If the line y=m x+7
Question: If the line $y=m x+7 \sqrt{3}$ is normal to the hyperbola $\frac{x^{2}}{24}-\frac{y^{2}}{18}=1$, then a value of $\mathrm{m}$ is :(1) $\frac{\sqrt{5}}{2}$(2) $\frac{\sqrt{15}}{2}$(3) $\frac{2}{\sqrt{5}}$(4) $\frac{3}{\sqrt{5}}$Correct Option: , 3 Solution: Since, $1 \mathrm{x}+\mathrm{my}+\mathrm{n}=0$ is a normal to $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, then $\frac{a^{2}}{l^{2}}-\frac{b^{2}}{m^{2}}=\frac{\left(a^{2}+b^{2}\right)^{2}}{n^{2}}$ but it is given that $m x-y+7 \sqrt{...
Read More →The following molecule acts as an :
Question: The following molecule acts as an : AntisepticAnti-depressantAnti-bacterialAnti-histamineCorrect Option: , 4 Solution: Synthetic drugs, brompheniramine (dimetapp) acts as antihistamines....
Read More →If the magnetic field of a plane electromagnetic wave is given by
Question: If the magnetic field of a plane electromagnetic wave is given by (The speed of light $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ) $\mathrm{B}=100 \times 10^{-6} \sin \left[2 \pi \times 2 \times 10^{15}\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right)\right]$ then the maximum electric field associated with it is: (1) $6 \times 10^{4} \mathrm{~N} / \mathrm{C}$(2) $3 \times 10^{4} \mathrm{~N} / \mathrm{C}$(3) $4 \times 10^{4} \mathrm{~N} / \mathrm{C}$(4) $4.510^{4} \mathrm{~N} / \mathrm{C}$C...
Read More →If the eccentricity of the standard hyperbola passing
Question: If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is 2 , then the equation of the tangent to the hyperbola at $(4,6)$ is :(1) $x-2 y+8=0$(2) $2 x-3 y+10=0$(3) $2 x-y-2=0$(4) $3 x-2 y=0$Correct Option: , 3 Solution: Let equation of hyperbola be $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ ....(i) $\because e=\sqrt{1+\frac{b^{2}}{a^{2}}} \Rightarrow b^{2}=a^{2}\left(e^{2}-1\right)$ $e=2 \Rightarrow b^{2}=3 a^{2}$ ...(ii) Equation (i) passes through $(4,6)$, $...
Read More →If a hyperbola passes through the point
Question: If a hyperbola passes through the point $P(10,16)$ and it has vertices at $(\pm 6,0)$, then the equation of the normal to it at $P$ is:(1) $3 x+4 y=94$(2) $2 x+5 y=100$(3) $x+2 y=42$(4) $x+3 y=58$Correct Option: , 2 Solution: Let the hyperbola is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ If a hyperbola passes through vertices at $(\pm 6,0)$, then $\therefore \quad a=6$ As hyperbola passes through the point $P(10,16)$ $\therefore \quad \frac{100}{36}-\frac{256}{b^{2}}=1 \Rightarrow b^...
Read More →The energy associated with electric field
Question: The energy associated with electric field is $\left(U_{E}\right)$ and with magnetic fields is $\left(U_{B}\right)$ for an electromagnetic wave in free space. Then :(1) $\quad U_{E}=\frac{U_{B}}{2}$(2) $\mathrm{U}_{\mathrm{E}}\mathrm{U}_{\mathrm{B}}$(3) $\mathrm{U}_{\mathrm{E}}\mathrm{U}_{\mathrm{B}}$(4) $\mathrm{U}_{\mathrm{E}}=\mathrm{U}_{\mathrm{B}}$Correct Option: , 4 Solution: (4) Average energy density of magnetic field, $u_{B}=\frac{B_{0}^{2}}{4 \mu_{0}}$ Average energy density o...
Read More →If a person is suffering from the deficiency of nor-adrenaline,
Question: If a person is suffering from the deficiency of nor-adrenaline, what kind of drug can be suggested?Anti-inflammatoryAntidepressantAntihistamineAnalgesicCorrect Option: , 2 Solution: If the level of noradrenaline is low, then the person suffers from depression. In such situations, antidepressant drugs are required....
