A man with normal near point (25 cm) reads a book with small print using a magnifying glass:
Question: A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm. (a)What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass? (b)What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope? Solution: (a)Focal length of the magnifying glass,f= 5 cm Least ...
Read More →If the starting material for the manufacture of silicones is RSiCl3
Question: If the starting material for the manufacture of silicones is RSiCl3, write thestructure of the product formed. Solution: $\mathrm{RSiCl}_{3}+3 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{RSi}(\mathrm{OH})_{3}+3 \mathrm{HCl}$ ....
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: (i) $\left|\begin{array}{ccc}a-b-c 2 a 2 a \\ 2 b b-c-a 2 b \\ 2 c 2 c c-a-b\end{array}\right|=(a+b+c)^{3}$ (ii) $\left|\begin{array}{llr}x+y+2 z x y \\ z y+z+2 x y \\ z x z+x+2 y\end{array}\right|=2(x+y+z)^{3}$ Solution: (i) $\Delta=\left|\begin{array}{ccr}a-b-c 2 a 2 a \\ 2 b b-c-a 2 b \\ 2 c 2 c c-a-b\end{array}\right|$ Applying $R_{1} \rightarrow R_{1}+R_{2}+R_{3}$, we have: $\Delta=\left|\begin{array}{lll}a+b+c a+b+c a+b+c \\ 2 b b-c...
Read More →A man with normal near point (25 cm) reads a book with small print using a magnifying glass:
Question: A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm. (a)What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass? (b)What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope? Solution: (a)Focal length of the magnifying glass,f= 5 cm Least ...
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: (i) $\left|\begin{array}{lll}x+4 2 x 2 x \\ 2 x x+4 2 x \\ 2 x 2 x x+4\end{array}\right|=(5 x+4)(4-x)^{2}$ (ii) $\left|\begin{array}{lll}y+k y y \\ y y+k y \\ y y y+k\end{array}\right|=k^{2}(3 y+k)$ Solution: (i) $\Delta=\left|\begin{array}{lll}x+4 2 x 2 x \\ 2 x x+4 2 x \\ 2 x 2 x x+4\end{array}\right|$ Applying $R_{1} \rightarrow R_{1}+R_{2}+R_{3}$, we have: $\Delta=\left|\begin{array}{lll}5 x+4 5 x+4 5 x+4 \\ 2 x x+4 2 x \\ 2 x 2 x x+4...
Read More →Elements of group 14
Question: Elements of group 14 (a) exhibit oxidation state of $+4$ only (b) exhibit oxidation state of $+2$ and $+4$ (c) form $\mathrm{M}^{2-}$ and $\mathrm{M}^{4+}$ ion (d) form $\mathrm{M}^{2+}$ and $\mathrm{M}^{4+}$ ions Solution: (b) The elements of group 14 have 4 valence electrons. Therefore, the oxidation state of the group is $+4$. However, as a result of the inert pair effect, the lower oxidation state becomes more and more stable and the higher oxidation state becomes less stable. Ther...
Read More →Thermodynamically the most stable form of carbon is
Question: Thermodynamically the most stable form of carbon is (a) diamond (b) graphite (c) fullerenes (d) coal Solution: (b)Graphite is thermodynamically the most stable form of carbon....
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: $\left|\begin{array}{lll}x x^{2} y z \\ y y^{2} z x \\ z z^{2} x y\end{array}\right|=(x-y)(y-z)(z-x)(x y+y z+z x)$ Solution: Let $\Delta=\left|\begin{array}{lll}x x^{2} y z \\ y y^{2} z x \\ z z^{2} x y\end{array}\right|$. Applying $R_{2} \rightarrow R_{2}-R_{1}$ and $R_{3} \rightarrow R_{3}-R_{1}$, we have: $\begin{aligned} \Delta =\left|\begin{array}{lcc}x x^{2} y z \\ y-x y^{2}-x^{2} z x-y z \\ z-x z^{2}-x^{2} x y-y z\end{array}\right|...
Read More →The type of hybridisation of boron in diborane is
Question: The type of hybridisation of boron in diborane is (a)sp (b)sp2 (c)sp3 (d)dsp2 Solution: (c) Boron in diborane is $s p^{3}$ hybridised....
Read More →Boric acid is polymeric due to
Question: Boric acid is polymeric due to (a) its acidic nature (b) the presence of hydrogen bonds (c) its monobasic nature (d) its geometry Solution: (b)Boric acid is polymeric because of the presence of hydrogen bonds. In the given figure, the dotted lines represent hydrogen bonds....
