The correct structure of product 'P' in the following reaction is:
Question: The correct structure of product 'P' in the following reaction is: Correct Option: , 2 Solution:...
Read More →Let a complex number be
Question: Let a complex number be $w=1-\sqrt{3} i$. Let another complex number $\mathrm{z}$ be such that $|z w|=1$ and $\arg (z)-\arg (w)=\frac{\pi}{2}$. Then the area of the triangle with vertices origin, $\mathrm{z}$ and $\mathrm{w}$ is equal to: (1) 4(2) $\frac{1}{2}$(3) $\frac{1}{4}$(4) 2Correct Option: , 2 Solution: $\mathrm{w}=1-\sqrt{3} \cdot i \Rightarrow \mid \mathrm{wl}=2$ Now, $|z|=\frac{1}{|w|} \Rightarrow|z|=\frac{1}{2}$ and $\operatorname{amp}(\mathrm{z})=\frac{\pi}{2}+\mathrm{amp}...
Read More →Let z1, z2 be the roots of the equation
Question: Let $z_{1}, z_{2}$ be the roots of the equation $z^{2}+a z+12=0$ and $\mathrm{z}_{1}, \mathrm{z}_{2}$ form an equilateral triangle with origin. Then, the value of lal is Solution: If $0, \mathrm{z}, \mathrm{z}_{2}$ are vertices of equilateral triangles $\Rightarrow a^{2}+z_{1}^{2}+z_{2}^{2}=0\left(z_{1}+z_{2}\right)+z_{1} z_{2}$ $\Rightarrow\left(z_{1}+z_{2}\right)^{2}=3 z_{1} z_{2}$ $\Rightarrow a^{2}=3 \times 12$ $\Rightarrow|a|=6$...
Read More →The correct sequence of amino acids present in the tripeptide given below is:
Question: The correct sequence of amino acids present in the tripeptide given below is: Val - Ser - ThrThr - Ser - ValLeu - Ser - ValThr - Ser - LeuCorrect Option: 1 Solution:...
Read More →If the equation
Question: If the equation $\mathrm{a}|\mathrm{z}|^{2}+\overline{\bar{\alpha}_{\mathrm{Z}}+\alpha \overline{\mathrm{z}}}+\mathrm{d}=0$ represents a circle where $\mathrm{a}, \mathrm{d}$ are real constants then which of the following condition is correct?(1) $|\alpha|^{2}-\operatorname{ad} \neq 0$(2) $|\alpha|^{2}-a d0$ and $a \in R-\{0\}$(3) $|\alpha|^{2}-a d \geq 0$ and $a \in R$(4) $\alpha=0, \mathrm{a}, \mathrm{d} \in \mathrm{R}^{+}$Correct Option: , 2 Solution: $\mathrm{az} \overline{\mathrm{...
Read More →Seven capacitors, each of capacitance
Question: Seven capacitors, each of capacitance $2 \mu \mathrm{F}$, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right) \mu \mathrm{F}$. Which of the combinations, shown in figures below, will achieve the desired value?(3) (4) Correct Option: , 2 Solution: (2) As required equivalent capacitance should bo $\mathrm{C}_{e q}=\frac{6}{13} \mu \mathrm{F}$ Therefore three capacitors must be in parallel and 4 must be in series with it. $\frac{1}{C_{\i...
Read More →Find the mean of daily wages of 40 workers in a factory as per data given below:
Question: Find the mean of daily wages of 40 workers in a factory as per data given below: Solution: We know that, Mean $=\frac{\sum x_{i} f_{i}}{\sum f_{i}}$ For the following data: Mean $=\frac{(250 \times 8)+(300 \times 11)+(350 \times 6)+(400 \times 10)+(450 \times 5)}{8+11+6+10+5}$ $=\frac{2000+3300+2100+4000+2250}{40}$ $=\frac{13650}{40}$ $=341.25$ Hence, the mean of daily wages of 40 workers in a factory is 341.25 ....
Read More →The increasing order of pKa of the following amino acids in aqueous solution is:
Question: The increasing order of pKa of the following amino acids in aqueous solution is: Gly Asp Lys ArgAsp $$ Gly $$ Arg $$ LysGly $$ Asp $$ Arg $$ LysAsp $$ Gly $$ Lys $$ ArgArg $$ Lys $$ Gly $$ AspCorrect Option: Solution: Structure of the given $\alpha$-amino acids are: Here, aspartic acid is an acidic and glycine is a neutral amino acid while lysine and arginine are basic amino acids. Also, arginine is more basic due to the stronger basic functional groups. $\therefore$ The order of $p K ...
Read More →Let S1, S2 and S3 be three sets defined as
Question: Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as $\mathrm{S}_{1}=\{\mathrm{z} \in \mathbb{C}:|\mathrm{z}-1| \leq \sqrt{2}\}$ $\mathrm{S}_{2}=\{\mathrm{z} \in \mathbb{C}: \operatorname{Re}((1-\mathrm{i}) \mathrm{z}) \geq 1\}$ $\mathrm{S}_{3}=\{\mathrm{z} \in \mathbb{C}: \operatorname{Im}(\mathrm{z}) \leq 1\}$ Then the set $S_{1} \cap S_{2} \cap S_{3}$ (1) is a singleton(2) has exactly two elements(3) has infinitely many elements(4) has exactly three elementsCorrect Option: , 3 So...
Read More →Find the mean of the following frequency distribution:
Question: Find the mean of the following frequency distribution: Solution: We will make the following table: Thus, we have: Mean $=\frac{\sum f_{i} x_{i}}{\sum x_{i}}$ $=\frac{2750}{50}=55$...
Read More →The following data give the number of boys of a particular age in a class of 40 students.
Question: The following data give the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students. Solution: We will make the following table: Thus, we have: Mean $=\frac{\sum f_{i} x_{i}}{\sum x_{i}}$ $=\frac{698}{40}=17.45$ years...
Read More →Major product of the following reaction is:
Question: Major product of the following reaction is: Correct Option: , 4 Solution: Mechanism for the formation of major product is as follows:...
Read More →The area of the triangle with vertices
Question: The area of the triangle with vertices $\mathrm{A}(\mathrm{z}), \mathrm{B}(\mathrm{iz})$ and $\mathrm{C}(\mathrm{z}+\mathrm{iz})$ is :(1) 1(2) $\frac{1}{2}|z|^{2}$(3) $\frac{1}{2}$(4) $\frac{1}{2}|\mathrm{z}+\mathrm{iz}|^{2}$Correct Option: , 3 Solution: $A=\frac{1}{2}|z||i z|$ $=\frac{|z|^{2}}{2}$...
Read More →The measurements (in mm) of the diameters of the heads of 50 screws are given below:
Question: The measurements (in mm) of the diameters of the heads of 50 screws are given below: Calculate the mean diameter of the heads of the screws. Solution: We know that, Mean $=\frac{\sum x_{i} f_{i}}{\sum f_{i}}$ For the following data: Mean $=\frac{(34 \times 5)+(37 \times 10)+(40 \times 17)+(43 \times 12)+(46 \times 6)}{5+10+17+12+6}$ $=\frac{170+370+680+516+276}{50}$ $=\frac{2012}{50}$ $=40.24$ Hence, the mean diameter of the heads of the screws is 40.24 ....
Read More →The least value of |z| where z
Question: The least value of $|z|$ where $z$ is complex number which satisfies the inequality $\exp \left(\frac{(|z|+3)(|z|-1)}{|| z|+1|} \log _{e} 2\right) \geq \log _{\sqrt{2}}|5 \sqrt{7}+9 i|$ $\mathrm{i}=\sqrt{-1}$, is equal to :(1) 3(2) $\sqrt{5}$(3) 2(4) 8Correct Option: 1 Solution: $\exp \left(\frac{(|z|+3)(|z|-1)}{|| z|+1|} \ln 2\right) \geq \log _{\sqrt{2}}|5 \sqrt{7}+9 i|$ $\Rightarrow 2^{\frac{(|z|+3)||||-1)}{(|z|+1)} \geq \log _{\sqrt{2}}(16)}$ $\Rightarrow 2^{\frac{(|z|+3)(|| \mid-1...
Read More →The following table shows the weights of 12 workers in a factory:
Question: The following table shows the weights of 12 workers in a factory: Find the mean weight of the workers. Solution: We will make the following table: Thus, we have: Mean $=\frac{\sum f_{i} x_{i}}{\sum x_{i}}$ $=\frac{771}{12}=64.25 \mathrm{~kg}$...
Read More →Correct statements among a to d regarding silicones are:
Question: Correct statements among a to d regarding silicones are: (a) They are polymers with hydrophobic character. (b) They are biocompatible. (c) In general, they have high thermal stability and low dielectric strength. (d) Usually, they are resistant to oxidation and used as greases.(a), (b), (c) and (d)(a), (b) and (c) only(a) and (b) only(a), (b) and (d) onlyCorrect Option: , 4 Solution: Silicones are polymers containing $\mathrm{Si}-\mathrm{O}-$ Si linkages with strong hydrophobic charact...
