MOCK 3 (week1-4) - (Sep 2025 - Mathematics I - Qualifier)

The due date for submitting this assignment has passed. Due on 2025-10-24, 23:59 IST. You may submit any number of times before the due date. The final submission will be considered for grading.

Note: Instructions:

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Question 1

Let $r(x)$ be a polynomial function which is obtained as the quotient after dividing the polynomial $p(x)=-\left(x+5\right)\left(x-3\right)\left(x^2-16\right)$ by the polynomial $q(x)=-\left(x-4\right)\left(x+4\right)$. Choose the correct option(s) which represent(s) the polynomial $r(x)$ most appropriately.

• 
• 
• 
• 

Accepted Answers:

• 

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Question 2

Let $R$= {$(a,c),(d,b),(b,d),(b,c),(c,a)$}, be a relation on the set   A ={$a,b,c,d$}. The relation $R$ is

• a function
• reflexive
• transitive
• not symmetric

Accepted Answers:

• not symmetric

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Question 3

How many students like all the three subjects? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 200

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Question 4

Find the number of students who like only one of the three subjects. Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 510

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Question 5

Find the number of students who like at least two of the given subjects. Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 430

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Question 6

Which of the following options are correct w.r.t triangle $ABC$

• Slope of the line segment $AB$ is $\frac{1}{2}$
• Slope of the line segment $BC$ is $-\frac{1}{2}$
• $\tan \alpha =-\frac{1}{2}$
• $\tan \alpha =\frac{3}{4}$

Accepted Answers:

• Slope of the line segment $AB$ is $\frac{1}{2}$
• $\tan \alpha =\frac{3}{4}$

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Question 7

Which of the following options represents the equation of the line $AC$

• $2y+11x-59=0$
• $6y=2x+2$
• $3y-x-1=0$
• $y=-5.5x+29.5$

Accepted Answers:

• $2y+11x-59=0$
• $y=-5.5x+29.5$

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Question 8

Using the above information, find the value of $k$. Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 15

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Question 9

Using the above information, what will be the $y-$coordinate of the point $A$? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 12.5

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Question 10

Which of the following statements is (are) correct?

• The product of the minimum value of the function $f(x)=5\left|x\right|+10$ and the maximum value of the function $g(x)=10-\left|x+12\right|$ is 100.
• There are infinitely many polynomial $p(x)$ of degree four such that $p(4)=0$, $p(5)=0$, $p(6)=0$.
• $y-4=(x+5{)}^2$ is an equation of a parabola whose vertex is at $(-5,4)$.
• Elements in Cartesian product will only be pairs.

Accepted Answers:

• The product of the minimum value of the function $f(x)=5\left|x\right|+10$ and the maximum value of the function $g(x)=10-\left|x+12\right|$ is 100.
• There are infinitely many polynomial $p(x)$ of degree four such that $p(4)=0$, $p(5)=0$, $p(6)=0$.
• $y-4=(x+5{)}^2$ is an equation of a parabola whose vertex is at $(-5,4)$.

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Question 11

Choose the most appropriate option for the statement given below: “The equation of the line joining the point $(-2,0)$ to the point of intersection of the lines $y+4x-2=0$ and $y-3x-2=0$ is equidistant from the points $(0,0)$ and $(2,2)$.

• True
• False
• Data insufficient
• None of the above

Accepted Answers:

• True

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Question 12

How many people actually contributed in group A? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 10

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Question 13

What is the contribution ($₹$) made by each person in group $B$? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 20

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Question 14

Which of the following could be the value of $k$.

• 4
• -5
• 10
• -10

Accepted Answers:

• 4

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Question 15

Find the possible number of values of $k$? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) 2

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Question 16

Which of the following are correct.

• The $x-$intercept of $p(x)$ in the given domain is 15.
• In the given domain $p(x)$ has 2 turning points.
• The $x-$coordinate of the vertex of $q(x)$ is 10.5 .
• The $x-$coordinate of the intersection point of $p(x)$ and $q(x)$ is 19.

Accepted Answers:

• The $x-$intercept of $p(x)$ in the given domain is 15.
• In the given domain $p(x)$ has 2 turning points.
• The $x-$coordinate of the vertex of $q(x)$ is 10.5 .
• The $x-$coordinate of the intersection point of $p(x)$ and $q(x)$ is 19.

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Question 17

What is the slope of the line $l(x)$? Your Answer: (Not answered)

Accepted Answers:

(Type: Numeric) -0.8

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