datavorous/entrance-exam-dataset huggingface dataset:
Distinguish anaphase of mitosis from anaphase I of meiosis.

Options:

None

Solution:
The main difference between anaphase of mitosis and anaphase I of meiosis are as follows:

Topic: Biology, Cell Cycle and Cell Division
Distinguish between
(a) Grazing food chain and detritus food chain
(b) Production and decomposition
(c) Upright and inverted pyramid
(d) Food chain and food web
(e) Litter and detritus
(f) Primary and secondary productivity

Options:

None

Solution:
(a) Grazing Food Chain (GFC) begins with primary producers or plants and ends in carnivores (tertiary or top carnivores) whereas Detritus Food Chain (DFC) begins with detritus or dead organic matter and it ends in carnivores. In GFC, energy for the food chain comes from sun whereas in DFC, energy for the food chain comes from organic remains or detritus.
(b) Production is the phenomenon in which the energy is produced by the process of synthesis of organic compound from inorganic substances(such as $\mathrm{CO}_2, \mathrm{H}_2 \mathrm{O}$ \& minerals) utilizing generally the sunlight. It traps energy. Decomposition refers to the breakdown of complex organic matter into simpler ones. It releases energy.
(c) In upright pyramid (e.g., grassland \& cropland ecosystem), biomass or number of organisms or amount of energy decreases on moving to upper trophic levels while in an inverted pyramid (eg. tree ecosystem) these quantities tend to increase on going to successive trophic levels.
(d) A food chain is a sequence of different types of organisms by which the flow of energy occurs from one trophic level to another whereas food web is the network of various food chains inter-connected to each other. Food webs increase adaptability and competitiveness of the organisms.
(e) Litter is the dead organic material fallen on the surface of the soil like leaves, remains of animals and excreta. Detritus is the dead organic matter found below the soil surface which is eaten up by the detritivores or broken down by decomposers.
(f) Primary productivity is the rate of synthesis of biomass or energy fixation by the plants. It is comparatively quite high.
Secondary productivity is the rate of synthesis of biomass by consumers (herbivores and carnivores). It is small and decreases with rise of trophic level.

Topic: Biology, Ecosystem
Distinguish between families - Fabaceae, solanaceae, Liliaceae on the basis of gynoecium characteristics (with figures). Also write economic importance of any one of the above family.

Options:

None

Solution:
The families in plant kingdom mainly differ from each other in their reproductive structures. Based on characteristics of gynoecium the difference between the three families include the following:

Topic: Biology, Morphology of Flowering Plants
Distinguish between intracellular and extracellular digestion?

Options:

None

Solution:
Intracellular digestion takes place inside the cells by cellular enzymes, which are secreted by the surrounding cytoplasm into the food vacuole and the digestive products are then diffused in cytoplasm. It mainly occurs in unicellular organism and also is a less efficient method. Extracellular digestion occurs with the help of digestive enzymes poured into gastrovascular cavity by secretory cells and then the digestive products are diffused across the intestinal wall into various parts of the body. It mainly occurs in multicellular organisms and is more efficient.

Topic: Biology, Animal Kingdom
Distinguish between the following:
(a) Hibernation and Aestivation
(b) Ectotherms and Endotherms

Options:

None

Solution:
$$
\begin{array}{|l|l|l|}
\hline & \text { Hibernation } & \text { Aestivation } \\
\hline \text { 1. } & \begin{array}{l}
\text { It is a sleep-like state in which some } \\
\text { animals pass the winter months as a way } \\
\text { of surviving food scarcity and cold } \\
\text { weather. }
\end{array} & \begin{array}{l}
\text { It is a state of inactivity occurring in some } \\
\text { animals, such as lungfish, during } \\
\text { prolonged periods of drought or heat. }
\end{array} \\
\hline 2 . & \begin{array}{l}
\text { Animals that hibernate include bats, } \\
\text { hedgehogs, many fishes and amphibians } \\
\text { and reptiles. }
\end{array} & \begin{array}{l}
\text { Various bodily activities, such as feeding, } \\
\text { respiration, movement, are slowed down } \\
\text { considerably. }
\end{array} \\
\hline
\end{array}
$$
$$
\begin{array}{|l|l|l|}
\hline & \text { Ectotherms } & \text { Endotherms } \\
\hline \text { 1. } & \begin{array}{l}
\text { Ectotherm are those animals that does not } \\
\text { have the ability to produce sufficient internal } \\
\text { metabolic heat to maintain a constant body } \\
\text { temperature. }
\end{array} & \begin{array}{l}
\text { Endotherms are animals which can } \\
\text { generate and maintain heat within its } \\
\text { body independently of the } \\
\text { environmental temperature. }
\end{array} \\
\hline \text { 2. } & \begin{array}{l}
\text { All animals except mammals and birds are } \\
\text { ectotherms, and are often described as } \\
\text { being cold-blooded animals. }
\end{array} & \begin{array}{l}
\text { Mammals and birds are endotherms and } \\
\text { are often described as homoiotherms or } \\
\text { warm-blooded animals. }
\end{array} \\
\hline
\end{array}
$$