Read More →The mechanism of action of "Terfenadine" (Seldane) is :
Question: The mechanism of action of "Terfenadine" (Seldane) is :Activates the histamine receptorInhibits the secretion of histamineHelps in the secretion of histamineInhibits the action of histamine receptorCorrect Option: , 4 Solution: Seldane is an anti-histamine drug that has inhibitory action on histamine receptor....
Read More →If the line y=m x+c is a common tangent to
Question: If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$ and the circle $x^{2}+y^{2}=36$, then which one of the following is true?(1) $c^{2}=369$(2) $5 m=4$(3) $4 c^{2}=369$(4) $8 m+5=0$Correct Option: , 3 Solution: General tangent to hyperbola in slope form is $y=m x \pm \sqrt{100 m^{2}-64}$ and the general tangent to the circle in slope form is $y=m x \pm 6 \sqrt{1+m^{2}}$ For common tangent, $36\left(1+m^{2}\right)=100 m^{2}-64$ $\Rightarrow ...
Read More →Solve each of the following quadratic equations:
Question: Solve each of the following quadratic equations: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$ Solution: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$ $\Rightarrow x^{2}-\sqrt{3} x-x+\sqrt{3}=0$ $\Rightarrow x(x-\sqrt{3})-1(x-\sqrt{3})=0$ $\Rightarrow(x-\sqrt{3})(x-1)=0$ $\Rightarrow x-\sqrt{3}=0$ or $x-1=0$ $\Rightarrow x=\sqrt{3}$ or $x=1$ Hence, 1 and $\sqrt{3}$ are the roots of the given equation....
Read More →Match the following drugs with their therapeutic actions:
Question: Match the following drugs with their therapeutic actions: (i)-(A); (ii)-(C); (iii)-(B); (iv)-(E)(i)-(D); (ii)-(A); (iii)-(B); (iv)-(C)(i)-(E); (ii)-(A);(iii)-(C);(iv)-(D)(i)-(D);(ii)-(C); (iii)-(A);(iv)-(E)Correct Option: , 2 Solution:...
Read More →Solve each of the following quadratic equations:
Question: Solve each of the following quadratic equations: $x^{2}-3 \sqrt{5} x+10=0$ Solution: We write, $-3 \sqrt{5} x=-2 \sqrt{5} x-\sqrt{5} x$ as $x^{2} \times 10=10 x^{2}=(-2 \sqrt{5} x) \times(-\sqrt{5} x)$ $\therefore x^{2}-3 \sqrt{5} x+10=0$ $\Rightarrow x^{2}-2 \sqrt{5} x-\sqrt{5} x+10=0$ $\Rightarrow x(x-2 \sqrt{5})-\sqrt{5}(x-2 \sqrt{5})=0$ $\Rightarrow(x-2 \sqrt{5})(x-\sqrt{5})=0$ $\Rightarrow x-\sqrt{5}=0$ or $x-2 \sqrt{5}=0$ $\Rightarrow x=\sqrt{5}$ or $x=2 \sqrt{5}$ Hence, the root...
Read More →A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction.
Question: A plane electromagnetic wave of frequency $50 \mathrm{MHz}$ travels in free space along the positive $x$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{E}}=6.3 \hat{j} \mathrm{~V} / \mathrm{m}$. The corresponding magnetic field $\overrightarrow{\mathrm{B}}$, at that point will be:(1) $18.9 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$(2) $2.1 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$(3) $6.3 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$(4) $18.9 \times 10^{8...
Read More →Let P(3,3) be a point on the hyperbola,
Question: Let $P(3,3)$ be a point on the hyperbola, $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. If the normal to it at $P$ intersects the $x$-axis at $(9,0)$ and $e$ is its eccentricity, then the ordered pair $\left(a^{2}, e^{2}\right)$ is equal to :(1) $\left(\frac{9}{2}, 3\right)$(2) $\left(\frac{3}{2}, 2\right)$(3) $\left(\frac{9}{2}, 2\right)$(4) $(9,3)$Correct Option: 1 Solution: $\because$ The equation of hyperbola is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ $\because$ Equation of hype...
