^5,\qquad 36=2^2\times3^2$
$\displaystyle \mathrm{HCF}(32,36)=2^2=4$
$\displaystyle \text{Also, }32\times36=\mathrm{HCF}(32,36)\times\mathrm{LCM}(32,36).$
$\displaystyle \therefore \text{The HCF of }32\text{ and }36\text{ is }4.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{The number }36\text{ can be expressed as a product of its primes as:}$
$\displaystyle \text{(a) }2^2\times3^2\qquad\text{(b) }2^1\times3^3\qquad\text{(c) }2^3\times3^1\qquad\text{(d) }2^0\times3^0$
$\displaystyle \text{Answer:}$
$\displaystyle 36=4\times9$
$\displaystyle =2^2\times3^2$
$\displaystyle \therefore 36=2^2\times3^2.$
$\displaystyle \therefore \text{Option (a) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{The number }7\times11\times13\times15+15\text{ is a:}$
$\displaystyle \text{(a) Prime number}\qquad\text{(b) Composite number}$
$\displaystyle \text{(c) Neither prime nor composite}\qquad\text{(d) None of the above}$
$\displaystyle \text{Answer:}$
$\displaystyle 7\times11\times13\times15+15$
$\displaystyle =15(7\times11\times13+1)$
$\displaystyle =15(1001+1)$
$\displaystyle =15\times1002$
$\displaystyle \text{Since the number has factors other than }1\text{ and itself, it is a composite number.}$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{If }p\text{ and }q\text{ are positive integers such that }p=ab^2\text{ and }q=a^2b,\text{ where}$
$\displaystyle a\text{ and }b\text{ are prime numbers, then the LCM of }p\text{ and }q\text{ is:}$
$\displaystyle \text{(a) }ab\qquad\text{(b) }a^2b^2\qquad\text{(c) }a^3b^2\qquad\text{(d) }a^3b^3$
$\displaystyle \text{Answer:}$
$\displaystyle p=ab^2=a^1b^2,\qquad q=a^2b=a^2b^1$
$\displaystyle \text{For the LCM, we take the highest power of each prime factor.}$
$\displaystyle \therefore \mathrm{LCM}(p,q)=a^2b^2.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Case Study - 2}$

$\displaystyle \text{A seminar is being conducted by an Educational Organisation, where the participants will be}$
$\displaystyle \text{educators of different subjects. The number of participants in Hindi, English and Mathematics}$
$\displaystyle \text{is }60,\ 84\text{ and }108\text{ respectively.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{In each room, the same number of participants are to be seated and all of them}$
$\displaystyle \text{are from the same subject. The maximum number of participants that can be}$
$\displaystyle \text{accommodated in each room is:}$
$\displaystyle \text{(a) }14\qquad\text{(b) }12\qquad\text{(c) }16\qquad\text{(d) }18$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Number of participants in Hindi, English and Mathematics are }60,84\text{ and }108.$
$\displaystyle \text{The maximum equal number of participants in each room}$
$\displaystyle =\mathrm{HCF}(60,84,108)$
$\displaystyle 60=2^2\times3\times5$
$\displaystyle 84=2^2\times3\times7$
$\displaystyle 108=2^2\times3^3$
$\displaystyle \mathrm{HCF}(60,84,108)=2^2\times3=12$
$\displaystyle \therefore \text{The maximum number of participants in each room is }12.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{What is the minimum number of rooms required during the event?}$
$\displaystyle \text{(a) }11\qquad\text{(b) }31\qquad\text{(c) }41\qquad\text{(d) }21$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Maximum number of participants accommodated in each room}=12$
$\displaystyle \text{Rooms required for Hindi participants}=\frac{60}{12}=5$
$\displaystyle \text{Rooms required for English participants}=\frac{84}{12}=7$
$\displaystyle \text{Rooms required for Mathematics participants}=\frac{108}{12}=9$
