Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
Question: Given below are the seats won by different political parties in the polling outcome of a state assembly elections: Draw a bar graph to represent the polling result. Solution:...
Read More →The following table shows the life expectancy (average age to which people live) in various countries in a particular year.
Question: The following table shows the life expectancy (average age to which people live) in various countries in a particular year. Represent the data by a bar graph. Solution:...
Read More →Let ABCD be a square of side of unit length.
Question: Let $\mathrm{ABCD}$ be a square of side of unit length. Let a circle $C_{1}$ centered at $A$ with unit radius is drawn. Another circle $\mathrm{C}_{2}$ which touches $\mathrm{C}_{1}$ and the lines $\mathrm{AD}$ and $\mathrm{AB}$ are tangent to it, is also drawn. Let a tangent line from the point $\mathrm{C}$ to the circle $\mathrm{C}_{2}$ meet the side $\mathrm{AB}$ at $\mathrm{E}$. If the length of $\mathrm{EB}$ is $\alpha+\sqrt{3} \beta$, where $\alpha, \beta$ areintegers, then $\alp...
Read More →The birth rate per thousand in five countries over a period of time is shown below:
Question: The birth rate per thousand in five countries over a period of time is shown below: Represent the above data by a bar graph. Solution:...
Read More →The air distances of four cities from Delhi (in km) are given below:
Question: The air distances of four cities from Delhi (in km) are given below: Draw a bar graph to represent the above data. Solution:...
Read More →Which of the following combination of statements is true
Question: Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? (a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. (b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number. (c) According to wave mechanics, the ground state angular momentum is equal to $\frac{\mathrm{h}}{2 \p...
Read More →The following table shows the number of scooters sold by a dealer during six consecutive years.
Question: The following table shows the number of scooters sold by a dealer during six consecutive years. Draw a bar graph to represent this data. Solution:...
Read More →Given below is a table which shows the yearwise strength of a school. Represent this data by a bar graph.
Question: Given below is a table which shows the yearwise strength of a school. Represent this data by a bar graph. Solution:...
Read More →An infinite number of point charges,
Question: An infinite number of point charges, each carrying $1 \mu \mathrm{C}$ charge, are placed along the $y$-axis at $y=1 \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}, 8 \mathrm{~m} \ldots \ldots \ldots \ldots \ldots$ The total force on a $1 \mathrm{C}$ point charge, placed at the origin, is $x \times 10^{3} \mathrm{~N}$. The value of $\mathrm{x}$, to the nearest integer, is $\left[\right.$ Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right]$ Solutio...
Read More →The following table shows the favourite sports of 250 students of a school. Represent the data by a bar graph.
Question: The following table shows the favourite sports of 250 students of a school. Represent the data by a bar graph. Solution:...
Read More →For emission line of atomic hydrogen from
Question: For emission line of atomic hydrogen from $n_{i}=8$ to $n_{f}=n$, the plot of wave number $(\bar{v})$ against $\left(\frac{1}{\mathrm{n}^{2}}\right)$ will be (The Rydberg constant, $R_{H}$ is in wave number uint)Linear with intercept $-\mathrm{R}_{\mathrm{H}}$Non linearLinear with slope $\mathrm{R}_{\mathrm{H}}$Linear with slope $-\mathrm{R}_{\mathrm{H}}$Correct Option: Solution: As we know, $\bar{v}=-R_{H}\left(\frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}}\right) Z^{2}($ where,$Z=1)$ After ...
Read More →The approximate velocities of some vehicles are given below:
Question: The approximate velocities of some vehicles are given below: Draw a bar graph to represent the above data. Solution: Take the name of vehicle along thex-axis and the velocity along they-axis....
Read More →On a certain day, the temperature in a city was recorded as under:
Question: On a certain day, the temperature in a city was recorded as under: Illustrate the data by a bar graph. Solution:...
Read More →The highest value of the calculated spin only magnetic moment
Question: The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is :5.926.933.874.90Correct Option: Solution: Magnetic moment, $\mu=\sqrt{n(n+2)} \mathrm{BM}$ (where, $n=$ no. of unpaired electrons) As transition metal atom/ion in a complex may have unpaired electrons ranging from zero to 5 . So, maximum number of unpaired electrons that may be present in a complex is 5 . $\therefore$ Maximum value of magnetic moment among all the transiti...
Read More →The following table shows the number of students participating in various games in a school.
Question: The following table shows the number of students participating in various games in a school. Draw a bar graph to represent the above data. Solution:...
Read More →A parallel plate capacitor has plate area
Question: A parallel plate capacitor has plate area $100 \mathrm{~m}^{2}$ and plate separation of $10 \mathrm{~m}$. The space between the plates is filled up to a thickness $5 \mathrm{~m}$ with a material of dielectric constant of 10 . The resultant capacitance of the system is 'x' pF. The value of $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{~F} \cdot \mathrm{m}^{-1}$ The value of ' $x$ ' to the nearest integer is Solution: $A=100 \mathrm{~m}^{2}$ Using $C=\frac{k \in_{0} A}{d}$ $\mathrm{C}_{1...
Read More →Among the following, the energy of
Question: Among the following, the energy of $2 \mathrm{~s}$ orbital is lowest in :KHLiNaCorrect Option: 1 Solution: As the value of $Z$ (atomic number) increases, energy of orbitals decreases (becomes more -ve value) $\therefore$ Order of energy of $2 s$ orbital is $\mathrm{H}\mathrm{Li}\mathrm{Na}\mathrm{K}$....
