Mock

Maths 1 - Mock Tests

This file contains consolidated questions from all available mock tests.

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Mock Test 3 (Weeks 1 to 4)

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:

• Option 1 (Image: mock 1 o1.png)

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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

Context for Q3-Q5: In a survey of 1000 students: 52% liked CT, 45% liked Stats, 60% liked Math. 25% liked CT & Stats, 28% liked Math & Stats, 30% liked CT & Math. 6% liked none of these subjects.

How many students like all the three subjects?

Accepted Answers:

• 200

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Question 4

(Same context as Q3) Find the number of students who like only one of the three subjects.

Accepted Answers:

• 510

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Question 5

(Same context as Q3) Find the number of students who like at least two of the given subjects.

Accepted Answers:

• 430

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Question 6

Context for Q6-Q7: Consider a triangle $ABC$. Line segments $AB,BC,CA$ represent the sides. Given $\angle ABC=\angle BCA=\alpha$.

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

(Same context as Q6) 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 10

Which of the following statements is (are) correct?

• The product of the minimum value of $f(x)=5|x|+10$ and the maximum value of $g(x)=10-|x+12|$ 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 $f(x)=5|x|+10$ and the maximum value of $g(x)=10-|x+12|$ 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 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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Mock Test 6 (Weeks 5 to 8)

Question 1

Simplify the expression $(\frac{a^x}{a^y}{)}^{(x+y-z)}\cdot (\frac{a^y}{a^z}{)}^{(y+z-x)}\cdot (\frac{a^z}{a^x}{)}^{(z+x-y)}$

• $a^{x+y+z}$
• $a^{x^2+y^2+z^2-xy-yz-zx}$
• 1
• $a$

Accepted Answers:

• 1

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Question 2

Which of the following statements are correct?

• $f(x)=-\sqrt{\ln (x)}$ and $g(x)=e^{x^2}$ are inverses.
• Domain of $f(x)=\sqrt{e^{x^2-8x}-1}$ is $(-\infty ,0]\cup [8,\infty )$.
• Line $x=3$ is a vertical asymptote of $f(x)=\ln (x^2+5x-24)$.
• $f$ may be continuous at $x=a$ even if $f$ is not differentiable at $x=a$.

Accepted Answers:

• Domain of real-valued function $f(x)=\sqrt{e^{x^2-8x}-1}$ is $(-\infty ,0]\cup [8,\infty )$.
• $f$ may be continuous at the point $x=a$ even if $f$ is not differentiable at a point $x=a$.

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Question 3

Suppose $f(x)=\frac{x+5}{x-3}$ and $g(x)=\sqrt{x^2-1}$. Which are correct?

• Domain of $(f\circ g)(x)$ is $(-\infty ,-\sqrt{10})\cup (-\sqrt{10},-1]\cup [1,\sqrt{10})\cup (\sqrt{10},\infty )$.
• Domain of $(f\circ g)(x)$ is $\mathbb{R}\setminus \{-\sqrt{10},\sqrt{10}\}$.
• $(f\circ g)(x)=\frac{\sqrt{x^2-1}+5}{\sqrt{x^2-1}-3}$.
• $(g\circ f)(x)=\frac{4\sqrt{x+1}}{|x-3|}$.

Accepted Answers:

• Domain of $(f\circ g)(x)$ is $(-\infty ,-\sqrt{10})\cup (-\sqrt{10},-1]\cup [1,\sqrt{10})\cup (\sqrt{10},\infty )$.
• $(f\circ g)(x)=\frac{\sqrt{x^2-1}+5}{\sqrt{x^2-1}-3}$.
• $(g\circ f)(x)=\frac{4\sqrt{x+1}}{|x-3|}$.

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Question 4

Consider $a_n=\frac{a_{n-1}+a_{n-2}}{2}$ for $n\ge 3$ and $a_1=0,a_2=1$. Which are correct?

• The sequence $\{a_n\}$ is not convergent.
• $\underset{n\to \infty }{\lim }{a}_n=\frac{2}{3}$.
• ${\sum }_{i=3}^n{a}_i=\frac{a_2+a_{n-1}}{2}+{\sum }_{i=3}^{n-2}{a}_i$.
• ${\sum }_{i=3}^n{a}_i=\frac{a_{n-1}}{2}+{\sum }_{i=2}^{n-2}{a}_i$.

Accepted Answers:

• $\underset{n\to \infty }{\lim }{a}_n=\frac{2}{3}$.

