The number of planks of dimensions (4 m × 5 m × 2 m) that can be stored in a pit which is 40 m long,
Question: The number of planks of dimensions (4 m 5 m 2 m) that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep, is(a) 190(b) 192(c) 184(d) 180 Solution: (b) 192 Number of planks $=\frac{\text { volume of the pit }}{\text { volume of } 1 \text { plank }}$ $=\frac{40 \times 12 \times 16}{4 \times 5 \times 2}$ $=\frac{7680}{40}$ $=192$...
Read More →The area (in sq. units) of the region
Question: The area (in sq. units) of the region $A=\left\{(x, y): x^{2} \leq y \leq x+2\right\}$ is:(1) $\frac{10}{3}$(2) $\frac{9}{2}$(3) $\frac{31}{6}$(4) $\frac{13}{6}$Correct Option: , 2 Solution: Required area is equal to the area under the curves $y \geq x^{2}$ and $yx+2$ $\therefore$ requried area $\int_{-1}^{2}\left((x+2)-x^{2}\right) d x$ $=\left(\frac{x^{2}}{2}+2 x-\frac{x^{3}}{3}\right)_{-1}^{2}$ $=\left(2+4-\frac{8}{3}\right)-\left(+\frac{1}{2}-2+\frac{1}{3}\right)=\frac{9}{2}$...
Read More →When photon of energy 4.0 eV strikes the surface of a metal A,
Question: When photon of energy $4.0 \mathrm{eV}$ strikes the surface of a metal $A$, the ejected photoelectrons have maximum kinetic energy $T_{A} \mathrm{eV}$ and de-Broglie wavelength $\lambda_{A}$. The maximum kinetic energy of photoelectrons liberated from another metal $B$ by photon of energy $4.50 \mathrm{eV}$ is $T_{B}=\left(T_{A}-1.5\right) \mathrm{eV}$. If the de-Broglie wavelength of these photoelectrons $\lambda_{B}=2 \lambda_{A}$, then the work function of metal B is:(1) $4 \mathrm{...
Read More →What is the maximum length of a pencil that can be placed in a rectangular box of dimensions
Question: What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm 6 cm 5 cm)?(a) 8 cm(b) 9.5 cm(c) 19 cm(d) 11.2 cm Solution: (d) 11.2 cmMaximum length of the pencil = diagonal of the box $=\sqrt{l^{2}+b^{2}+h^{2}}$ $=\sqrt{8^{2}+6^{2}+5^{2}} \mathrm{~cm}$ $=\sqrt{64+36+25} \mathrm{~cm}$ $=\sqrt{125} \mathrm{~cm}$ $=11.2 \mathrm{~cm}$...
Read More →Let s(alpha)
Question: Let $\mathrm{S}(\alpha)=\left\{(x, y): y^{2} \leq x, 0 \leq x \leq \alpha\right\}$ and $\mathrm{A}(\alpha)$ is area of the region $S(\alpha)$. If for $a \lambda, 0\lambda4, A(\lambda): A(4)=2: 5$, then $\lambda$ equals : (1) $2\left(\frac{4}{25}\right)^{\frac{1}{3}}$(2) $2\left(\frac{2}{5}\right)^{\frac{1}{3}}$(3) $4\left(\frac{2}{5}\right)^{\frac{1}{3}}$(4) $4\left(\frac{4}{25}\right)^{\frac{1}{3}}$Correct Option: , 4 Solution: Area of the region $=2 \times \int_{0}^{\lambda} y d x=2 ...
Read More →The length of the longest rod that can be placed in a room of dimensions
Question: The length of the longest rod that can be placed in a room of dimensions (10 m 10 m 5 m) is(a) 15 m(b) 16 m (c) $10 \sqrt{5} \mathrm{~m}$ (d) 12 m Solution: (a) 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid $=\sqrt{l^{2}+b^{2}+h^{2}}$ $=\sqrt{100+100+25} \mathrm{~m}$ $=\sqrt{225} \mathrm{~m}$ $=15 \mathrm{~m}$...
Read More →The major product of the following reaction is:
Question: The major product of the following reaction is: Correct Option: 1 Solution:...
Read More →An electron of mass m and a photon have the same energy E in the range of a few eV.
Question: An electron (of mass $m$ ) and a photon have the same energy $E$ in the range of a few $\mathrm{eV}$. The ratio of the deBroglie wavelength associated with the electron and the wavelength of the photon is $(c=$ speed of light in vacuum $)$\text { (1) } \frac{1}{c}\left(\frac{2 E}{m}\right)^{1 / 2}(2) $c(2 m E)^{1 / 2}$(3) $\frac{1}{c}\left(\frac{E}{2 m}\right)^{1 / 2}$(4) $\left(\frac{E}{2 m}\right)^{1 / 2}$Correct Option: , 3 Solution: (3) De-Broglie wavelength of electron $\left(\lam...
