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

A circle cuts a chord of length 4 a on the

Question: A circle cuts a chord of length 4 a on the $x$-axis and passes through a point on the $y$-axis, distant $2 \mathrm{~b}$ from the origin. Then the locus of the centre of this circle, is :(1) a hyperbola(2) an ellipse(3) a straight line(4) a parabolaCorrect Option: , 4 Solution: Let centre be $C(h, k)$ $C Q=C P=r$ $\Rightarrow \quad C Q^{2}=C P^{2}$ $(h-0)^{2}+(k \pm 0)^{2}=C M^{2}+M P^{2}$ $h^{2}+(k \pm 2 b)^{2}=k^{2}+4 a^{2}$ $h^{2}+k^{2}+4 b^{2} \pm 4 b k=k^{2}+4 a^{2}$ Then, the locu...

Fructose and glucose cari be distinguished by:

Question: Fructose and glucose cari be distinguished by:Benedict's testFehling's testBarfoed's testSeliwanoff's testCorrect Option: , 4 Solution: Seliwanoff's test is used to distinguish aldose and ketose sugars....

Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area A,

Question: Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area A, separated by a distance $d$. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $\mathrm{K}_{1}, \mathrm{~K}_{2}$ and $\mathrm{K}_{3}$. The first capacitors is filled as shown in Fig. I, and the second one is filled as shown in Fig. II. If these two modified capacitors are charged by the same potential V, the ratio of th...

The mean of 11 numbers is 42.

Question: The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46, find the 6th number. Solution: Mean of 11 numbers $=42$ Sum of 11 numbers $=42 \times 11=462$ Mean of the first 6 numbers $=37$ Sum of the first 6 numbers $=37 \times 6=222$ Mean of the last 6 numbers $=46$ Sum of the last 6 numbers $=46 \times 6=276$ $\therefore 6$ th number $=[($ Sum of the first 6 numbers $+$ Sum of the last 6 numbers $)-$ Sum of 11 numbers $]$ $=[(222+276)-4...

The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62,

Question: The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result. Solution: Mean of 31 results = 60 Sum of 31 results $=31 \times 60=1860$ Mean of the first 16 results $=58$ Sum of the first 16 results $=58 \times 16=928$ Mean of the last 16 results = 62 Sum of the last 16 results $=62 \times 16=992$ Value of the 16th result $=$ (Sum of the first 16 results $+$ Sum of the last 16 results) $-$ Sum of 31 results $=(928+99...

Two circles with equal radii are intersecting at the points

Question: Two circles with equal radii are intersecting at the points $(0$, 1) and $(0,-1)$. The tangent at the point $(0,1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :(1) 1(2) 2(3) $2 \sqrt{2}$(4) $\sqrt{2}$Correct Option: , 2 Solution: $\because$ Two circles of equal radii intersect each other orthogonally. Then $R$ is mid point of $P Q$. and $P R=O_{1} R=O_{2} R$ $P R=\frac{1}{2} \sqrt{(0-0)^{2}+(1+1)^{2}}=1...

The structure of Nylon-6 is:

Question: The structure of Nylon-6 is:Correct Option: , 3 Solution: Nylon-6 is prepared from caprolactam....

The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were misread as 52 and 8 instead of 152 and 88 respectively.

Question: The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were misread as 52 and 8 instead of 152 and 88 respectively. Find the correct men. Solution: Mean of 150 items = 60 Sum of 150 items $=(150 \times 60)=9000$ New sum $=[9000-(52+8)+(152+88)]=9180$ Correct mean $=\frac{\text { New sum }}{\text { Total items }}=\frac{9180}{150}=61.2$ Therefore, the correct mean is $61.2$....

A square is inscribed in the circle

Question: A square is inscribed in the circle $x^{2}+y^{2}-6 x+8 y-103=0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :(1) 6(2) $\sqrt{137}$(3) $\sqrt{41}$(4) 13Correct Option: , 3 Solution: The equation of circle is, $x^{2}+y^{2}-6 x+8 y-103=0$ $\Rightarrow \quad(x-3)^{2}+(y+4)^{2}=(8 \sqrt{2})^{2}$ $C(3,-4), r=8 \sqrt{2}$ $\Rightarrow \quad$ Length of side of square $=\sqrt{2} r=16$ $\Rightarrow \quad P(-5,4),...