Topic: Biology, Organisms and Populations
Distinguishing reagent between silver and lead salts is

Options:
A $\mathrm{H}_2 \mathrm{~S}$ gas
B Hot dilute $\mathrm{HCl}$ solution
C $\mathrm{NH}_4 \mathrm{Cl}$ (solid) $+\mathrm{NH}_4 \mathrm{OH}$ solution
D $\mathrm{NH}_4 \mathrm{Cl}$ (solid) $+\left(\mathrm{NH}_4\right)_2 \mathrm{CO}_3$ solution

The correct answer is:
Hot dilute $\mathrm{HCl}$ solution

Solution:
Both $P b$ and $A g$ form white ppt. of their chlorides. But $\mathrm{PbCl}_2$ is soluble in hot water while $\mathrm{AgCl}$ does not dissolve in hot water.

Topic: Chemistry, Practical Chemistry, JEE Main
Disymmetric object is one which is

Options:
A Superimposable on its mirror image
B Non-superimposible on its mirror image
C Optically inactive
D Achiral

The correct answer is:
Non-superimposible on its mirror image

Solution:
Non superimposible on its mirror image.

Topic: Chemistry, General Organic Chemistry, JEE Main
Divide 10 into two parts such that the sum of double of the first and the square of the second is minimum

Options:
A $(6,4)$
B $(7,3)$
C $(8,2)$
D $(9,1)$

The correct answer is:
$(9,1)$

Solution:
Let $x$ and $y$ be the two parts of the number 10 .
$\therefore$
$x+y=10\ldots$ (i)
According to the question, Let $\quad \begin{aligned} A &=2 x+y^{2} \\ &=2 x+(10-x)^{2} \\ &=2 x+100+x^{2}-20 x \\ &=x^{2}-18 x+100 \end{aligned}$
On differentiating w.r.t. $x$, we get $\frac{d A}{d x}=2 x-18$
For max or min of $A$, Put $\quad \frac{d A}{d x}=0=2 x-18$
$\Rightarrow$
$x=9$
Now, $\quad \frac{d^{2} A}{d x^{2}}=2>0 \quad(\min )$
On putting $x=9$ in Eq. (i), we get $y=1$
$\therefore \quad(x, y)=(9,1)$

Topic: Mathematics, Application of Derivatives, JEE Main
DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorrect base structure.

Options:
A

B

C

D

The correct answer is:

Solution:
Are bases of DNA molecule. As DNA contain four bases, which are adenine, guanine, cytosine and thymine.

Topic: Chemistry, Biomolecules, JEE Main, JEE Main 2024 (06 Apr Shift 1)
Do ecosystems need a constant supply of energy to maintain order?

Options:
A Yes
B No
C Sometimes
D Can't say

The correct answer is:
Yes

Solution:
Ecosystems need a constant supply of energy to counteract the universal tendency toward increasing disorderliness as stated by the Second Law of Thermodynamics.

Topic: Biology, Ecosystem, NEET
Do mechanisms of breathing vary among different groups of animals?

Options:
A No, they are the same for all animals
B Only among lower invertebrates
C Only among mammals
D Yes, they vary depending on habitats and levels of organization

The correct answer is:
Yes, they vary depending on habitats and levels of organization

Solution:
Mechanisms of breathing vary among different groups of animals depending mainly on their habitats and levels of organisation.

Topic: Biology, Breathing and Exchange of Gases, NEET
Do you think that reproductive health in our country has improved in the past 50 years? If yes, mention some such areas of improvement.