Read More →A ratio of the 5th term from the begining to the 5 th term from
Question: A ratio of the $5^{\text {th }}$ term from the begining to the 5 th term from the end in the binomial expansion of $\left(2^{1 / 3}+\frac{1}{2(3)^{1 / 3}}\right)^{10}$ is: (1) $1: 2(6)^{\frac{1}{3}}$(2) $1: 4(16)^{\frac{1}{3}}$(3) $4(36)^{\frac{1}{3}}: 1$(4) $2(36)^{\frac{1}{3}}: 1$Correct Option: , 2, 3 Solution: $\left(2^{\frac{1}{3}}+\frac{1}{2(3)^{\frac{1}{3}}}\right)^{10}={ }^{10} C_{0}\left(2^{\frac{1}{3}}\right)^{0}\left(\frac{1}{2(3)^{1 / 3}}\right)^{10}+$ $\cdots+{ }^{10} C_{1...
Read More →The electrons are more likely to be found:
Question: The electrons are more likely to be found: in the region $a$ and $c$in the region $a$ and $b$only in the region $a$only in the region $c$Correct Option: 1 Solution: Probability of finding an electron will have maximum value at both 'a' and 'c'. There is zero probability of finding an electron at ' $b$ '....
Read More →Let L be the lower class boundary of a class in a frequency distribution and m be the midpoint of the class.
Question: LetLbe the lower class boundary of a class in a frequency distribution andmbe the midpoint of the class. Which one of the following is the upper class boundary of the class? (a) $m+\frac{(m+L)}{2}$ (b) $L+\frac{m+L}{2}$ (c) $2 m-L$ (d) $m-2 L$ Solution: (c) 2m-L Mid value $=\frac{\text { Lower limit+Upper limit }}{2}$ $\Rightarrow m=\frac{L+U}{2}$ $\Rightarrow U=2 m-L$ $\therefore$ Upper class boundary of the class $=2 m-L$...
Read More →A 2 muF capacitor C
Question: A $2 \mu \mathrm{F}$ capacitor $\mathrm{C}_{1}$ is first charged to a potential difference of $10 \mathrm{~V}$ using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor $\mathrm{C}_{2}$ of $8 \mu \mathrm{F}$. The charge in $\mathrm{C}_{2}$ on equilibrium condition is $--\mu \mathrm{C}$. (Round off to the Nearest Integer) Solution: (16) $20=\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right) \mathrm{V} \Rightarrow \mathrm{V}=2$ volt $\mathrm{Q}_{2}=\ma...
Read More →if
Question: Let $(x+10)^{50}+(x-10)^{50}=\mathrm{a}_{0}+\mathrm{a}_{1} x+\mathrm{a}_{2} x^{2}+\ldots .+\mathrm{a}_{50} x^{50}$, for all $x \in \mathbf{R} ;$ then $\frac{\mathrm{a}_{2}}{\mathrm{a}_{0}}$ is equal to :(1) $12.50$(2) $12.00$(3) $12.25$(4) $12.75$Correct Option: , 3 Solution: $(x+10)^{50}+(x-10)^{50}$ $=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{50} x^{50}$ $\therefore \quad a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{50} x^{50}$ $=2\left({ }^{50} C_{0} x^{50}+{ }^{50} C_{2} x^{48} \cdot 10^{2}+{ }^{...
Read More →The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9.
Question: The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are :Lyman and PaschenBalmer and BrackettBrackett and PfundPaschen and PfundCorrect Option: 1 Solution: For determined shortest wavelength, $n_{2}=\infty$ Lyman series $\bar{v}_{L}=\frac{1}{\lambda_{L}}=R\left[\frac{1}{(1)^{2}}-\frac{1}{\infty^{2}}\right]$ Paschen series $\bar{v}_{P}=\frac{1}{\lambda_{P}}=R\left[\frac{1}{(3)^{2}}-\frac{1}{\infty^{2}}\right]$ $\fr...
Read More →The width of each of the five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10.
Question: The width of each of the five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is(a) 45(b) 25(c) 35(d) 40 Solution: (c) 35We have:Class width = 5Lower class limit of the lowest class = 10Now, Upper class limit of the highest class $=10+5 \times 5=35$...
Read More →Let x, y be positive real numbers and m n positive integers.
Question: Let $x, y$ be positive real numbers and $\mathrm{m}, \mathrm{n}$ positive integers. The maximum value of the expression $\frac{x^{\mathrm{m}} y^{\mathrm{n}}}{\left(1+x^{2 \mathrm{~m}}\right)\left(1+y^{2 \mathrm{n}}\right)}$ is:(1) 1(2) $\frac{1}{2}$(3) $\frac{1}{4}$(4) $\frac{\mathrm{m}+\mathrm{n}}{6 \mathrm{mn}}$Correct Option: , 3 Solution: $A=\frac{x^{m} y^{n}}{\left(1+x^{2 m}\right)\left(1+y^{2 n}\right)}=\frac{1}{\left(x^{-m}+x^{m}\right)\left(y^{-n}+y^{n}\right)}$ $\frac{x^{m}+y^...
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