$\displaystyle \therefore \text{Minimum number of rooms required}=5+7+9=21$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{The LCM of }60,84\text{ and }108\text{ is:}$
$\displaystyle \text{(a) }3780\qquad\text{(b) }3680\qquad\text{(c) }4780\qquad\text{(d) }4680$
$\displaystyle \text{Answer:}$
$\displaystyle 60=2^2\times3\times5$
$\displaystyle 84=2^2\times3\times7$
$\displaystyle 108=2^2\times3^3$
$\displaystyle \mathrm{LCM}(60,84,108)=2^2\times3^3\times5\times7$
$\displaystyle =4\times27\times5\times7$
$\displaystyle =3780$
$\displaystyle \therefore \text{The LCM of }60,84\text{ and }108\text{ is }3780.$
$\displaystyle \therefore \text{Option (a) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{The product of HCF and LCM of }60,84\text{ and }108\text{ is:}$
$\displaystyle \text{(a) }55360\qquad\text{(b) }35360\qquad\text{(c) }45500\qquad\text{(d) }45360$
$\displaystyle \text{Answer:}$
$\displaystyle \mathrm{HCF}(60,84,108)=12$
$\displaystyle \mathrm{LCM}(60,84,108)=3780$
$\displaystyle \therefore \text{Product of HCF and LCM}=12\times3780$
$\displaystyle =45360$
$\displaystyle \therefore \text{The product of HCF and LCM is }45360.$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{The number }108\text{ can be expressed as a product of its primes as:}$
$\displaystyle \text{(a) }2^3\times3^2\qquad\text{(b) }2^3\times3^3\qquad\text{(c) }2^2\times3^2\qquad\text{(d) }2^2\times3^3$
$\displaystyle \text{Answer:}$
$\displaystyle 108=4\times27$
$\displaystyle =2^2\times3^3$
$\displaystyle \therefore 108=2^2\times3^3.$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Case Study - 3}$

$\displaystyle \text{A mathematics exhibition is being conducted in your school, and one of your friends is making a}$
$\displaystyle \text{model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the}$
$\displaystyle \text{audience. Observe the following factor tree and answer the questions that follow.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{What will be the value of }x\text{?}$
$\displaystyle \text{(a) }15005\qquad\text{(b) }13915\qquad\text{(c) }56920\qquad\text{(d) }17429$
$\displaystyle \text{Answer:}$
$\displaystyle \text{From the factor tree, }x=5\times2783.$
$\displaystyle x=13915$
$\displaystyle \therefore \text{The value of }x\text{ is }13915.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{What will be the value of }y\text{?}$
$\displaystyle \text{(a) }23\qquad\text{(b) }22\qquad\text{(c) }11\qquad\text{(d) }19$
$\displaystyle \text{Answer:}$
$\displaystyle \text{From the factor tree, }2783=y\times253.$
$\displaystyle y=\frac{2783}{253}=11$
$\displaystyle \therefore \text{The value of }y\text{ is }11.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{What will be the value of }z\text{?}$
$\displaystyle \text{(a) }22\qquad\text{(b) }23\qquad\text{(c) }17\qquad\text{(d) }19$
$\displaystyle \text{Answer:}$
$\displaystyle \text{From the factor tree, }253=11\times z.$
$\displaystyle z=\frac{253}{11}=23$
$\displaystyle \therefore \text{The value of }z\text{ is }23.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{According to the Fundamental Theorem of Arithmetic, }13915\text{ is a:}$
$\displaystyle \text{(a) Composite number}\qquad\text{(b) Prime number}$
$\displaystyle \text{(c) Neither prime nor composite}\qquad\text{(d) Even number}$
$\displaystyle \text{Answer:}$
$\displaystyle 13915=5\times2783$
$\displaystyle =5\times11\times253$
$\displaystyle =5\times11\times11\times23$
$\displaystyle \text{Since }13915\text{ has factors other than }1\text{ and itself, it is a composite number.}$
