What are the functional groups present in the structure of maltose?
Question: What are the functional groups present in the structure of maltose?One ketal and hemiketalTwo acetalsOne acetal and one hemiacetalOne acetal and one ketalCorrect Option: , 3 Solution: One acetal and one hemi acetal group is present in maltose....
Read More →Effective capacitance of parallel combination of two capacitors
Question: Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10 \mu \mathrm{F}$. When these capacitors are individually connected to a voltage source of $1 \mathrm{~V}$, the energy stored in the capacitor $C_{2}$ is 4 times that of $C_{1}$. If these capacitors are connected in series, their effective capacitance will be:(1) $4.2 \mu \mathrm{F}$(2) $3.2 \mu \mathrm{F}$(3) $1.6 \mu \mathrm{F}$(4) $8.4 \mu \mathrm{F}$Correct Option: , 3 Solution: (3) In parallel...
Read More →The mean of 20 numbers is 43.
Question: The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers, what will be the new mean? Solution: Let the numbers be $x_{1}, x_{2}, \ldots x_{20}$. We know: Mean $=\frac{\text { Sum of observations }}{\text { Number of observations }}$ Thus, we have: $43=\frac{x_{1}+x_{2}+\ldots \ldots+x_{20}}{20}$ $\Rightarrow 860=x_{1}+x_{2}+\ldots \ldots+x_{20} \ldots \ldots$ (i) Numbers after subtraction: $\left(x_{1}-6\right),\left(x_{2}-6\right), \ldots\left(x_{20}-6\right)$ $\there...
Read More →If the circles
Question: If the circles $x^{2}+y^{2}+5 K x+2 y+K=0$ and $2\left(x^{2}+y^{2}\right)+2 K x+3 y-1=0,(K \in \mathbf{R})$, intersect at the points $P$ and $Q$, then the line $4 x+5 y-K=0$ passes through $P$ and $Q$, for :(1) infinitely many values of $\mathrm{K}$(2) no value of $\mathrm{K}$.(3) exactly two values of $\mathrm{K}$(4) exactly one value of $K$Correct Option: , 2 Solution: $\mathrm{S}_{1} \equiv x^{2}+y^{2}+5 K x+2 y+K=0$ $\mathrm{~S}_{2} \equiv x^{2}+y^{2}+K x+\frac{3}{2} y-\frac{1}{2}=...
Read More →Which of the following will react with
Question: Which of the following will react with $\mathrm{CHCl}_{3}+$ alc. $\mathrm{KOH}$ ?Adenine and prolineThymine and prolineAdenine and lysineAdenine and thymineCorrect Option: , 3 Solution: Compounds having $1^{\circ}$ amine give carbylamine reaction with $\mathrm{CHCl}_{3}$ and alc. $\mathrm{KOH}$....
Read More →A 60 p F capacitor is fully charged by a 20 v supply.
Question: A $60 p F$ capacitor is fully charged by a $20 \vee$ supply. It is then disconnected from the supply and is connected to another uncharged $60 p F$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $\mathrm{nJ}$ ) Solution: (6) In the first condition, electrostatic energy is $U_{i}=\frac{1}{2} C V_{0}^{2}=\frac{1}{2} \times 60 \times 10^{-12} \times 400=12 \times 10^{-9} \mathrm{~J}$ In the second co...
Read More →A 60 p F capacitor is fully charged by a 20 v supply.
Question: A $60 p F$ capacitor is fully charged by a $20 \vee$ supply. It is then disconnected from the supply and is connected to another uncharged $60 p F$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $\mathrm{nJ}$ ) Solution: (6) In the first condition, electrostatic energy is $U_{i}=\frac{1}{2} C V_{0}^{2}=\frac{1}{2} \times 60 \times 10^{-12} \times 400=12 \times 10^{-9} \mathrm{~J}$ In the second co...
Read More →The common tangent to the circles
Question: The common tangent to the circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}+6 x+8 y-24=0$ also passes through the point:(1) $(4,-2)$(2) $(-6,4)$(3) $(6,-2)$(4) $(-4,6)$Correct Option: , 3 Solution: By the diagram, $d_{c_{1} c_{2}}=\left|r_{1}-r_{2}\right|$ Equation of common tangent is, $\mathrm{S}_{1}-\mathrm{S}_{2}=0$ $6 x+8 y-20=0 \Rightarrow 3 x+4 y-10=0$ Hence $(6,-2)$ lies on it....
Read More →The mean of 24 numbers is 35.