Options:

None

Solution:
Yes, in the last 50 years, reproductive health in our country has improved. Some such areas of improvement are (i) massive child immunization (ii) maternity and child health
(iii) increasing use of contraceptives (iv) family planning. Bringing sexual and reproductive health services to the millions of people living in countries which still suffer from short life expectancies, high levels of child and maternal mortality, child labour and illiteracy and poor overall health remains a major challenge for governments and non government organizations.

Topic: Biology, Reproductive Health
Does acceleration due to gravity increase or decrease with increasing depth (assuming the earth to be a sphere of uniform density)?

Options:
A Increases
B Decreases
C Remains constant
D Fluctuates unpredictably

The correct answer is:
Decreases

Solution:
Correct Option is : (B)
Decreases

Topic: Chemistry, Gravitation, NEET
Does an unsymmetrical double convex thin lens change the position of the image of a point object on its axis when the lens is reversed?

Options:
A Yes, the position of the image changes.
B No, the position of the image remains the same.
C It depends on the refractive index of the lens material.
D The image position changes, but the magnitude remains constant.

The correct answer is:
No, the position of the image remains the same.

Solution:
Correct Option is : (B)
No, the position of the image remains the same.

Topic: Chemistry, Ray Optics, NEET
Does the chromosome number increase during the S phase?

Options:
A Yes
B No
C It depends
D None of the above

The correct answer is:
No

Solution:
If the cell had diploid or 2n number of chromosomes at G₁, even after S phase the number of chromosomes remains the same, i.e., 2n.

Topic: Biology, Cell Cycle and Cell Division, NEET
Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume ?
(a) \(\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2\) (g)
(b) \(\mathrm{CaO}(\mathrm{s})+\mathrm{CO}_2\) (g) \(\rightleftharpoons \mathrm{CaCO}_3\) (s)
(c) \(3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_2 \mathrm{O}\) (g) \(\rightleftharpoons \mathrm{Fe}_3 \mathrm{O}_4(\mathrm{~s})+4 \mathrm{H}_2\) (g)

Options:

None

Solution:
Applying Le Chatelier's principle, on decreasing the pressure, moles of reaction products will
(a) increase
(b) decrease
(c) remain same ( \(\because n_p=n_r\) gaseous)

Topic: Chemistry, Equilibrium
Does the number of moles of reaction products increase, decrease or remain the same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume? (a) PCl5(g) ⇌ PCl3(g) + Cl2(g) (b) CaO (s) + CO2(g) ⇌ CaCO3(s) (c) 3Fe (s) + 4H2O (g) ⇌ Fe3O4(s) + 4H2(g)

Options:
A Increase, Decrease, Decrease
B Decrease, Increase, Decrease
C Decrease, Decrease, Increase
D Increase, Increase, Increase

The correct answer is:
Increase, Decrease, Decrease

Solution:
Correct Option is : (A)
Increase, Decrease, Decrease

Topic: Chemistry, Ionic Equilibrium, NEET
Domain $\cos ^{-1}[x]$ is, where [] denotes a greatest integer function

Options:
A $(-1,2]$
B $(-1,2)$
C $[-1,2]$
D $[-1,2)$

The correct answer is:
$[-1,2)$

Solution:
Let $y=\cos ^{-1}[x]$
We know, for $\cos ^{-1} x$
$$
\Rightarrow \quad-1 \leq x \leq 1
$$
Therefore, for $\cos ^{-1}[x]$
$$
\Rightarrow \quad-1 \leq[x] \leq 1 \Rightarrow-1 \leq x < 2 \Rightarrow x \in[-1,2)
$$

Topic: Mathematics, Functions, KCET, KCET 2022
Domain of $\cos ^{-1}\left[\log _5\left(x^2+7 x+15\right)\right]$ is

Options:
A The set of all real numbers
B $(-\infty,-5] \cup[-2, \infty)$
C $R-\{-5,-2\}$, where $R$ is the set of real numbers
D $[-5,-2]$