$\displaystyle \therefore \text{Option (a) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{The prime factorisation of }13915\text{ is:}$
$\displaystyle \text{(a) }5\times11^3\times13^2\qquad\text{(b) }5\times11^3\times23^2$
$\displaystyle \text{(c) }5\times11^2\times23\qquad\text{(d) }5\times11^2\times13^2$
$\displaystyle \text{Answer:}$
$\displaystyle 13915=5\times2783$
$\displaystyle =5\times11\times253$
$\displaystyle =5\times11\times11\times23$
$\displaystyle =5\times11^2\times23$
$\displaystyle \therefore \text{The prime factorisation of }13915\text{ is }5\times11^2\times23.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \text{POLYNOMIALS}$

$\displaystyle \textbf{Case Study - 1}$

$\displaystyle \text{The pictures below show a few natural examples of parabolic shapes, which can be represented}$
$\displaystyle \text{by quadratic polynomials. A parabolic arch is an arch in the shape of a parabola. In structures,}$
$\displaystyle \text{the curved shape helps distribute loads efficiently. Hence, parabolic arches can be found in}$
$\displaystyle \text{bridges and various forms of architecture.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{In the standard form of a quadratic polynomial, }ax^2+bx+c,\ a,b\text{ and }c\text{ are:}$
$\displaystyle \text{(a) All are real numbers}\qquad\text{(b) All are rational numbers}$
$\displaystyle \text{(c) }a\text{ is a non-zero real number and }b\text{ and }c\text{ are any real numbers}$
$\displaystyle \text{(d) All are integers}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The standard form of a quadratic polynomial is }ax^2+bx+c,\text{ where }a\ne0.$
$\displaystyle \text{Here, }a,b\text{ and }c\text{ are real numbers, with }a\ne0.$
$\displaystyle \therefore a\text{ is a non-zero real number and }b,c\text{ are any real numbers.}$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{If the roots of the quadratic polynomial are equal, where the discriminant}$
$\displaystyle D=b^2-4ac,\text{ then:}$
$\displaystyle \text{(a) }D>0\qquad\text{(b) }D<0\qquad\text{(c) }D\geq0\qquad\text{(d) }D=0$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For a quadratic polynomial }ax^2+bx+c,\text{ the discriminant is }D=b^2-4ac.$
$\displaystyle \text{If the roots are real and equal, then the discriminant is zero.}$
$\displaystyle \therefore D=0.$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{If }\alpha\text{ and }\frac{1}{\alpha}\text{ are the zeroes of the quadratic polynomial}$
$\displaystyle 2x^2-x+8k,\text{ then }k\text{ is:}$
$\displaystyle \text{(a) }4\qquad\text{(b) }\frac14\qquad\text{(c) }-\frac14\qquad\text{(d) }2$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For }ax^2+bx+c,\text{ product of zeroes}=\frac{c}{a}.$
$\displaystyle \therefore \alpha\times\frac{1}{\alpha}=\frac{8k}{2}$
$\displaystyle 1=4k$
$\displaystyle \therefore k=\frac14.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{The graph of }x^2+1=0\text{:}$
$\displaystyle \text{(a) Intersects x-axis at two distinct points}$
$\displaystyle \text{(b) Touches x-axis at a point}$
$\displaystyle \text{(c) Neither touches nor intersects x-axis}$
$\displaystyle \text{(d) Either touches or intersects x-axis}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For }x^2+1=0,\quad a=1,\quad b=0,\quad c=1.$
$\displaystyle D=b^2-4ac=0^2-4(1)(1)=-4<0$
$\displaystyle \therefore \text{The equation has no real zeroes.}$
$\displaystyle \therefore \text{Its graph neither touches nor intersects the x-axis.}$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{If the sum of the roots is }-p\text{ and product of the roots is }-\frac1p,\text{ then}$