Question: The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean? Solution: Let the numbers bex1,x2,...x24. We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Thus, we have: $35=\frac{x_{1}+x_{2}+\ldots \ldots \ldots+x_{24}}{24}$ $\Rightarrow 840=x_{1}+x_{2}+\ldots \ldots+x_{24} \ldots \ldots$ (i) After addition, the new numbers become $\left(x_{1}+3\right),\left(x_{2}+3\right), \ldots\left(x_{24}+3\right)$ New mean: $=\frac{\l...
Read More →If a tangent to the circle
Question: If a tangent to the circle $x^{2}+y^{2}=$ lintersects the coordinate axes at distinct points $P$ and $Q$, then the locus of the midpoint of $\mathrm{PQ}$ is:(1) $x^{2}+y^{2}-4 x^{2} y^{2}=0$(2) $x^{2}+y^{2}-2 x y=0$(3) $x^{2}+y^{2}-16 x^{2} y^{2}=0$(4) $x^{2}+y^{2}-2 x^{2} y^{2}=0$Correct Option: 1, Solution: Let any tangent to circle $x^{2}+y^{2}=1$ is $x \cos \theta+y \sin \theta=1$ Since, $P$ and $Q$ are the point of intersection on the coordinate axes. Then $P \equiv\left(\frac{1}{...
Read More →A parallel plate capacitor has plates of area A separated by distance ' d ' between them.
Question: A parallel plate capacitor has plates of area $A$ separated by distance ' $d$ ' between them. It is filled with a dielectric which has a dielectric constant that varies as $k(x)=K(1+\alpha x)$ where ' $x$ ' is the distance measured from one of the plates. If $(\alpha d)1$, the total capacitance of the system is best given by the expression: (1) $\frac{A K \in_{0}}{d}\left(1+\frac{\alpha d}{2}\right)$(2) $\frac{A \in_{0} K}{d}\left(1+\left(\frac{\alpha d}{2}\right)^{2}\right)$(3) $\frac...
Read More →The mean of the marks scored by 50 students was found to be 39
Question: The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean. Solution: Let the marks scored by 50 students bex1,x2,...x50.Mean = 39We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Thus, we have: $39=\frac{x_{1}+x_{2}+\ldots+x_{50}}{50}$ $\Rightarrow x$ $\Rightarrow x_{1}+x_{2}+\ldots+x_{50}=1950 \ldots \ldots$ (i) Also, a score of 43 was misread as 23. $\th...
Read More →The correct observation in the following reactions is :
Question: The correct observation in the following reactions is : Formation of blue colourGives no colourFormation of red colourFormation of violet colourCorrect Option: , 3 Solution: Seliwanoff reagent $\rightarrow$ [Resorcinol + Conc. HCl] It is used to distinguish aldoses and ketoses. Ketoses show red colour whereas aldoses show light pink colour with Seliwanoff Reagent....
Read More →The tangent and the normal lines
Question: The tangent and the normal lines at the point $(\sqrt{3}, 1)$ to the circle $x^{2}+y^{2}=4$ and the $x$-axis form a triangle. The area of this triangle (in square units) is :(1) $\frac{4}{\sqrt{3}}$(2) $\frac{1}{3}$(3) $\frac{2}{\sqrt{3}}$(4) $\frac{1}{\sqrt{3}}$Correct Option: , 3 Solution: Equation of tangent to circle at point $(\sqrt{3}, 1)$ is $\sqrt{3} x+y=4$ $\therefore$ coordinates of the point $\quad\left(\frac{}{\sqrt{ }}, 0\right)$ Area $=\frac{1}{2} \times O A \times P M=\f...
Read More →The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg.
Question: The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. Find the weight of the sixth boy. Solution: The individual weights of five boys are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg.Now,Let the weight of the sixth boy bexkg.We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ Also,Given mean = 48 kgThus, we have: $\Rightarrow 48=\frac{51+45+49+46+44+x}{6}$ $\Rightarrow 288=235+x$ $\Ri...
Read More →Consider the following reactions :
Question: Consider the following reactions : $5,4 \ 5$$4,6 \ 5$$4,5 \ 5$$5,6 \ 5$Correct Option: , 2 Solution:...
Read More →The sum of the squares of the lengths
Question: The sum of the squares of the lengths of the chords intercepted on the circle, $x^{2}+y^{2}=16$, by the lines, $x+y=\mathrm{n}$, $n \in N$, where $N$ is the set of all natural numbers, is :(1) 320(2) 105(3) 160(4) 210Correct Option: , 4 Solution: Let the chord $x+y=n$ cuts the circle $x^{2}+y^{2}=16$ at $P$ and $Q$ Length of perpendicular from $\mathrm{O}$ on $P Q$ $=\left|\frac{0+0-n}{\sqrt{1^{2}+1^{2}}}\right|=\frac{n}{\sqrt{2}}$ Then, length of chord $P Q=2 \sqrt{4^{2}-\left(\frac{n...
