COMEDK 2026 Morning Shift

A square plate is contracting at a uniform rate of $2 \mathrm{~cm}^2 / \mathrm{min}$. The rate at which the perimeter is decreasing when the side of the square is 16 cm is:

The behaviour of the function $f(x)=\sin \left(2 x+\frac{\pi}{4}\right)$ on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$ is:

If the function $f(x)=x^4-31 x^2+\boldsymbol{a} x+5$ has a turning point at $x=1$, then the value of ' $\boldsymbol{a}$ ' is $\_\_\_\_$ and the function attains a $\_\_\_\_$ at $x=1$

If $\mathbf{3 ~ c m} / \mathbf{s}$ is the rate at which the side of an equilateral triangle increases, then the rate of change of area, when the side is $\mathbf{1 2 ~ c m}$ is:

The area of the region in the first quadrant enclosed by the $x$-axis, the line $x=\sqrt{3} y$ and the circle $x^2+y^2=4$ is

The area of the region bounded by the line $y=x+2$ and the curve $x=-y^2$ is

\text { The remainder when } \mathbf{7}^{\mathbf{1 0 3}} \text { is divided by } \mathbf{2 5} \text { is }

The radius of a circle is $\mathbf{5 ~ c m}$. A chord of this circle is equal to the radius. Then the length of the arc of this chord is:

\(\text { The conjugate of } z=\frac{(\mathbf{4}+\boldsymbol{i})(\mathbf{1}-\boldsymbol{i})}{(\mathbf{1}+\boldsymbol{i})(\mathbf{2}-\boldsymbol{i})}\)

\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^5 x \cos ^7 x d x=\)

$$ \text { The solution of } \boldsymbol{d} \boldsymbol{y}=\boldsymbol{\operatorname { c o s }} \boldsymbol{x}(\mathbf{2}-\boldsymbol{y} \boldsymbol{\operatorname { c o s e c }} \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \quad \text { wh...

In a bank the principal increases continuously at the rate of $4 \%$ per annum. In how many years will ₹ 1000 triple itself?

\(\text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{R} \text { and } y=2 \text { when } x=0 \text { is }\)

The order and degree of the differential equation $\left(\frac{d y}{d x}\right)^2+\frac{d x}{d y}=x$ is:

\(\text { If } x=a(\theta-\sin \theta) \text { and } y=a(1-\cos \theta) \text {, then } \frac{\left(\mathbf{1}+\boldsymbol{y}_{\mathbf{1}}{ }^{\mathbf{2}}\right)^{\mathbf{3} / \mathbf{2}}}{\boldsymbol{y}_{\mathbf{2}}}=\)

The derivative of $y=\sin ^2\left[\cot ^{-1}\left(\sqrt{\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}}\right)\right]$ is

The length of the latus rectum of the curve represented by $x=3(\cos t+\sin t)$ and $y=4(\cos t-\sin t)$ is:

The difference between the distance of any point on the hyperbola from the two foci is $\mathbf{1 6}$ and the eccentricity is $\mathbf{2}$. Then the equation of the hyperbola is

\(\int \frac{e^{\log \left(1+\frac{1}{x^2}\right)}}{x^2+\frac{1}{x^2}} d x=\)

\(\int e^{2 x} \cos (5 x+3) d x=\)

\(\int \sqrt{2 a x-x^2} d x=\)

\(\int \frac{x+1}{x\left(1+x e^x\right)} d x=\)

Which of the following is the simplest form of the expression $\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}}\left(\frac{\sqrt{\mathbf{1 + x ^ { \mathbf { 2 } }}}-\mathbf{1}}{\boldsymbol{x}}\right)$ where $x \neq 0$

The value of the expression $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\sin ^{-1}\left(\sin \frac{22 \pi}{3}\right)+\tan ^{-1}\left(\tan \frac{4 \pi}{5}\right)$ is:

\(\mathop {\lim }\limits_{x \to 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \text { is equal to: }\)

The function $y=||x|-1|$ is differentiable for all values of ' $x$ ' except

If $f(x)=\left\{\begin{array}{l}\frac{\sqrt{1+x}-\sqrt{1-x}}{\sin x} \\ \boldsymbol{k}, x=0\end{array}, x \neq 0\right.$ is continuous at $x=0$, then $\boldsymbol{k}=$