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Question 5

Stock price $y=-7{\log }_2(x+a)+35$. January is $x=0,a\in \mathbb{N}$. Price goes to zero in November ($x=10$). Find $a$.

Accepted Answers:

• 32

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Question 6

Ravi borrowed ₹3,000 (SI, 7%, 4yr) and ₹12,000 (CI, 10%, x yr). CI received is thrice the SI received. Find $x$.

Accepted Answers:

• (Type: Range) 2.1, 2.3

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Question 12

Which are correct?

• If $n$ is odd, then $\lfloor \frac{n}{2}\rfloor =\frac{n-1}{2}$.
• If $n$ is even, then $\lfloor \frac{n}{2}\rfloor =\frac{n}{2}+1$.
• If $n$ is odd, then $\lfloor \frac{n}{2}\rfloor =\frac{n+1}{2}$.
• If $n$ is even, then $\lfloor \frac{n}{2}\rfloor =\frac{n}{2}$.

Accepted Answers:

• If $n$ is odd, then $\lfloor \frac{n}{2}\rfloor =\frac{n-1}{2}$.
• If $n$ is even, then $\lfloor \frac{n}{2}\rfloor =\frac{n}{2}$.

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End Term Mock Test

Question 1

A firework is projected from the lowest corner of a pole of height $15\text{m}$ into the air and reaches a maximum height which is same as the height of the pole. The path of the firework is parabolic and it lands $30\text{m}$ from the launch site $B$. Taking $B$ as the origin $(0,0)$, find the equation of the curve.

• $y-15=-\frac{1}{15}{x}^2$
• $y-15=-\frac{1}{15}(x-15{)}^2$
• $y-30=-\frac{1}{30}(x-30{)}^2$
• $y-30=-\frac{1}{30}{x}^2$

Accepted Answers:

• $y-15=-\frac{1}{15}(x-15{)}^2$

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Question 2

(Same context) A ball is thrown from the top of the pole which follows the parabolic path (vertex at $(h,20)$) and lands at a distance of $20\text{m}$ from the ground. Find out the equation of the curve followed by the ball.

• $y-15=-\frac{15}{20}(x-15{)}^2$
• $y-20=-\frac{1}{20^2}{x}^2$
• $y-20=-\frac{15}{20^2}{x}^2$
• $y-15=-\frac{15}{20^2}{x}^2$

Accepted Answers:

• $y-20=-\frac{15}{20^2}{x}^2$

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Question 4

Choose the option(s) which has the most possible representation of the graph of a function $f(x).$

• $f(x)=-\log (-x^2-14x-45)$
• $f(x)=-\log (-x^2+14x-45)$
• $f(x)=-\log (x^2+14x+45)$
• $f(x)=\log (-x^2-14x-45)$

Accepted Answers:

• $f(x)=-\log (-x^2+14x-45)$

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Question 5

Let $X$ be the set of natural numbers divisible by $100$, $Y$ be numbers divisible by $25$, and $Z$ be perfect squares.

• $625$ is in $E$.
• $200$ is in $G$.
• $2500$ is in $G$.
• $25$ is in $F$.
• $A$ and $F$ are empty.

Accepted Answers:

• $2500$ is in $G$.
• $25$ is in $F$.
• $A$ and $F$ are empty.

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Question 11

Define $f(x)=\{\begin{array}{ll}{x}^2-3x+2& \text{if }x\ne 2\\ x-2& \text{if }x=2\end{array}$. Which option(s) is/are true?

• $\underset{x\to 2^{+}}{\lim }f(x)=f(2)$.
• $\underset{x\to 2^{-}}{\lim }f(x)=f(2)$.
• $f$ is continuous at $x=2$.
• $f$ is differentiable at $x=2$.
• $f^{\prime }(3)=f^{\prime }(-3)=1$.
• $f$ is not differentiable at $x=1$.

Accepted Answers:

• $f^{\prime }(3)=f^{\prime }(-3)=1$.
• $f$ is not differentiable at $x=1$.

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Question 13

Consider $f(x)=|x(x-3)|$ in the domain $[-4,4]$. Which is true?

• The number of critical points is 3.
• The number of discontinuities of $f(x)$ is 2.
• The number of points where $f(x)$ is not differentiable is 2.
• $x=0$ is a critical point.
• The maximum value of $f(x)$ is $\frac{9}{4}$.

Accepted Answers:

• The number of critical points is 3.
• The number of points where $f(x)$ is not differentiable is 2.
• $x=0$ is a critical point.

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Question 15

What is the weight of a minimum cost spanning tree of the graph given below?

Accepted Answers:

• 25

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