$\displaystyle \text{the quadratic polynomial is:}$
$\displaystyle \text{(a) }k\left(-px^2-\frac{x}{p}+1\right)\qquad\text{(b) }k\left(px^2-\frac{x}{p}-1\right)$
$\displaystyle \text{(c) }k\left(x^2+px-\frac1p\right)\qquad\text{(d) }k\left(x^2-px+\frac1p\right)$
$\displaystyle \text{Answer:}$
$\displaystyle \text{A quadratic polynomial with zeroes }\alpha,\beta\text{ is }k[x^2-(\alpha+\beta)x+\alpha\beta].$
$\displaystyle \text{Given, }\alpha+\beta=-p\text{ and }\alpha\beta=-\frac1p.$
$\displaystyle \therefore \text{The polynomial is }k\left(x^2+px-\frac1p\right).$
$\displaystyle \text{Multiplying the expression inside the bracket by }-p,$
$\displaystyle k\left(x^2+px-\frac1p\right)=k'\left(-px^2-p^2x+1\right),\text{ where }k'\ne0.$
$\displaystyle \therefore \text{Option (c) directly represents the required quadratic polynomial.}$
$\displaystyle \\$

$\displaystyle \textbf{Case Study - 2}$

$\displaystyle \text{An asana is a body posture. Originally, the term referred to a sitting meditation pose, but it}$
$\displaystyle \text{was later extended in hatha yoga and modern yoga to include different types of poses, such as}$
$\displaystyle \text{reclining, standing, inverted, twisting and balancing poses. In the figure, one can observe that}$
$\displaystyle \text{the shape formed by the poses can be related to the graph of a quadratic polynomial.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{The shape of the poses shown is:}$
$\displaystyle \text{(a) Spiral}\qquad\text{(b) Ellipse}\qquad\text{(c) Linear}\qquad\text{(d) Parabola}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The curved shape represented by the poses resembles a parabola.}$
$\displaystyle \therefore \text{The shape of the poses shown is a parabola.}$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{The graph of a parabola opens downwards, if:}$
$\displaystyle \text{(a) }a\geq0\qquad\text{(b) }a=0\qquad\text{(c) }a<0\qquad\text{(d) }a>0$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For a quadratic polynomial }y=ax^2+bx+c,\text{ the direction of opening depends on }a.$
$\displaystyle \text{If }a<0,\text{ the parabola opens downwards.}$
$\displaystyle \therefore a<0.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{In the graph, how many zeroes are there for the polynomial?}$
$\displaystyle \text{(a) }0\qquad\text{(b) }1\qquad\text{(c) }2\qquad\text{(d) }3$ $\displaystyle \text{Answer:}$
$\displaystyle \text{The zeroes of a polynomial are the x-coordinates of the points where its graph}$
$\displaystyle \text{intersects the x-axis.}$
$\displaystyle \text{The given parabola intersects the x-axis at two distinct points.}$
$\displaystyle \therefore \text{The polynomial has }2\text{ zeroes.}$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{The two zeroes in the above shown graph are:}$
$\displaystyle \text{(a) }2,4\qquad\text{(b) }-2,4\qquad\text{(c) }-8,4\qquad\text{(d) }2,-8$
$\displaystyle \text{Answer:}$
$\displaystyle \text{From the graph, the parabola intersects the x-axis at }x=-2\text{ and }x=4.$
$\displaystyle \therefore \text{The two zeroes of the polynomial are }-2\text{ and }4.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{The zeroes of the quadratic polynomial }4\sqrt3x^2+5x-2\sqrt3\text{ are:}$
$\displaystyle \text{(a) }\frac{2}{\sqrt3},\frac{\sqrt3}{4}\qquad\text{(b) }-\frac{2}{\sqrt3},\frac{\sqrt3}{4}$
$\displaystyle \text{(c) }\frac{2}{\sqrt3},-\frac{\sqrt3}{4}\qquad\text{(d) }-\frac{2}{\sqrt3},-\frac{\sqrt3}{4}$
$\displaystyle \text{Answer:}$