The correct answer is:
$(-\infty,-5] \cup[-2, \infty)$

Solution:
We have, $f(x)=\cos ^{-1}\left[\log _5\left(x^2+7 x+15\right)\right]$
$f(x)$ is defined of
$\begin{array}{ll}
& \log _5\left(x^2+7 x+15\right) \in[-1,1] \\
& -1 \leq \log _5\left(x^2+7 x+15\right) \leq 1 \\
& \frac{1}{5} \leq x^2+7 x+15 \leq 5 \\
\because \quad & x^2+7 x+15 \leq 5 \Rightarrow x^2+7 x+10 \leq 0 \\
& (x+5)(x+2) \leq 0 \Rightarrow x \in[-5,-2]
\end{array}$

Topic: Mathematics, Functions, TS EAMCET, TS EAMCET 2020 (14 Sep Shift 2)
Domain of definition of the function $f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right)$ is

Options:
A $(1,2)$
B $(-1,0) \cup(1,2)$
C $(1,2) \cup(2, \infty)$
D $(-1,0) \cup(1,2) \cup(2, \infty)$

The correct answer is:
$(-1,0) \cup(1,2) \cup(2, \infty)$

Solution:
$\begin{aligned} & f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right) \text {. So, } 4-x^2 \neq 0 \Rightarrow x \neq \pm \sqrt{4} \\ & \text { and } x^3-x\gt0 \Rightarrow x\left(x^2-1\right)\gt0 \Rightarrow x\gt0, x\gt1\end{aligned}$
$\therefore D=(-1,0) \cup(1, \infty)-\{\sqrt{4}\}$ i.e. $D=(-1,0) \cup(1,2) \cup(2, \infty)$

Topic: Mathematics, Functions, JEE Main
Domain of definition of the function $f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right)$, is

Options:
A
$(-1,0) \cup(1,2) \cup(2, \infty)$

B
$(0,2)$

C
$(-1,0) \cup(0,2)$

D
$(1,2) \cup(2, \infty)$

The correct answer is:
$(-1,0) \cup(1,2) \cup(2, \infty)$

Solution:
$f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right)$
$4-x^2 \neq 0 ; x^3-x>0 ; x \neq \pm \sqrt{4}$
$\therefore \mathrm{D}=(-1,0) \bigcup(1, \infty)-\{\sqrt{4}\}$
$\mathrm{D}=(-1,0) \bigcup(1,2) \bigcup(2, \infty)$

Topic: Mathematics, Functions, JEE Main, JEE Main 2003
Domain of $f(x)=\frac{x}{1-|x|}$ is

Options:
A $R-[-1,1]$
B $(-\infty, 1)$
C $(-\infty, 1) \cup(0,1)$
D $R-\{-1,1\}$

The correct answer is:
$R-\{-1,1\}$

Solution:
Given function,
$f(x)=\frac{x}{1-|x|}$
$\because$ Denominator can't be zero.
$\begin{array}{lc}
\therefore & 1-|x| \neq 0 \\
\Rightarrow & |x| \neq 1 \\
\Rightarrow & x \neq \pm 1
\end{array}$
Hence, domain is $R-\{-1,1\}$.

Topic: Mathematics, Functions, KCET, KCET 2021
Domain of $f(x)=\log |\log x|$ is

Options:
A $(0, \infty)$
B $(1, \infty)$
C $(0,1) \cup(1, \infty)$
D $(-\infty, 1)$

The correct answer is:
$(0,1) \cup(1, \infty)$

Solution:
$f(x)=\log |\log x|, f(x)$ is defined if $|\log x|\gt0$ and $x\gt0$ i.e., if $x\gt0$ and $x \neq 1$
$\begin{aligned}
& (|\log x|\gt0 \text { if } x \neq 1) \\
& \Rightarrow x \in(0,1) \cup(1, \infty) .
\end{aligned}$

Topic: Mathematics, Functions, JEE Main
Domain of $f(x)=\left(x^2-1\right)^{-1 / 2}$ is

Options:
A $(-\infty,-1) \cup(1, \infty)$
B $(-\infty,-1] \cup(1, \infty)$
C $(-\infty,-1] \cup[1, \infty)$
D None of these

The correct answer is:
$(-\infty,-1) \cup(1, \infty)$

Solution:
Here $|x|\gt1$, therefore $x \in(-\infty,-1) \cup(1, \infty)$.