Read More →If the mean of five observations
Question: If the mean of five observationsx, x+ 2,x+ 4,x+ 6,x+ 8 is 13, find the value ofxand hence find the mean of the last three observations. Solution: We know that, Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ The first five observations arex, x+ 2,x+ 4,x+ 6 andx+ 8. Mean of these numbers $=\frac{x+(x+2)+(x+4)+(x+6)+(x+8)}{5}$ $\Rightarrow 13=\frac{5 x+20}{5}$ $\Rightarrow 13 \times 5=5 x+20$ $\Rightarrow 65=5 x+20$ $\Rightarrow 5 x=65-20$ $\Rightarrow 5 x...
Read More →For the given input voltage waveform
Question: For the given input voltage waveform $V_{\text {in }}(t)$, the output voltage waveform $\mathrm{V}_{0}(t)$, across the capacitor is correctly depicted by: (1) (2) (3) (4) Correct Option: 1, Solution: (1) When first pulse is applied, the potential across capacitor $V_{0}(t)=V_{\text {in }}\left(1-e^{\frac{1}{R C}}\right)$ At $t=5 \mu s=5 \times 10^{-6} s$ $V_{0}(t)=5\left(1-e^{\frac{5 \times 10^{-6}}{10^{3} \times 10 \times 10^{-9}}}\right)=5\left(1-e^{-0.5}\right)=2 V$ When no pulse is...
Read More →If the curves,
Question: If the curves, $x^{2}-6 x+y^{2}+8=0$ and $x^{2}-8 y+y^{2}+16-k=0$, $(k0)$ touch each other at a point, then the largest value of $k$ is______. Solution: The given equation of circle $x^{2}-6 x+y^{2}+8=0$ $(x-3)^{2}+y^{2}=1$ .........(1) So, centre of circle (1) is $C_{1}(3,0)$ and radius $r_{1}=1$. And the second equation of circle $x^{2}-8 y+y^{2}+16-k=0(k0)$ $x^{2}+(y-4)^{2}=(\sqrt{k})^{2}$........(2) So, centre of circle (2) is $C_{2}(0,4)$ and radius $r_{2}=\sqrt{k}$ Two circles to...
Read More →Seliwanoff test and Xanthoproteic test are used for the identification of
Question: Seliwanoff test and Xanthoproteic test are used for the identification of ____________and ___________ respectivelyketoses, proteinsproteins, ketosesaldoses, ketosesketoses, aldosesCorrect Option: 1 Solution: Seliwanoff test and Xanthaproteic test are used for identification of 'Ketoses' and proteins respectively....
Read More →The daily minimum temperature recorded (in degree F) at a place during a week was as under:
Question: The daily minimum temperature recorded (in degree F) at a place during a week was as under: Find the mean temperature. Solution: Daily minimum temperatures = 35.5, 30.8,27.3, 32.1, 23.8 and 29.9Thus, we have: Mean temperature $=\frac{35.5+30.8+27.3+32.1+23.8+29.9}{6}$ $=\frac{179.4}{6}$ $=29.9^{\circ} \mathrm{F}$...
Read More →Match List-I with List-II.
Question: Match List-I with List-II. Choose the correct answer from the options given below:(a) $-($ iii $),(b)-($ ii $),(c)-($ i $)$(a) $-$ (iii), (b) - (i), (c) - (ii)(a) $-$ (i), (b) - (iii), (c) - (ii)(a) $-$ (ii), (b) $-$ (i), (c) - (iii)Correct Option: , 4 Solution: Sucrose $\rightarrow \alpha-\mathrm{D}$ - Glucose and $\beta-\mathrm{D}$ - Fructose Lactose $\rightarrow \beta-\mathrm{D}$ - Galactose and $\beta-\mathrm{D}$ - Glucose Maltose $\rightarrow \alpha-D-$ Glucose and $\alpha-D-$ Glu...
Read More →The following are the number of books issued in a school library during a week:
Question: The following are the number of books issued in a school library during a week:105, 216, 322, 167, 273, 405 and 346.Find the average number of books issued per day. Solution: Numbers of books issued in the school library: 105, 216, 322, 167, 273, 405 and 346Thus, we have: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ $=\frac{105+216+322+167+273+405+346}{7}$ $=\frac{346}{7}$ $=262$...
Read More →