Maltose on treatment with dilute HCI gives :

Question: Maltose on treatment with dilute $\mathrm{HCl}$ gives :D-Glucose and D-FructoseD-FructoseD-GalactoseD-GlucoseCorrect Option: , 4 Solution: Hydrolysis of maltose gives glucose as maltose is composed of two $\alpha-\mathrm{D}$ glucose units....

Figure shows charge (q) versus voltage (V) graph for series and parallel

Question: Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are : (1) $40 \mu \mathrm{F}$ and $10 \mu \mathrm{F}$(2) $60 \mu \mathrm{F}$ and $40 \mu \mathrm{F}$(3) $50 \mu \mathrm{F}$ and $30 \mu \mathrm{F}$(4) $20 \mu \mathrm{F}$ and $30 \mu \mathrm{F}$Correct Option: 1 Solution: (1) Equivalent capacitance in series combination (C') is given by $\frac{1}{\mathrm{C}},=\frac{1}{\mathrm{C}_{1}}+\frac{1}{\mathrm{C}_{2}} \R...

A, B and C are three biomolecules.

Question: A, B and C are three biomolecules. The results of the tests performed on them are given below: $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are respectively:$\mathrm{A}=$ Glucose, $\mathrm{B}=$ Fructose, $\mathrm{C}=$ Albumin$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Glucose, $\mathrm{C}=$ Albumin$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Glucose, $\mathrm{C}=$ Alanine$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Fructose, $\mathrm{C}=$ AlanineCorrect Option: , 2 Solution: Molisch's test is used to check the ...

The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3.

Question: The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded number. Solution: Mean of 8 numbers = 35 Sum of 8 numbers $=35 \times 8=280$ Let the excluded number bex.Now,New mean =35-3 = 32Thus, we have: $\frac{\text { Sum of 8 numbers- } x}{7}=32$ $\Rightarrow \frac{280-x}{7}=32$ $\Rightarrow 280-x=224$ $\Rightarrow x=56$ Therefore, the excluded number is 56....

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man.

Question: The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man. Find the weight of the new man. Solution: Let the average weight of 10 oarsmen bexkg.Sum of the weights of 10 oarsmen = 10xkg New average weight = (x+ 1.5) kgNow, we have: New average weight $=\frac{\text { Sum of the weights of initial } 10 \text { oarsmen- } 58+\text { Weight of the new man }}{10}$ $\Rightarrow x+1.5=\frac{10 x-58+\text { Weight of the new...

If the area of an equilateral triangle inscribed

Question: If the area of an equilateral triangle inscribed in the circle, $x^{2}+y^{2}+10 x+12 y+c=0$ is $27 \sqrt{3}$ sq. units then $\mathrm{c}$ is equal to:(1) 13(2) 20(3) $-25$(4) 25Correct Option: , 4 Solution: Let the sides of equilateral $\Delta$ inscribed in the circle be $a$, then $\cos 30^{\circ}=\frac{a}{2 r}$ $\frac{\sqrt{3}}{2}=\frac{a}{2 r}$ $a=\sqrt{3} r$ Then, area of the equilateral triangle $=\frac{\sqrt{3}}{4} a^{2}$ $=\frac{\sqrt{3}}{4}(\sqrt{3} r)^{2}$ $=\frac{3 \sqrt{3}}{4}...

Which polymer has 'chiral' monomer(s)?

Question: Which polymer has 'chiral' monomer(s)?NeopreneBuna- $N$Nylon 6,6PHBVCorrect Option: Solution: Both monomers of PHBV have chiral centre...

The parallel combination of two air filled parallel plate capacitors of capacitance

Question: The parallel combination of two air filled parallel plate capacitors of capacitance $\mathrm{C}$ and $n \mathrm{C}$ is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $\mathrm{K}$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is:(1) $\frac{n \mathrm{~V}}{\mathrm{~K}+n}$(2) $\mathrm{V}$(3) $\frac{\mathrm{V}}{\mathr...

The average weight of a class of 39 students is 40 kg. When a new student is admitted to the class, the average decreases by 200 g

Question: The average weight of a class of 39 students is 40 kg. When a new student is admitted to the class, the average decreases by 200 g. Find the weight of the new student. Solution: Average weight of 39 students = 40 kg Sum of the weights of 39 students $=(40 \times 39) \mathrm{kg}=1560 \mathrm{~kg}$ Decrease in the average when new student is admitted in the class = 200 g = 0.2 kg New average weight = (40-0.2) kg = 39.8 kgNow,Let the weight of the new student bexkg.Thus, we have: $\frac{\...