Topic: Mathematics, Functions, JEE Main
Domain of function $f(x)=\sin ^{-1} 5 x$ is

Options:
A $\left(-\frac{1}{5}, \frac{1}{5}\right)$
B $\left[-\frac{1}{5}, \frac{1}{5}\right]$
C $R$
D $\left(0, \frac{1}{5}\right)$

The correct answer is:
$\left[-\frac{1}{5}, \frac{1}{5}\right]$

Solution:
$-1 \leq 5 x \leq 1 \Rightarrow \frac{-1}{5} \leq x \leq \frac{1}{5}$. Hence domain is $\left[\frac{-1}{5}, \frac{1}{5}\right]$.

Topic: Mathematics, Functions, JEE Main
Domain of the function $\sqrt{2-x}-\frac{1}{\sqrt{9-x^2}}$ is

Options:
A $(-3,1)$
B $[-3,1]$
C $(-3,2]$
D $[-3,1)$

The correct answer is:
$(-3,2]$

Solution:
(i) $x \leq 2$
(ii) $\sqrt{9-x^2}\gt0 \Rightarrow|x| \lt 3$ or $-3 \lt x \lt 3$. Hence domain is $(-3,2]$.

Topic: Mathematics, Functions, JEE Main
Domain of the function $f(x)=\sqrt{2-2 x-x^2}$ is

Options:
A $-\sqrt{3} \leq x \leq \sqrt{3}$
B $-1-\sqrt{3} \leq x \leq-1+\sqrt{3}$
C $-2 \leq x \leq 2$
D $-2+\sqrt{3} \leq x \leq-2-\sqrt{3}$

The correct answer is:
$-1-\sqrt{3} \leq x \leq-1+\sqrt{3}$

Solution:
The quantity under root is positive, when
$-1-\sqrt{3} \leq x \leq-1+\sqrt{3} .$
\(\begin{aligned} & \text{as, } 2-2 x-x^2 \geqslant 0 \Rightarrow x^2+2 x-2 \leqslant 0 \\ & \Rightarrow(x-(-1-\sqrt{3}))(x+(1-\sqrt{3})) \end{aligned}\)

Topic: Mathematics, Functions, JEE Main
Domain of the function $f(x)=\left[\log _{10}\left(\frac{5 x-x^2}{4}\right)\right]^{1 / 2}$ is

Options:
A $-\infty \lt x \lt \infty$
B $1 \leq x \leq 4$
C $4 \leq x \leq 16$
D $-1 \leq x \leq 1$

The correct answer is:
$1 \leq x \leq 4$

Solution:
We have
$f(x)=\left[\log _{10}\left(\frac{5 x-x^2}{4}\right)\right]^{1 / 2}$ ....(i)
From (i), clearly $f(x)$ is defined for those values of $x$ for which
$\begin{aligned}
& \text { From (i), clearly } f(x) \text { is defined for those values of } x \text { for which } \log _{10}\left[\frac{5 x-x^2}{4}\right] \geq 0 \\
& \Rightarrow\left(\frac{5 x-x^2}{4}\right) \geq 10^0 \Rightarrow\left(\frac{5 x-x^2}{4}\right) \geq 1
\end{aligned}$
$\Rightarrow x^2-5 x+4 \leq 0 \Rightarrow(x-1)(x-4) \leq 0$
Hence domain of the function is $[1,4]$.

Topic: Mathematics, Functions, JEE Main
Domain of the function $f(\mathrm{x})=\log _{x} \cos x$, is

Options:
A $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\{1\}$
B $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{1\}$
C $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
D None of these

The correct answer is:
None of these

Solution:
We have
$f(x)=\log _{x} \cos x$ $f(x)$ is defined for $\cos x>0$ $x>0, x \neq 1$ $\cos x>0 \Rightarrow-\frac{\pi}{2} < x < \frac{\pi}{2}$ Also, $x>0, x \neq 1$ $\therefore$ Domain of $f$ is $\left(0, \frac{\pi}{2}\right)-\{1\}$
$\therefore$ Domain of $f$ is $\left(0, \frac{\pi}{2}\right)-\{1\}$

Topic: Mathematics, Three Dimensional Geometry, VITEEE, VITEEE 2010
Domain of the function $f(x)=\frac{1}{\sqrt{\left[x^{2}\right]-[x]-6}}$
where $[x]$ is greatest integer $\leq x$ is