$\displaystyle 4\sqrt3x^2+5x-2\sqrt3=0$
$\displaystyle 4\sqrt3x^2+8x-3x-2\sqrt3=0$
$\displaystyle 4x(\sqrt3x+2)-\sqrt3(\sqrt3x+2)=0$
$\displaystyle (\sqrt3x+2)(4x-\sqrt3)=0$
$\displaystyle \therefore \sqrt3x+2=0\quad\text{or}\quad4x-\sqrt3=0$
$\displaystyle x=-\frac{2}{\sqrt3}\quad\text{or}\quad x=\frac{\sqrt3}{4}$
$\displaystyle \therefore \text{The zeroes are }-\frac{2}{\sqrt3}\text{ and }\frac{\sqrt3}{4}.$
$\displaystyle \therefore \text{Option (b) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Case Study - 3}$

$\displaystyle \text{Basketball and soccer are played with spherical balls. Although athletes dribble the ball in}$
$\displaystyle \text{both sports, a basketball player uses the hands, whereas a soccer player primarily uses the feet.}$
$\displaystyle \text{Soccer is usually played outdoors on a large field, while basketball is generally played indoors}$
$\displaystyle \text{on a court. The path traced by a soccer ball or basketball when projected through the air is}$
$\displaystyle \text{approximately parabolic and can be represented by the graph of a quadratic polynomial.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 1: }\text{The shape of the path traced shown is:}$
$\displaystyle \text{(a) Spiral}\qquad\text{(b) Ellipse}\qquad\text{(c) Linear}\qquad\text{(d) Parabola}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The path traced by a projectile is represented by a parabola.}$
$\displaystyle \therefore \text{The shape of the path traced is a parabola.}$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{The graph of a parabola opens upwards, if:}$
$\displaystyle \text{(a) }a=0\qquad\text{(b) }a<0\qquad\text{(c) }a>0\qquad\text{(d) }a\geq0$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For a quadratic polynomial }y=ax^2+bx+c,\text{ we have }a\ne0.$
$\displaystyle \text{If }a>0,\text{ the parabola opens upwards.}$
$\displaystyle \therefore a>0.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{In the above graph, how many zeroes are there for the polynomial?}$
$\displaystyle \text{(a) }0\qquad\text{(b) }1\qquad\text{(c) }2\qquad\text{(d) }3$ $\displaystyle \text{Answer:}$
$\displaystyle \text{The zeroes of a polynomial are the x-coordinates of the points where its graph}$
$\displaystyle \text{intersects the x-axis.}$
$\displaystyle \text{The given graph intersects the x-axis at three distinct points.}$
$\displaystyle \therefore \text{The polynomial has }3\text{ zeroes.}$
$\displaystyle \therefore \text{Option (d) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{The three zeroes in the above shown graph are:}$
$\displaystyle \text{(a) }2,3,-1\qquad\text{(b) }-2,3,1$
$\displaystyle \text{(c) }-3,-1,2\qquad\text{(d) }-2,-3,-1$
$\displaystyle \text{Answer:}$
$\displaystyle \text{From the graph, the curve intersects the x-axis at }x=-3,-1\text{ and }2.$
$\displaystyle \therefore \text{The three zeroes of the polynomial are }-3,-1\text{ and }2.$
$\displaystyle \therefore \text{Option (c) is correct.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{What will be the expression of the polynomial?}$
$\displaystyle \text{(a) }x^3+2x^2-5x-6\qquad\text{(b) }x^3+2x^2-5x+6$
$\displaystyle \text{(c) }x^3+2x^2+5x-6\qquad\text{(d) }x^3+2x^2+5x+6$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The zeroes of the polynomial are }-3,-1\text{ and }2.$
$\displaystyle \therefore p(x)=(x+3)(x+1)(x-2)$
$\displaystyle =(x^2+4x+3)(x-2)$
$\displaystyle =x^3+2x^2-5x-6$
$\displaystyle \therefore \text{The polynomial is }x^3+2x^2-5x-6.$
$\displaystyle \therefore \text{Option (a) is correct.}$
$\displaystyle \\$