Read More →Solve each of the following quadratic equations:
Question: Solve each of the following quadratic equations: $\sqrt{3} x^{2}-2 \sqrt{2} x-2 \sqrt{3}=0$ Solution: We write, $-2 \sqrt{2} x=-3 \sqrt{2} x+\sqrt{2} x$ as $\sqrt{3} x^{2} \times(-2 \sqrt{3})=-6 x^{2}=(-3 \sqrt{2} x) \times(\sqrt{2} x)$ $\therefore \sqrt{3} x^{2}-2 \sqrt{2} x-2 \sqrt{3}=0$ $\Rightarrow \sqrt{3} x^{2}-3 \sqrt{2} x+\sqrt{2} x-2 \sqrt{3}=0$ $\Rightarrow \sqrt{3} x(x-\sqrt{6})+\sqrt{2}(x-\sqrt{6})=0$ $\Rightarrow(x-\sqrt{6})(\sqrt{3} x+\sqrt{2})=0$ $\Rightarrow x-\sqrt{6}=...
Read More →Solve each of the following quadratic equations:
Question: Solve each of the following quadratic equations: $3 x^{2}-2 \sqrt{6} x+2=0$ Solution: We write, $-2 \sqrt{6} x=-\sqrt{6} x-\sqrt{6} x$ as $3 x^{2} \times 2=6 x^{2}=(-\sqrt{6} x) \times(-\sqrt{6} x)$ $\therefore 3 x^{2}-2 \sqrt{6} x+2=0$ $\Rightarrow 3 x^{2}-\sqrt{6} x-\sqrt{6} x+2=0$ $\Rightarrow \sqrt{3} x(\sqrt{3} x-\sqrt{2})-\sqrt{2}(\sqrt{3} x-\sqrt{2})=0$ $\Rightarrow(\sqrt{3} x-\sqrt{2})(\sqrt{3} x-\sqrt{2})=0$ $\Rightarrow(\sqrt{3} x-\sqrt{2})^{2}=0$ $\Rightarrow \sqrt{3} x-\sqr...
Read More →A hyperbola having the transverse axis
Question: A hyperbola having the transverse axis of length $\sqrt{2}$ has the same foci as that of the ellipse $3 x^{2}+4 y^{2}=12$, then this hyperbola does not pass through which of the following points?(1) $\left(\frac{1}{\sqrt{2}}, 0\right)$(2) $\left(-\sqrt{\frac{3}{2}}, 1\right)$(3) $\left(1,-\frac{1}{\sqrt{2}}\right)$(4) $\left(\sqrt{\frac{3}{2}}, \frac{1}{\sqrt{2}}\right)$Correct Option: , 4 Solution: The given ellipse : $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ $\because c=\sqrt{a^{2}-b^{2}}=...
Read More →The antifertility drug "Novestrol" can react with :
Question: The antifertility drug "Novestrol" can react with :$\mathrm{ZnCl}_{2} / \mathrm{HCl} ; \mathrm{FeCl}_{3} ;$ Alcoholic $\mathrm{HCN}$$\mathrm{Br}_{2}$ / water; $\mathrm{ZnCl}_{2} / \mathrm{HCl} ; \mathrm{FeCl}_{3}$Alcoholic $\mathrm{HCN} ; \mathrm{NaOCl} ; \mathrm{ZnCl}_{2} / \mathrm{HCl}$$\mathrm{Br}_{2} /$ water; $\mathrm{ZnCl}_{2} / \mathrm{HCl} ; \mathrm{NaOCl}$Correct Option: , 4 Solution: Novestrol has phenolic, alcoholic and terminal alkyne groups, so it can react with $\mathrm{B...
Read More →Solve this
Question: $4 \sqrt{6} x^{2}-13 x-2 \sqrt{6}=0$ Solution: Given: $4 \sqrt{6} \mathrm{x}^{2}-13 \mathrm{x}-2 \sqrt{6}=0$ $\Rightarrow 4 \sqrt{6} \mathrm{x}^{2}-16 \mathrm{x}+3 \mathrm{x}-2 \sqrt{6}=0$ $\Rightarrow 4 \sqrt{2} \mathrm{x}(\sqrt{3} \mathrm{x}-2 \sqrt{2})+\sqrt{3}(\sqrt{3} \mathrm{x}-2 \sqrt{2})=0$ $\Rightarrow(4 \sqrt{2} \mathrm{x}+\sqrt{3})(\sqrt{3} \mathrm{x}-2 \sqrt{2})=0$ $\Rightarrow 4 \sqrt{2} \mathrm{x}+\sqrt{3}=0$ or $\sqrt{3} \mathrm{x}-2 \sqrt{2}=0$ $\Rightarrow \mathrm{x}=\...
