eSaral - JEE | NEET | Class 8-10 Exam Prep App

The average height of 30 boys was calculated to be 150 cm.

Question: The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean. Solution: We know that, Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Mean of height of 30 boys $=\frac{\sum_{i=1}^{30} x_{i}}{30}$ $\Rightarrow 150=\frac{\sum_{i=1}^{30} x_{i}}{30}$ $\Rightarrow \sum_{i=1}^{30} x_{i}=150 \times 30$ $\Rightarrow \sum_{i=1}^{30} x_{...

If the circles

Question: If the circles $x^{2}+y^{2}-16 x-20 y+164=r^{2}$ and $(x-4)^{2}+(y-7)^{2}=36$ intersect at two distinct points, then:(1) $r11$(2) $0\mathrm{r}1$(3) $\mathrm{r}=11$(4) $1\mathrm{r}11$Correct Option: 4, Solution: Consider the equation of circles as, $x^{2}+y^{2}-16 x-20 y+164=r^{2}$ i.e. $(x-8)^{2}+(y-10)^{2}=r^{2}$............(1) and $(x-4)^{2}+(y-7)^{2}=36$...............(2) Both the circles intersect each other at two distinct points. Distance between centres $=\sqrt{(8-4)^{2}+(10-7)^...

Which of the following statement is not true for glucose?

Question: Which of the following statement is not true for glucose?Glucose exists in two crystalline forms $\alpha$ and $\beta$Glucose gives Schiff's test for aldehydeGlucose reacts with hydroxylamine to form oxime The pentaacetate of glucose does notreact with hydroxylamine to give oximeCorrect Option: , 2 Solution: Glucose exists in cyclic form in which aldehyde group is not free, therefore it does not give Schiff's test....

Which of the following statements is correct?

Question: Which of the following statements is correct?Gluconic acid can form cyclic (acetal/hemiacetal) structureGluconic acid is a dicarboxylic acidGluconic acid is a partial oxidation product of glucoseGluconic acid is obtained by oxidation of glucose with $\mathrm{HNO}_{3}$Correct Option: , 3 Solution: Gluconic acid is obtained by partial oxidation of glucose by mild oxidising agent e.g. Tollen's reagent, Fehling solution, $\mathrm{Br}_{2}$ water. Gluconic acid can not form hemiacetal or ace...

A parallel plate capacitor has

Question: A parallel plate capacitor has $1 \mu \mathrm{F}$ capacitance. One of its two plates is given $+2 \mu \mathrm{C}$ charge and the other plate, $+4 \mu \mathrm{C}$ charge. The potential difference developed across the capacitor is :(1) $3 \mathrm{~V}$(2) $1 \mathrm{~V}$(3) $5 \mathrm{~V}$(4) $2 \mathrm{~V}$Correct Option: , 2 Solution:...

Three circles of radii a, b, c

Question: Three circles of radii $a, b, c^{\prime \prime}(abc)$ touch each other externally. If they have $x$-axis as a common tangent, then:(1) $\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{b}}+\frac{1}{\sqrt{c}}$(2) $\frac{1}{\sqrt{b}}=\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{c}}$(3) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P(4) $\sqrt{a}, \sqrt{b}, \sqrt{c}$ are in A.P.Correct Option: 1 Solution: $A M^{2}=A C^{2}-M C^{2}$ $=(a+c)^{2}-(a-c)^{2}=4 a c$ $\Rightarrow A M^{2}=X Y^{2}=4 a c$ $\Rightarrow X Y=2 ...

The correct match between Item-I and Item - II is:

Question: The correct match between Item-I and Item - II is: (A) - (III), (B) - (IV), (C) - (I), (D) - (II)(A) - (III), (B) -(IV), (C) - (II), (D) - (I)$(\mathrm{A})-(\mathrm{IV}),(\mathrm{B})-(\mathrm{III}),(\mathrm{C})-(\mathrm{II}),(\mathrm{D})-(\mathrm{I})$(A) -(IV), (B) - (III), (C) - (I), (D) - (II)Correct Option: , 3 Solution: (A) Natural rubber - Polymer of isoprene (B) Neoprene - Polymer of chloroprene (C) Buna N - Polymer of 1,3-butadiene and acrylonitrile (D) Buna S - Polymer of 1,3-b...

The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20.

Question: The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number. Solution: Let the numbers bex1,x2,...,x6.Mean = 23We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Thus, we have: $23=\frac{x_{1}+x_{2}+\ldots+x_{6}}{6}$ $x_{1}+x_{2} \ldots \ldots \ldots x_{6}=138$ If one number, say,x6, is excluded, then we have: $20=\frac{x_{1}+x_{2}+\ldots+x_{5}}{5}$ $x_{1}+x_{2} \ldots \ldots+x...