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: (i) $\left|\begin{array}{lll}1 a a^{2} \\ 1 b b^{2} \\ 1 c c^{2}\end{array}\right|=(a-b)(b-c)(c-a)$ (ii) $\left|\begin{array}{lll}1 1 1 \\ a b c \\ a^{3} b^{3} c^{3}\end{array}\right|=(a-b)(b-c)(c-a)(a+b+c)$ Solution: (i) Let $\Delta=\left|\begin{array}{lll}1 a a^{2} \\ 1 b b^{2} \\ 1 c c^{2}\end{array}\right|$. Applying $R_{1} \rightarrow R_{1}-R_{3}$ and $R_{2} \rightarrow R_{2}-R_{3}$, we have: $\begin{aligned} \Delta =\left|\begin{arr...
Read More →An aqueous solution of borax is
Question: An aqueous solution of borax is (a) neutral (b) amphoteric (c) basic (d) acidic Solution: (c) Borax is a salt of a strong base $(\mathrm{NaOH})$ and a weak acid $\left(\mathrm{H}_{3} \mathrm{BO}_{3}\right)$. It is, therefore, basic in nature....
Read More →If the sum of n terms of an A.P. is (pn + qn2),
Question: If the sum of $n$ terms of an A.P. is $\left(p n+q n^{2}\right)$, where $p$ and $q$ are constants, find the common difference, Solution: It is known that, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ According to the given condition, $\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}]=\mathrm{pn}+\mathrm{qn}^{2}$ $\Rightarrow \frac{\mathrm{n}}{2}[2 \mathrm{a}+\mathrm{nd}-\mathrm{d}]=\mathrm{pn}+\mathrm{qn}^{2}$ $\Rightarrow \mathrm{na}+\mathrm{n}^{2} \frac{\mathrm{d}}{2}-\mathrm{n} \cdot...
Read More →Give one method for industrial preparation and one for laboratory preparation
Question: Give one method for industrial preparation and one for laboratory preparation of $\mathrm{CO}$ and $\mathrm{CO}_{2}$ each. Solution: Caron dioxide In the laboratory, CO2can be prepared by the action of dilute hydrochloric acid on calcium carbonate. The reaction involved is as follows: $\mathrm{CaCO}_{3}+2 \mathrm{HCl}_{(a q)} \longrightarrow \mathrm{CaCl}_{2(a q)}+\mathrm{CO}_{2(g)}+\mathrm{H}_{2} \mathrm{O}_{(r)}$ $\mathrm{CO}_{2}$ is commercially prepared by heating limestone. The re...
Read More →Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Question: Find the sum to $n$ terms of the A.P. whose $k^{k h}$ term is $5 k+1$. Solution: It is given that the $k^{\text {th }}$ term of the A.P. is $5 k+1$. $k^{\text {th }}$ term $=a_{k}=a+(k-1) d$ $\therefore a+(k-1) d=5 k+1$ $a+k d-d=5 k+1$ Comparing the coefficient of $k$, we obtain $d=5$ $a-d=1$ $\Rightarrow a-5=1$ $\Rightarrow a=6$ $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ $=\frac{n}{2}[2(6)+(n-1)(5)]$ $=\frac{n}{2}[12+5 n-5]$ $=\frac{n}{2}(5 n+7)$...
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: $\left|\begin{array}{ccc}-a^{2} a b a c \\ b a -b^{2} b c \\ c a c b -c^{2}\end{array}\right|=4 a^{2} b^{2} c^{2}$ Solution: $\Delta=\left|\begin{array}{ccc}-a^{2} a b a c \\ b a -b^{2} b c \\ c a c b -c^{2}\end{array}\right|$ $=a b c\left|\begin{array}{lll}-a b c \\ a -b c \\ a b -c\end{array}\right| \quad$ [Taking out factors $a, b, c$ from $\mathrm{R}_{1}, \mathrm{R}_{2}$, and $\left.\mathrm{R}_{3}\right]$ $=a^{2} b^{2} c^{2}\left|\beg...
Read More →A person looking at a person wearing a shirt with a pattern comprising vertical
Question: A person looking at a person wearing a shirt with a pattern comprising vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal ones. What is this defect due to? How is such a defect of vision corrected? Solution: In the given case, the person is able to see vertical lines more distinctly than horizontal lines. This means that the refracting system (cornea and eye-lens) of the eye is not working in the same way in different planes. This defect...
Read More →A myopic person has been using spectacles of power −1.0 dioptre for distant vision.