The value of $\mathop {\lim }\limits_{x \to 3}\left[\frac{1}{x-3}+\frac{9 x}{27-x^3}\right]$ is:

Which of the following is NOT a comer point of the feasible region determined by the constraints:
$$ \begin{aligned} & x+2 y \leq 4 \\ & x+y \geq 2 \\ & x \geq 0 \text { and } y \geq 0 \end{aligned} $$

"A storage room must be kept at a temperature (T) such that triple the temperature is at least $\mathbf{1 5}^{\circ} \mathbf{C}$, but the temperature plus $\mathbf{8}$ is strictly not more than $\mathbf{2 0}^{\circ} \mathbf{C}$. What is the...

If A and B are two square matrices of the same order such that $\mathrm{AB}=\mathrm{A}$ and $\mathrm{BA}=\mathrm{B}$, then $(\boldsymbol{A}+\boldsymbol{B})^2$ is equal to:

Given $A=\left(\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right)$ and $f(x)=x^2-2 x-3$ then $f(A)$ is:

If $x=4$ is a root of $\left|\begin{array}{cc}x & 3 \\ 1 & x-2\end{array}\right|=5$, then the other root is:

Given $P=\left[\begin{array}{lll}2 & \boldsymbol{\alpha} & 1 \\ 1 & 2 & 2 \\ 1 & 3 & 3\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix A and $|A|=3$, then the value of $\boldsymbol{\alpha}$ is:

Given the matrices $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 2\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 1 & 0 \\ 1 & 1 & 2 \\ 0 & 2 & 1\end{array}\right]$, then the minor $\boldsymbol{M}_{\mathbf{2 3}}$ of th...

In how many ways can the squares of a $\mathbf{4} \times \mathbf{2}$ grid ( 4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?

The range of the function $f(x)={ }^{(7-x)} P_{(x-3)}$ is

A batch of $\mathbf{1 0}$ cupcakes consists of $\mathbf{5}$ chocolate, $\mathbf{3}$ vanilla, and $\mathbf{2}$ strawberry. If 4 cupcakes are selected to be put into a gift box, find the number of different ways they can be chosen if the sele...

Advika chooses one of three scarves every morning: Red, Blue, or Green.


The probability she chooses Red is $20 \%$.

The probability she chooses Blue is twice the probability of choosing Red.

On the remaining days she wears a Green scarf...

The odds against Arjun solving a problem are $\mathbf{5 : 2}$ and the odds in favour of Bhavana solving the same problem are 3:4. What is the probability that the problem is NOT solved by either of them?

A teacher has two jars of candy on her desk:
Jar 1: Contains 3 Strawberry candies and 2 Orange candies.
Jar 2: Contains 1 Strawberry candy and 4 Orange candies.
The teacher randomly picks two candies from Jar 1 and drops them into Jar 2.
Th...

Samhita faces a three-headed dragon. She wins a "Tactical medal" if she manages to defeat exactly one of the three heads.
The battle proceeds head-by-head under the following conditions:

The probability of defeating the first head is $\fra...

An engineering team is testing a new prototype drone. The drone has constant success rate of $\frac{\mathbf{2}}{\mathbf{7}}$ for every autonomous landing attempt. Two engineers, Sarah and Swarna, take turns initiating the landing sequence, ...

The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14 . Find the numbers.

Let ' $\boldsymbol{a}$ ' and ' $\mathbf{b}$ ' be two numbers where $\boldsymbol{a}<\boldsymbol{b}$. The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 24 . Then ...

Consider the following list of ordered pairs: $(1,0),(-2,-1),(7,-6),(-3,4)$ and $(0,2)$
Which of the following options correctly identifies only those pairs that are NOT elements of the relation $R=\{(x, y): y=1-|x| ; x, y \in \mathbb{Q}\}$...

The set expression $A \cup\left(B \cap\left(A^{\prime} \cup B^{\prime}\right)\right)$ is equivalent to

If $A=\{x: x$ is the first three odd numbers $\}$
$B=\{2 x+3: 0 \leq x<5, x \in \mathbb{N}\}$, then which of the following is true

If for a distribution of 20 items, $\sum(x-4)=10$ and $\sum(x-4)^2=85$ then the standard deviation is:

Distance between $8 x+15 y-20=0$ and $8 x+15 y+14=0$ is: