Week-3 Mathematics For DS

 There are some questions which have functions with discrete valued domains (such as day, month, year etc). For simplicity, we treat them as continuous functions.

For NAT type question, enter only one right answer, even if you get multiple answers for that particular question.

Notations:

$\mathbb{R}$ = Set of real numbers $\mathbb{Q}$ = Set of rational numbers
$\mathbb{Z}$ = Set of integers
$\mathbb{N}$ = Set of natural numbers

The set of natural numbers includes 0.

If the slope of parabola $y=a{x}^2+bx+c$, where $a,b,c\in$$\mathbb{R}$ \$\{0\}$ at points $(3,2)$ and $(2,3)$ are $44$ and $19$ respectively, then find the value of $a$.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 12.5

1 point

A class of $352$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 32

1 point

A class of $234$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 26

1 point

A class of $352$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 32

1 point

A class of $234$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 26

1 point

A class of $140$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 20

1 point

A class of $494$ students are arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 38

1 point

The product of two consecutive odd natural numbers is $323$. Find the largest number among them.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 19

1 point

The slope of a parabola $y=3x^2-11x+10$ at a point $P$ is 1. Find the $y-$ coordinate of the point $P$.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 0.0

1 point

1 point

Find out the points where the curve $y=4x^2+x$ and the straight line $y=2x-3$ intersect with each other.

$(\frac{3}{2},0)$ and $(\frac{3}{2},\frac{21}{2})$.

Only at the origin.

The curve and the straight line do not intersect.

$(1,-1)$ and $(1,5)$.

Yes, the answer is correct.
Score: 1

Accepted Answers:

The curve and the straight line do not intersect.

A water fountain is designed to shoot a stream of water in the shape of a parabolic arc. The equation of the parabola is given by $h(t)=-0.5t^2+4t+1$, where $h(t)$ represents the height of the water stream in meters and t  represents the time in seconds since the water was shot.
Determine the time (in seconds) it takes for the water stream to reach its maximum height.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 4

1 point

1 point

Which of the following is/are correct

$x$ intercepts of the quadratic function $f(x)$ are known as the real roots of the quadratic equation $f(x)=0$.

If discriminant for two quadratic equations are same then they must be the same quadratic equations.

The slope at the vertex of the quadratic function is zero.

Every Quadratic function has axis of symmetry.

Suppose $P(x)$ is a Quadratic function and L be any straight line, then L must intersect the graph of $P(x)$.

Yes, the answer is correct.
Score: 1

Accepted Answers:

$x$ intercepts of the quadratic function $f(x)$ are known as the real roots of the quadratic equation $f(x)=0$.

The slope at the vertex of the quadratic function is zero.

Every Quadratic function has axis of symmetry.

1 point

Based on the Figure M1W3-1,which of the following is/are correct

 

                      
                                                            Fig:M1W3-1

The graph can be represented by \(y = ax^2 +bx +c\) given $b\mathrm{\ne }0$ and $a,b\in \mathbb{R}$,$a>0$

The graph can be represented by \(y = ax^2 +bx +c\) given $b=0$ and $a,b\in$$\mathbb{R}$,$a>0$

The graph can be represented by \(y = ax^2 +bx +c\) given $b<0$ and $a,b\in$$\mathbb{R}$,$a>0$

None

Yes, the answer is correct.
Score: 1

Accepted Answers:

The graph can be represented by \(y = ax^2 +bx +c\) given $b=0$ and $a,b\in$$\mathbb{R}$,$a>0$

1 point

Consider three Airports A, B, and C. Two friends Ananya and Madhuri want to meet at Airport C. Ananya Boarded Flight 1 from Point A to C which is 1200 km, due to bad weather, Flight 1 slowed down, and the average speed was reduced by 200 km/h and the time increased by 30 minutes. Madhuri boarded Flight 2 from Point B to C which is 1800 km, the average speed of Flight 2 is 720 km/h. What is the waiting time, and who will be waiting at the airport? (Given Ananya and Madhuri boarded at the same time)

Waiting Time is 1 hr and Ananya is waiting.

Waiting Time is 1 hr and Madhuri is waiting.

Waiting Time is 30 min and Ananya is waiting.

Waiting Time is 30 min and Madhuri is waiting.

Yes, the answer is correct.
Score: 1

Accepted Answers:

Waiting Time is 30 min and Ananya is waiting.

1 point

Which of the following options is/are true?

The point at which the slope of the equation $x^2+2x-5$ equals 10 is (4,17)

$x=2$ is the axis of symmetry of the quadratic function $f(x)=x^2+4x+5$

If two different quadratic equations have the same discriminant then the roots of both equations can be the same.

The point at which the slope of the equation $x^2+2x-5$ equals 10 is (4,19)

Yes, the answer is correct.
Score: 1

Accepted Answers:

If two different quadratic equations have the same discriminant then the roots of both equations can be the same.

The point at which the slope of the equation $x^2+2x-5$ equals 10 is (4,19)