Question: A myopic person has been using spectacles of power 1.0 dioptre for distant vision. During old age he also needs to use separate reading glass of power + 2.0 dioptres. Explain what may have happened. Solution: The power of the spectacles used by the myopic person,P= 1.0 D Focal length of the spectacles, $f=\frac{1}{P}=\frac{1}{-1 \times 10^{-2}}=-100 \mathrm{~cm}$ Hence, the far point of the person is 100 cm. He might have a normal near point of 25 cm. When he uses the spectacles, the o...
Read More →If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Question: If the sum of a certain number of terms of the A.P. $25,22,19, \ldots$ is 116 . Find the last term Solution: Let the sum ofnterms of the given A.P. be 116. $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ Here, $a=25$ and $d=22-25=-3$ $\therefore S_{n}=\frac{n}{2}[2 \times 25+(n-1)(-3)]$ $\Rightarrow 116=\frac{n}{2}[50-3 n+3]$ $\Rightarrow 232=n(53-3 n)=53 n-3 n^{2}$ $\Rightarrow 3 n^{2}-53 n+232=0$ $\Rightarrow 3 n^{2}-24 n-29 n+232=0$ $\Rightarrow 3 n(n-8)-29(n-8)=0$ $\Rightarrow(n-8)(3 n-29)=0$ $\R...
Read More →By using properties of determinants, show that:
Question: By using properties of determinants, show that: $\left|\begin{array}{lll}0 a -b \\ -a 0 -c \\ b c 0\end{array}\right|=0$ Solution: We have, $\Delta=\left|\begin{array}{lll}0 a -b \\ -a 0 -c \\ b c 0\end{array}\right|$ Applying $\mathrm{R}_{1} \rightarrow c \mathrm{R}_{1}$, we have:] $\Delta=\frac{1}{c}\left|\begin{array}{lll}0 a c -b c \\ -a 0 -c \\ b c 0\end{array}\right|$ Applying $\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-b \mathrm{R}_{2}$, we have: $\begin{aligned} \Delta =\frac{1}...
Read More →Does short-sightedness (myopia) or long-sightedness (hypermetropia)
Question: Does short-sightedness (myopia) or long-sightedness (hypermetropia) imply necessarily that the eye has partially lost its ability of accommodation? If not, what might cause these defects of vision? Solution: A myopic or hypermetropic person can also possess the normal ability of accommodation of the eye-lens. Myopia occurs when the eye-balls get elongated from front to back. Hypermetropia occurs when the eye-balls get shortened. When the eye-lens loses its ability of accommodation, the...
Read More →For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm in front of the eye.
Question: For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm in front of the eye. The cornea of the eye provides a converging power of about 40 dioptres, and the least converging power of the eye-lens behind the cornea is about 20 dioptres. From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye-lens) of a normal eye. Solution: Least distance of distinct vision,d= 25 cm Far point of a normal eye, $d^...
Read More →Write balanced equations for:
Question: Write balanced equations for: (i) $\mathrm{BF}_{3}+\mathrm{LiH} \rightarrow$ (ii) $\mathrm{B}_{2} \mathrm{H}_{6}+\mathrm{H}_{2} \mathrm{O} \rightarrow$ (iii) $\mathrm{NaH}+\mathrm{B}_{2} \mathrm{H}_{6} \rightarrow$ (iv) $\mathrm{H}_{3} \mathrm{BO}_{3} \stackrel{\Delta}{\longrightarrow}$ (v) $\mathrm{Al}+\mathrm{NaOH} \rightarrow$ (vi) $\mathrm{B}_{2} \mathrm{H}_{6}+\mathrm{NH}_{3} \rightarrow$ Solution:...
Read More →In an A.P., if pth term is and qth term is , prove that the sum of first pq terms is
Question: In an A.P., if $p^{\text {th }}$ term is $\frac{1}{q}$ and $q^{\text {th }}$ term is $\frac{1}{p}$, prove that the sum of first $p q$ terms is $\frac{1}{2}(p q+1)$ where $p \neq q$. Solution: It is known that the general term of an A.P. isan=a+ (n 1)d According to the given information, $p^{\text {th }}$ term $=a_{p}=a+(p-1) d=\frac{1}{q}$$\ldots(1)$ $q^{\text {th }}$ term $=a_{q}=a+(q-1) d=\frac{1}{p}$ $\ldots(2)$ Subtracting (2) from (1), we obtain $(p-1) d-(q-1) d=\frac{1}{q}-\frac{...
Read More →You are given prisms made of crown glass and flint glass with a wide variety of angles.
Question: You are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms which will (a)deviate a pencil of white light without much dispersion, (b)disperse (and displace) a pencil of white light without much deviation. Solution: (a)Place the two prisms beside each other. Make sure that their bases are on the opposite sides of the incident white light, with their faces touching each other. When the white light is incident on the first prism...
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