Read More →The area (in sq. units) of the region
Question: The area (in sq. units) of the region $\mathrm{A}=\left\{(x, y) \in \mathrm{R} \times \mathrm{R} \mid 0 \leq x \leq 3,0 \leq y \leq 4, y \leq x^{2}+3 x\right\}$ is :(1) $\frac{53}{6}$(2) 8(3) $\frac{59}{6}$(4) $\frac{26}{3}$Correct Option: , 3 Solution: Since, the relation $y \leq x^{2}+3 x$ represents the region below the parabola in the $1^{\text {st }}$ quadrant $\because y=4$ $\Rightarrow x^{2}+3 x=4 \Rightarrow x=1,-4$ $\therefore$ the required area $=$ area of shaded region $=\in...
Read More →A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre
Question: A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is(a) 27 kg(b) 48 kg(c) 36 kg(d) 56 kg Solution: (c) 36 kgLength = 9 mBreadth = 40 cm = 0.4 mHeight = 20 cm = 0.2 m $\therefore$ Weight of the beam = volume of the beam $\times$ weight of iron per cubic metre $=9 \times 0.4 \times 0.2 \times 50$ $=36 \mathrm{~kg}$...
Read More →The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively.
Question: The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is(a) 45 m2(b) 21 m2(c) 201 m2(d) 90 m2 Solution: Length of the cuboid,l= 15 mBreadth of the cuboid,b= 6 mHeight of the cuboid,h= 5 dm = 0.5 m (1 m = 10 dm) Lateral surface area of the cuboid = 2h(l+b) = 2 0.5 (15 + 6) = 20.5 21 = 21 cm2Hence, the correct answer is option (b)....
Read More →Given f(x) =
Question: Given: $f(x)=\left\{\begin{array}{cc}x , 0 \leq x\frac{1}{2} \\ \frac{1}{2} , \quad x=\frac{1}{2} \\ 1-x , \quad \frac{1}{2}x \leq 1\end{array}\right.$ and $g(x)=\left(x-\frac{1}{2}\right)^{2}, x \in \mathrm{R}$. Then the area (in sq. units) of the region bounded by the curves, $y=f(x)$ and $y=g(x)$ between the lines, $2 x=1$ and $2 x=\sqrt{3}$, is :(1) $\frac{1}{3}+\frac{\sqrt{3}}{4}$(2) $\frac{\sqrt{3}}{4}-\frac{1}{3}$(3) $\frac{1}{2}-\frac{\sqrt{3}}{4}$(4) $\frac{1}{2}+\frac{\sqrt{3...
Read More →The increasing order of reactivity of the following
Question: The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is: $\mathrm{D}\mathrm{A}\mathrm{C}\mathrm{B}$$\mathrm{B}\mathrm{C}\mathrm{A}\mathrm{D}$$ABCD$$DBAC$Correct Option: 1 Solution:...
Read More →A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is
Question: A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is(a) 864 cm2(b) 552 cm2(c) 432 cm2(d) 276 cm2 Solution: (b) $552 \mathrm{~cm}^{2}$ Total surface area of the cuboid $=2(l b+b h+l h) \mathrm{cm}^{2}$ $=2(12 \times 9+8 \times 9+12 \times 8) \mathrm{cm}^{2}$ $=2(108+72+96) \mathrm{cm}^{2}$ $=552 \mathrm{~cm}^{2}$...
Read More →The length, breadth and height of a cuboid are 15 cm,
Question: The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is(a) 243 cm3(b) 405 cm3(c) 810 cm3(d) 603 cm3 Solution: (c) 810 cm3 Volume of the cuboid $=l \times b \times h$ $=15 \times 12 \times 4.5 \mathrm{~cm}^{3}$ $=810 \mathrm{~cm}^{3}$...
Read More →The area (in sq. units) of the region
Question: The area (in sq. units) of the region $\left\{(x, y) \in R^{2}: x^{2} \leq y \leq|3-2 x|\right.$, is:(1) $\frac{32}{3}$(2) $\frac{34}{3}$(3) $\frac{29}{3}$(4) $\frac{31}{3}$Correct Option: 1 Solution: Point of intersection of $y=x^{2}$ and $y=-2 x+3$ is obtained by $x^{2}+2 x-3=0$ $\Rightarrow \quad x=-3,1$ So, required area $=\int_{-3}^{1}($ line $-$ parabola $) d z$ $=\int_{-2}^{1}\left(3-2 x-x^{2}\right) d x$ $=\left[3 x-x^{2}-\frac{x^{3}}{3}\right]_{-3}^{1}$ $=(3) 4-2\left(\frac{1^...