Preparation of Bakelite proceeds via reactions:

Question: Preparation of Bakelite proceeds via reactions:Electrophilic addition and dehydrationCondensation and eliminationElectrophilic substitution and dehydrationNucleophilic addition and dehydrationCorrect Option: , 3 Solution: Formation of Bakelite follows electrophilic substitution reaction of phenol with formaldehyde followed by dehydration....

The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g.

Question: The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g. Find the weight of the student who left. Solution: Mean weight of 36 students = 41 kg Sum of the weights of 36 students $=(41 \times 36) \mathrm{kg}=1476 \mathrm{~kg}$ Decrease in the mean when one of the students left the class = 200 g = 0.2 kgMean weight of 35 students = (41-0.2) kg = 40.8 kgNow,Let the weight of the student who left the class bexkg. Thus, ...

If a circle C passing through the point

Question: If a circle $C$ passing through the point $(4,0)$ touches the circle $x^{2}+y^{2}+4 x-6 y=12$ externally at the point $(1,-1)$, then the radius of $\mathrm{C}$ is:(1) $2 \sqrt{5}$(2) 4(3) 5(4) $\sqrt{57}$Correct Option: , 3 Solution: The equation of circle $x^{2}+y^{2}+4 x-6 y=12$ can be written as $(x+2)^{2}+(y-3)^{2}=25$ Let $P=(1,-1) \ Q=(4,0)$ Equation of tangent at $P(1,-1)$ to the given circle : $x(1)+y(-1)+2(x+1)-3(y-1)-12=0$ $3 x-4 y-7=0$$\ldots(1)$ The required circle is tange...

A capacitor with capacitance

Question: A capacitor with capacitance $5 \mu \mathrm{F}$ is charged to $5 \mu \mathrm{C}$. If the plates are pulled apart to reduce the capacitance to $2 \mu \mathrm{F}$, how much work is done?(1) $6.25 \times 10^{-6} \mathrm{~J}$(2) $\quad 3.75 \times 10^{-6} \mathrm{~J}$(3) $2.16 \times 10^{-6} \mathrm{~J}$(4) $\quad 2.55 \times 10^{-6} \mathrm{~J}$Correct Option: 2, Solution: (2) $W=U_{f}-U_{i}=\frac{q^{2}}{2}\left(\frac{1}{C_{f}}-\frac{1}{C_{i}}\right)\left(\because \mathrm{U}=\frac{\mathrm...

The mean weight of a class of 34 students is 46.5 kg.

Question: The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean is rises by 500 g. Find the weight of the teacher. Solution: Mean weight of 34 students = 46.5 kg Sum of the weights of 34 students $=(46.5 \times 34) \mathrm{kg}=1581 \mathrm{~kg}$ Increase in the mean weight when the weight of the teacher is included = 500 g = 0.5 kg New mean weight = (46.5 + 0.5) kg = 47 kgNow,Let the weight of the teacher bexkg.Thus, we have: $\frac{\text { Sum ...

Determine the charge on the capacitor in the following circuit:

Question: Determine the charge on the capacitor in the following circuit: (1) $60 \mu \mathrm{C}$(2) $2 \mu \mathrm{C}$(3) $10 \mu \mathrm{C}$(4) $200 \mu \mathrm{C}$Correct Option: , 4 Solution: (4) At steady state, there is no current in capacitor. $2 \Omega$ and $10 \Omega$ are in series. There equivalent resistance is $12 \Omega$. This $12 \Omega$ is in parallel with $4 \Omega$ and there combined resistance is $12 \times 4 /(12+4)$. This resistance is in series with $6 \Omega$. Therefore, cu...

Two monomers in maltose are:

Question: Two monomers in maltose are:$\alpha-D-g l u c o s e$ and $\beta-D-g l u c o s e$$\alpha-\mathrm{D}-\mathrm{glucose}$ and $\alpha-\mathrm{D}$-galactose$\alpha-\mathrm{D}-\mathrm{glucose}$ and $\alpha-\mathrm{D}$-fructose$\alpha-\mathrm{D}-\mathrm{glucose}$ and $\alpha-\mathrm{D}-\mathrm{glucose}$Correct Option: , 4 Solution: Maltose on hydrolysis gives two moles of $\alpha$-D-glucose....

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