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.

 

 

1 point

 

7. Find out the points where the curve $y=4x^2+x+6$ and the straight line passing through the points $(1,6)$ and $(4,5)$ intersect.

 

 

$(\genfrac{}{}{0ex}{}{-1}{2},\genfrac{}{}{0ex}{}{13}{2})$

 

 

$(\genfrac{}{}{0ex}{}{1}{6},\genfrac{}{}{0ex}{}{113}{18})$

 

 

$(0,6)$

 

The curve and the straight line do not intersect.

Yes, the answer is correct.
Score: 1

Accepted Answers:

 

$(\genfrac{}{}{0ex}{}{-1}{2},\genfrac{}{}{0ex}{}{13}{2})$

 

 

$(\genfrac{}{}{0ex}{}{1}{6},\genfrac{}{}{0ex}{}{113}{18})$

 

 

1 point

8. 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 $P(x)$.

 

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.

8.

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 $b\ne 0$ 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

 

11. An Architect is designing an arch which is in the shape of figure M1W3-PARABOLA,
 The details of the design are as follows:
 Height of arch is 20m, width of arch at height of 8m is 4m.
 Consider the axis of symmetry as $x=0$, find the equation of the arch.


   
                                                   fig:M1W3-PARABOLA

 

 

$y=-3x^2+20$

 

 

$y=\genfrac{}{}{0ex}{}{-3}{4}{x}^2+20$

 

 

$y=-x^2+x+20$

 

 

$y=-2x^2-2x+20$

 

Yes, the answer is correct.
Score: 1

Accepted Answers:

 

$y=-3x^2+20$