Voltage rating of a parallel plate capacitor is 500 V.

Question: Voltage rating of a parallel plate capacitor is $500 \mathrm{~V}$. Its dielectric can withstand a maximum electric field of $10^{6}$ $\mathrm{V} / \mathrm{m}$. The plate area is $10^{-4} \mathrm{~m}^{2}$. What is the dielectric constant if the capacitance is $15 \mathrm{pF}$ ? (given $\epsilon_{0}=8.86 \times 10^{-12} \mathrm{C}^{2} \mathrm{~m}^{2}$ )(1) $3.8$(2) $8.5$(3) $4.5$(4) $6.2$Correct Option: , 2 Solution: (2) Capacitance of a capacitor with a dielectric of dielectric constant...

A circle touching the x-axis at (3,0)

Question: A circle touching the $x$-axis at $(3,0)$ and making an intercept of length 8 on the $y$-axis passes through the point :(1) $(3,10)$(2) $(3,5)$(3) $(2,3)$(4) $(1,5)$Correct Option: 1 Solution: A circle touching the $x$-axis at $(3,0)$ and making an intercept of length 8 on the $y$-axis passes through the point : $C B=\sqrt{M C^{2}+M B^{2}}$ $\sqrt{3^{2}+4^{2}}=5=$ radius of circle $\therefore$ equation of circle is, $(x-3)^{2}+(y-5)^{2}=5^{2}$ $(3,10)$ satisfies this equation. Although...

Which one of the following statements is not true?

Question: Which one of the following statements is not true?Lactose contains $\alpha$-glycosidic linkage between $\mathrm{C}_{1}$ of galactose and $\mathrm{C}_{4}$ of glucose.Lactose is a reducing sugar and it gives Fehling's test.Lactose $\left(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ is a disaccharide and it contains 8 hydroxyl groups.On acid hydrolysis, lactose gives one molecule of $D(+)$-glucose and one molecule of $D(+)$-galactoseCorrect Option: 1 Solution: Lactose contains ...

Consider the Assertion and Reason given below.

Question: Consider the Assertion and Reason given below. Assertion (A) : Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure is used to make buckets and dustbins. Reason (R) : High density polymers are closely packed and are chemically inert. Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure is used to make buckets and dustbins.(A) is correct but (R) is wrong.Both (A) and (R) are correct and (R) is not the corr...

Two identical capacitors A and B,

Question: Two identical capacitors $\mathrm{A}$ and $\mathrm{B}$, charged to the same potential 5V are connected in two different circuits as shown below at time $t=0$. If the charge on capacitors $\mathrm{A}$ and $\mathrm{B}$ at time $t=\mathrm{CR}$ is $\mathrm{Q}_{\mathrm{A}}$ and $\mathrm{Q}_{\mathrm{B}}$ respectively, then (Here e is the base of natural logarithm) (1) $\mathrm{Q}_{\mathrm{A}}=\frac{\mathrm{VC}}{e}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{CV}}{2}$(2) $\mathrm{Q}_{\mathrm{A}}=\m...

If the angle of intersection at a point where

Question: If the angle of intersection at a point where the two circles with radii $5 \mathrm{~cm}$ and $12 \mathrm{~cm}$ intersect is $90^{\circ}$, then the length (in $\mathrm{cm}$ ) of their common chord is :(1) $\frac{13}{5}$(2) $\frac{120}{13}$(3) $\frac{60}{13}$(4) $\frac{13}{2}$Correct Option: , 2 Solution: According to the diagram, In $\Delta P C_{1} C_{2}, \tan \alpha=\frac{5}{12} \Rightarrow \sin \alpha=\frac{5}{13}$ In $\triangle P C_{1} M, \sin \alpha=\frac{P M}{12} \Rightarrow \frac...

The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers

Question: The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers. Solution: Let the numbers bex1,x2,...x20.We know Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Thus, we have: $18=\frac{x_{1}+x_{2}+\ldots \ldots+x_{20}}{20}$ $\Rightarrow x_{1}+x_{2}+\ldots \ldots+x_{20}=360 \quad \ldots \ldots$ (i) New numbers are: $\left(x_{1}+3\right),\left(x_{2}+3\right), \ldots\left(x_{10}+3\right), x_{11}, \l...

The number of chiral carbons present in sucrose is

Question: The number of chiral carbons present in sucrose is ________________ . Solution: (9)...