Read More →Obtain the mean of the following distribution:
Question: Obtain the mean of the following distribution: Solution: We know that, Mean $=\frac{\sum x_{i} f_{i}}{\sum f_{i}}$ For the following data: Mean $=\frac{(4 \times 4)+(6 \times 8)+(8 \times 14)+(10 \times 11)+(12 \times 3)}{4+8+14+11+3}$ $=\frac{16+48+112+110+36}{40}$ $=\frac{322}{40}$ $=8.05$ Hence, the mean of the following distribution is 8.05 ....
Read More →The correct name of the following polymer is:
Question: The correct name of the following polymer is: PolyisobutanePolytert-butylenePolyisoprenePolyisobutyleneCorrect Option: , 4 Solution:...
Read More →The average monthly salary of 20 workers in an office is ₹ 45900. If the manager's salary is added, the average salary becomes ₹ 49200 per month.
Question: The average monthly salary of 20 workers in an office is ₹ 45900. If the manager's salary is added, the average salary becomes ₹ 49200 per month. What's manager's monthly salary? Solution: Average monthly salary of 20 workers = Rs 45900 Sum of the monthly salaries of 20 workers $=\operatorname{Rs}(45900 \times 20)=$ Rs 918000 By adding the manager's monthly salary, we get:Average salary = Rs 49200Now,Let the manager's monthly salary be Rsx.Thus, we have: $\frac{\text { Sum of the month...
Read More →Let z and w be two complex numbers such that
Question: Let $z$ and $w$ be two complex numbers such that $\mathrm{w}=\mathrm{z} \overline{\mathrm{z}}-2 \mathrm{z}+2,\left|\frac{\mathrm{z}+\mathrm{i}}{\mathrm{z}-3 \mathrm{i}}\right|=1 \quad$ and $\quad \operatorname{Re}(\mathrm{w})$ has minimum value. Then,the minimum value of $\mathrm{n} \in \mathbb{N}$ for which $\mathrm{w}^{\mathrm{n}}$ is real, is equal to_____________. Solution: $\omega=z \bar{z}-2 z+2$ $\left|\frac{z+i}{z-3 i}\right|=1$ $\Rightarrow \quad|z+i|=|z-3 i|$ $\Rightarrow \qu...
Read More →Which of the given statements is INCORRECT
Question: Which of the given statements is INCORRECT about glycogen?It is a straight chain polymer similar to amylose.Only $\alpha$-linkages are present in the molecule.It is present in animal cells.It is present in some yeast and fungi.Correct Option: 1 Solution: Structure of glycogen is similar to amylopectin. It is found in yeast and fungi and stored in animal body. It contains $\alpha$-glycosidic linkages....
Read More →Which of the given statements is INCORRECT
Question: Which of the given statements is INCORRECT about glycogen?It is a straight chain polymer similar to amylose.Only $\alpha$-linkages are present in the molecule.It is present in animal cells.It is present in some yeast and fungi.Correct Option: 1 Solution: Structure of glycogen is similar to amylopectin. It is found in yeast and fungi and stored in animal body. It contains $\alpha$-glycosidic linkages....
Read More →The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively.
Question: The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls. Solution: Let the number of girls bexand the number of boys bey. Mean marks of boys $=\frac{\text { sum of marks obtained by boys }}{\text { Total }}$ $\Rightarrow 70=\frac{\text { sum of marks obtained by boys }}{y}$ $\Rightarrow 70 y=$ sum of marks obtained by boys $\ld...
Read More →In the figure shown below,
Question: In the figure shown below, the charge on the left plate of the $10 \mu \mathrm{F}$ capacitor is $-30 \mu \mathrm{C}$. The charge on the right plate of the $6 \mu \mathrm{F}$ capacitor is : (1) $-12 \mu \mathrm{C}$(2) $+12 \mu \mathrm{C}$(3) $-18 \mu \mathrm{C}$(4) $+18 \mu \mathrm{C}$Correct Option: , 4 Solution: As given in the figure, $6 \mu \mathrm{F}$ and $4 \mu \mathrm{F}$ are in parallel. Now using charge conservation\ Charge on $6 \mu \mathrm{F}$ capacitor $=\frac{6}{6+4} \times...
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