Read More →Solve this
Question: Note Take $\pi=\frac{22}{7}$, unless stated otherwise. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere? Solution: Let the radius of the solid hemisphere berunits. Numerical value of surface area of the solid hemisphere $=3 \pi r^{2}$ Numercial value of volume of the solid hemisphere $=\frac{2}{3} \pi r^{3}$ It is given that the volume and surface area of the solid hemisphere are numerically equal. $\therefore \frac{2}{3} \pi r...
Read More →A beam of electromagnetic radiation of intensity
Question: A beam of electromagnetic radiation of intensity $6.4 \times 10^{-5} \mathrm{~W} / \mathrm{cm}^{2}$ is comprised of wavelength, $\lambda=310 \mathrm{~nm}$. It falls normally on a metal (work function $\varphi=2 \mathrm{eV}$ ) of surface area of $1 \mathrm{~cm}^{2}$. If one in $10^{3}$ photons ejects an electron, total number of electrons ejected in $1 \mathrm{~s}$ is $10^{x} .\left(h c=1240 \mathrm{eVnm}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right)$, then $x$ is Solution: (11....
Read More →Polysubstitution is a major drawback in :
Question: Polysubstitution is a major drawback in :Friedel Craft's alkylationReimer Tiemann reactionAcetylation of anilineFriedel Craft's acylationCorrect Option: 1 Solution: Polysubstitution is a major drawback in Friedel Craft's alkylation because the introduced alkyl group is activating and gives polyalkylated product....
Read More →Polysubstitution is a major drawback in :
Question: Polysubstitution is a major drawback in :Friedel Craft's alkylation Reimer Tiemann reactionAcetylation of anilineFriedel Craft's acylationCorrect Option: 1 Solution: Polysubstitution is a major drawback in Friedel Craft's alkylation because the introduced alkyl group is activating and gives polyalkylated product....
Read More →Solve this
Question: Note Take $\pi=\frac{22}{7}$, unless stated otherwise. The diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon? Solution: Let the radius of the moon and earth berunits andRunits, respectively. $\therefore 2 r=\frac{1}{4} \times 2 R$ $\Rightarrow r=\frac{R}{4}$ ........(1) $\therefore \frac{\text { Volume of the moon }}{\text { Volume of the earth }}=\frac{\frac{4}{3} \pi r^{3}}{\frac{4}{3} \pi...
Read More →The area (in sq. units) of the region
Question: The area (in sq. units) of the region $\left\{(x, y) \in R^{2} \mid 4 x^{2} \leq y \leq 8 x+12\right\}$ is:(1) $\frac{125}{3}$(2) $\frac{128}{3}$(3) $\frac{124}{3}$(4) $\frac{127}{3}$Correct Option: , 2 Solution: Given curves are $4 x^{2}=y$ $y=8 x+12$ From eqns. (i) and (ii), $4 x^{2}=8 x+12$ $\Rightarrow x^{2}-x-3=0$ $\Rightarrow x^{2}-2 x-3=0$ $\Rightarrow x^{2}-3 x+x-3=0$ $\Rightarrow(x+1)(x-3)=0$ $\Rightarrow x=-1,3$ Required area bounded by curves is given by $A=\int_{-1}^{3}\lef...
Read More →The major product of the following reaction is:
Question: The major product of the following reaction is: Correct Option: , 4 Solution:...
Read More →Solve this
Question: Note Take $\pi=\frac{22}{7}$, unless stated otherwise. A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of₹ 32 per 100 cm2. Solution: Inner radius of the bowl, $r=\frac{10.5}{2}=5.25 \mathrm{~cm}$ $\therefore$ Inner curved surface area of the bowl $=2 \pi r^{2}=2 \times \frac{22}{7} \times(5.25)^{2}=173.25 \mathrm{~cm}^{2}$ Rate of tin-plating $=₹ 32$ per $100 \mathrm{~cm}^{2}$ Cost of tin-plating the bowl on the i...
Read More →The time period of revolution of electron in its ground state orbit in a hydrogen atom
Question: The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \mathrm{~s}$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$ ) is:(1) $1.6 \times 10^{14}$(2) $7.8 \times 10^{14}$(3) $6.2 \times 10^{15}$(4) $5.6 \times 10^{12}$Correct Option: 2, Solution: (2) For first excited state $n^{\prime}=3$ Time period $T \propto \frac{n^{3}}{z^{2}}$ $\Rightarrow \frac{T_{2}}{T_{1}}=\frac{n^{\prime 3}}{n^{3}}$ $\t...
Read More →