Options:
A $(-\infty,-2) \cup[4, \infty)$
B $(-\infty,-2) \cup[3, \infty]$
C $[-\infty,-2] \cup[4, \infty]$
D $[-\infty,-2] \cup[3, \infty)$

The correct answer is:
$(-\infty,-2) \cup[4, \infty)$

Solution:
Given function,
$f(x)=\frac{1}{\sqrt{[x]^{2}-[x]-6}}$
where $[x]$ is greatest integer $\leq x$.
$\begin{array}{ll} & {[x]^{2}-[x]-6>0} \\ \Rightarrow & {[x]^{2}-3[x]+2[x]-6>0} \\ \Rightarrow & ([x]-3)([x]+2)>0 \\ \Rightarrow & ([x]-3)>0,[x]+2 < 0 \\ \Rightarrow & {[x]>3,[x] < -2} \\ \Rightarrow & x \in[4, \infty), x \in(-\infty,-2) \\ \therefore & x \in(-\infty,-2) \cup[4, \infty)\end{array}$

Topic: Mathematics, Functions, KCET, KCET 2021
Domain of the function $f(x)=\frac{x^2-3 x+2}{x^2+x-6}$

Options:
A $\{x: x \in R, \quad x \neq 3\}$
B $\{x: x \in R, \quad x \neq 2\}$
C $\{x: x \in R\}$
D $\{x: x \in R, x \neq 2, x \neq-3\}$

The correct answer is:
$\{x: x \in R, x \neq 2, x \neq-3\}$

Solution:
$f(x)=\frac{(x-2)(x-1)}{(x-2)(x+3)}$
Hence domain is $\{x: x \in R, x \neq 2, x \neq-3\}$

Topic: Mathematics, Functions, JEE Main
Domain of the function $\sqrt{\left.\log ^{\prime}\left(5 x-x^2\right) / 6\right\}}$ is

Options:
A $(2,3)$
B $[2,3]$
C $[1,2]$
D $[1,3]$

The correct answer is:
$[2,3]$

Solution:
$\log \left\{\frac{5 x-x^2}{6}\right\} \geq 0 \Rightarrow \frac{5 x-x^2}{6} \geq 1$ or $x^2-5 x+6 \leq 0$ or $(x-2)(x-3) \leq 0$. Hence $2 \leq x \leq 3$

Topic: Mathematics, Functions, JEE Main
Domain of the function $\log \left|x^2-9\right|$ is

Options:
A $R$
B $R-[-3,3]$
C $R-\{-3,3\}$
D None of these

The correct answer is:
$R-\{-3,3\}$

Solution:
For $\quad x=-3,3,\left|x^2-9\right|=0$
Therefore $\log \left|x^2-9\right|$ does not exist at $x=-3,3$.
Hence domain of function is $R-\{-3,3\}$.

Topic: Mathematics, Functions, JEE Main
Domain of the function $\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is

Options:
A $(-1,1)$
B $(-1,1)-\{0\}$
C $[-1,1]$
D $[-1,1]-\{0\}$

The correct answer is:
$[-1,1]-\{0\}$

Solution:
$1+x \geq 0 \Rightarrow x \geq-1 ; \quad 1-x \geq 0 \Rightarrow x \leq 1, x \neq 0$
Hence domain is $[-1,1]-\{0\}$

Topic: Mathematics, Functions, JEE Main
Domain of the real valued function $f(x)=\frac{x+2}{9-x^{2}}$ is

Options:
A $-3 \leq x \leq 3$
B $R-\{-3,3\}$
C $R$
D $R-\{3\}$

The correct answer is:
$R-\{-3,3\}$

Solution:
$f(x)=\frac{x+2}{9-x^{2}}$ is not defined if $9-x^{2}=0 \Rightarrow x=\pm 3$
$\therefore$ Required domain $=\mathrm{R}-\{\pm 3\}$

Topic: Mathematics, Functions, JEE Main
Domain of the real valued function $f(x)=\frac{x+2}{9-x^{2}}$ is

Options:
A $-3 \leq x \leq 3$
B $R-\{-3,3\}$
C $R$
D $R-\{3\}$

The correct answer is:
$R-\{-3,3\}$

Solution:
$f(x)=\frac{x+2}{9-x^{2}}$ is not defined if $9-x^{2}=0 \Rightarrow x=\pm 3$
$\therefore$ Required domain $=\mathrm{R}-\{\pm 3\}$