A capacitor is made of two square plates each of side 'a ' making a very small angle a between them,

Question: A capacitor is made of two square plates each of side ' $a$ ' making a very small angle a between them, as shown in figure. The capacitance will be close to: (1) $\frac{\in_{0} a^{2}}{d}\left(1-\frac{\alpha a}{2 d}\right)$(2) $\frac{\in_{0} a^{2}}{d}\left(1-\frac{\alpha a}{4 d}\right)$(3) $\frac{\epsilon_{0} a^{2}}{d}\left(1+\frac{\alpha a}{d}\right)$(4) $\frac{\in_{0} a^{2}}{d}\left(1-\frac{3 \alpha a}{2 d}\right)$Correct Option: 1, Solution: Consider an infinitesimal strip of capacit...

The locus of the centres of the circles,

Question: The locus of the centres of the circles, which touch the circle, $x^{2}+y^{2}=1$ externally, also touch the $y$-axis and lie in the first quadrant, is:(1) $x=\sqrt{1+4 y}, y \geq 0$(2) $y=\sqrt{1+2 x}, x \geq 0$(3) $y=\sqrt{1+4 x}, x \geq 0$(4) $x=\sqrt{1+2 y}, y \geq 0$Correct Option: 2, Solution: Let centre of required circle is $(h, k)$. $\therefore \mathrm{OO}^{\prime}=r+r^{\prime} \quad$ [By the diagram] $\Rightarrow \sqrt{h^{2}+k^{2}}=1+h$ $\Rightarrow h^{2}+k^{2}=1+h^{2}+2 h$ $\...

Which one of the following polymers is not obtained by

Question: Which one of the following polymers is not obtained by condensation polymerisation?Nylon 6,6Buna - NBakeliteNylon 6Correct Option: , 2 Solution: Buna- $\mathrm{N}$ is obtained by addition polymerisation....

The mean of 12 numbers is 40. If each number is divided by 8,

Question: The mean of 12 numbers is 40. If each number is divided by 8, what will be the mean of the new numbers? Solution: Let the numbers bex1,x2,...x12.We know: Mean $=\frac{\text { Sum of observations }}{\text { Number of observations }}$ Thus, we have: $40=\frac{x_{1}+x_{2}+\ldots+x_{12}}{12}$ $\Rightarrow x_{1}+x_{2}+\ldots+x_{12}=480 \quad \ldots \ldots(\mathrm{i})$ After division, the numbers become: $\frac{x_{1}}{8}, \frac{x_{2}}{8}, \ldots, \frac{x_{12}}{8}$ $\therefore$ New mean $=\fr...

The number of chiral carbons (s) present in peptide,

Question: The number of chiral carbons (s) present in peptide, IleAge-Pro, is ___________________ Solution: (4)...

If the line a x+y=c, touches both the curves

Question: If the line $a x+y=c$, touches both the curves $x^{2}+y^{2}=1$ and $y^{2}=4 \sqrt{2} x$, then $|c|$ is equal to(1) 2(2) $\frac{1}{\sqrt{2}}$(3) $\frac{1}{2}$(4) $\sqrt{2}$Correct Option: 4, Solution: Equation of tangent on $y^{2}=4 \sqrt{2} x$ is $y t=x+\sqrt{2} t^{2}$ This is also tangent on circle $\therefore\left|\frac{\sqrt{2} t^{2}}{\sqrt{1+t^{2}}}=1\right| \Rightarrow 2 t^{4}=1+t^{2} \Rightarrow t^{2}=1$ Hence, equation is $\pm y=x+\sqrt{2} \Rightarrow|\mathrm{c}|=\sqrt{2}$...

The mean of 15 numbers is 27. If each number is multiplied by 4,

Question: The mean of 15 numbers is 27. If each number is multiplied by 4, what will be the mean of the new numbers? Solution: Let the numbers bex1,x2,...x15We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Thus, we have: $27=\frac{x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}}{15}$ $\Rightarrow x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}=405 \ldots \ldots \ldots$ (i) After multiplication, the numbers become $4 x_{1}, 4 x_{2}, \ldots 4 x_{15}$ $\therefore$ New Mean $...

Which of the following is not an essential amino acid?

Question: Which of the following is not an essential amino acid?TyrosineLeucineValineLysineCorrect Option: 1 Solution: Tyrosine is a non-essential amino acid....

The line x=y touches a circle at the point

Question: The line $x=y$ touches a circle at the point $(1,1)$. If the circle also passes through the point $(1,-3)$, then its radius is:(1) 3(2) $2 \sqrt{2}$(3) 2(4) $3 \sqrt{2}$Correct Option: , 2 Solution: Equation of circle which touches the line $y=x$ at $(1,1)$ is, $(x-1)^{2}+(y-1)^{2}+\lambda(y-x)=0$ This circle passes through $(1,-3)$ $\therefore 0+16+\lambda(-3-1)=0$ $\Rightarrow 16+\lambda(-4)=0 \Rightarrow \lambda=4$ Hence, equation of circle will be, $(x-1)^{2}+(y-1)^{2}+4 y-4 x=0$ $...

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