Topic: Mathematics, Functions, MHT CET, MHT CET 2020 (12 Oct Shift 2)
Domain of $y=\sqrt{\log _{10} \frac{3 x-x^2}{2}}$ is

Options:
A $x < 1$
B $2 < x$
C $1 \leq x \leq 2$
D $2 < x < 3$

The correct answer is:
$1 \leq x \leq 2$

Solution:
$$
\log _{10}\left(\frac{3 x-x^2}{2}\right) \geq 0
$$
or $\log _{10}\left(\frac{3 x-x^2}{2}\right) \geq \log _{10} 1$
or $x^2-3 x+2 \leq 0$
or $x \in[1,2]$ and $\frac{3 x-x^2}{2}>0$
$$
\Rightarrow \mathrm{X} \in[1,2]
$$

Topic: Mathematics, Functions, WBJEE, WBJEE 2022
Doppler shift in frequency does not depend upon

Options:
A The frequency of the wave produced
B The velocity of the source
C The velocity of the observer
D Distance from the source to the listener

The correct answer is:
Distance from the source to the listener

Solution:
The formula for Doppler effect is given by,
$f_s=f_o\left(\frac{v \pm v_o}{v \pm v_s}\right)$
where, $f_o$ is the frequency of the observer, $f_s$ is the frequency heard, $v$ is the speed of sound, $v_o$ is the velocity of obserber and $v_s$ is the speed of source. Clearly we see that the change depends on everything except for the distance from the source to the listener.

Topic: Physics, Waves and Sound, JEE Main
Doppler's effect will not be applicable when the velocity of sound source is

Options:
A Equal to that of the sound velocity
B Less than the velocity of sound
C Greater than the velocity of sound
D Zero

The correct answer is:
Greater than the velocity of sound

Solution:
Doppler effect is defined only for waves with velocity lesser than or equal to that of sound. Hence, any wave with velocity greater than the velocity of sound will not have doppler effect.

Topic: Physics, Waves and Sound, JEE Main
Dormancy of seeds is broken by ethylene, whereas it is induced by

Options:
A Abscisic acid
B Auxin
C Cytokinin
D Gibberellic acid

The correct answer is:
Abscisic acid

Solution:
Hormonal regulation may be a highly conserved mechanism of seed dormancy among seed plants. Induction and maintenance of seed dormancy by abscisic acid (ABA).

Topic: Biology, Plant - Growth and Development, NEET
Drained sewage has B.O.D.

Options:
A More than water
B Less than water
C Equal than water
D None of the above.

The correct answer is:
More than water

Solution:
Drained Sewage has more B.O.D. as it has more micro organisms.

Topic: Chemistry, Environmental Chemistry, JEE Main
→ Drastic condition KMnO 4 ,  H 2 SO 4 , Δ X → Drastic conditions KMnO 4 ,  H 2 SO 4 , Δ Y → Drastic conditions KMnO 4 ,  H 2 SO 4 , Δ Z
The number of C-atoms present in the final product 'Z' is

Options:

The correct answer is:
2

Solution:

Topic: Chemistry, Alcohols Phenols and Ethers, JEE Main
Draw the graph for $y=\left|x^2-2 x-3\right|$.

Options:
A

B

C

D

The correct answer is:

Solution:
As we know the graph for $y=x^2-2 x-3=(x-3)(x+1)$ is a parabola; so to sketch $y=\left|x^2-2 x-3\right|$ we have to follow two steps.
(i) Leave the positive part of $y=x^2-2 x-3$, as it is.
(ii) Take the image of negative part of $y=x^2-2 x-3$, i.e., the part below $x$-axis in the $x$-axis as plane mirror shown as in
Graph for $y=x^2-2 x-3=(x-3)(x+1)$ :
Graph for $y=\left|x^2-2 x-3\right|$ :
Clearly above curve is differentiable for all $x \in R-\{-1,3\}$.

Topic: Mathematics, Functions, JEE Main
Draw the output signal Y in the given combination of gates.

Options:
A

B

C

D

The correct answer is:

Solution:
According to gates by Demorgan's law A¯+B¯=A·B¯ By observation.

Topic: Physics, Semiconductors, JEE Main, JEE Main 2021 (26 Feb Shift 2)