Read More →If you spill a chemical toilet cleaning liquid on your hand, your first aid would be :
Question: If you spill a chemical toilet cleaning liquid on your hand, your first aid would be :vinegaraqueous $\mathrm{NaOH}$aqueous $\mathrm{NaHCO}_{3}$aqueous $\mathrm{NH}_{3}$Correct Option: , 3 Solution: In toilet cleaning liquid, the main constituent is $\mathrm{HCl}$, which can cause skin burn, so it should be treated with $\mathrm{NaHCO}_{3}$, which can easily neutralise the acid....
Read More →A line parallel to the straight line
Question: A line parallel to the straight line $2 x-y=0$ is tangent to the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{2}=1$ at the point $\left(x_{1}, y_{1}\right)$. Then $x_{1}^{2}+5 y_{1}^{2}$ is equal to :(1) 6(2) 8(3) 10(4) 5Correct Option: 1 Solution: The tangent to the hyperbola at the point $\left(x_{1}, y_{1}\right)$ is, $x x_{1}-2 y y_{1}-4=0$ The given equation of tangent is $2 x-y=0$ $\Rightarrow \frac{x_{1}}{2 y_{1}}=2$ $\Rightarrow x_{1}=4 y_{1}$ ...(i) Since, point $\left(x_{1}, y_{1}...
Read More →A plane electromagnetic wave having a frequency
Question: A plane electromagnetic wave having a frequency $v=23.9 \mathrm{GHz}$ propagates along the positive $z$-direction in free space. The peak value of the Electric Field is $60 \mathrm{~V} / \mathrm{m}$. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?(1) $\vec{B}=2 \times 10^{7} \sin \left(0.5 \times 10^{3} z+1.5 \times 10^{11} t\right) \hat{i}$(2) $\vec{B}=2 \times 10^{-7} \sin \left(0.5 \times 10^{3} z-1.5 \times 10^{11} t\right) \hat{i}...
Read More →Solve each of the following quadratic equations:
Question: Solve each of the following quadratic equations: $\sqrt{7} x^{2}-6 x-13 \sqrt{7}=0$ Solution: We write, $-6 x=7 x-13 x$ as $\sqrt{7} x^{2} \times(-13 \sqrt{7})=-91 x^{2}=7 x \times(-13 x)$ $\therefore \sqrt{7} x^{2}-6 x-13 \sqrt{7}=0$ $\Rightarrow \sqrt{7} x^{2}+7 x-13 x-13 \sqrt{7}=0$ $\Rightarrow \sqrt{7} x(x+\sqrt{7})-13(x+\sqrt{7})=0$ $\Rightarrow(x+\sqrt{7})(\sqrt{7} x-13)=0$ $\Rightarrow x+\sqrt{7}=0$ or $\sqrt{7} x-13=0$ $\Rightarrow x=-\sqrt{7}$ or $x=\frac{13}{\sqrt{7}}=\frac{...
Read More →Solve this
Question: $3 \sqrt{7} x^{2}+4 x-\sqrt{7}=0$ Solution: Given: $3 \sqrt{7} x^{2}+4 x-\sqrt{7}=0$ $\Rightarrow 3 \sqrt{7} x^{2}+7 x-3 x-\sqrt{7}=0$ $\Rightarrow \sqrt{7} x(3 x+\sqrt{7})-1(3 x+\sqrt{7})=0$ $\Rightarrow(3 x+\sqrt{7})(\sqrt{7} x-1)=0$ $\Rightarrow 3 x+\sqrt{7}=0$ or $\sqrt{7} x-1=0$ $\Rightarrow x=\frac{-\sqrt{7}}{3}$ or $x=\frac{1}{\sqrt{7}}=\frac{1 \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}}=\frac{\sqrt{7}}{7}$ Hence, the roots of the equation are $\frac{-\sqrt{7}}{3}$ and $\frac{\sq...
Read More →Match List-I with List-II
Question: Match List-I with List-II $(\mathrm{a})-(\mathrm{iv}),(\mathrm{b})-(\mathrm{iii}),(\mathrm{c})-(\mathrm{ii}),(\mathrm{d})-(\mathrm{i})$$(\mathrm{a})-(\mathrm{i}),(\mathrm{b})-(\mathrm{iii}),(\mathrm{c})-(\mathrm{i} v),(\mathrm{d})-(\mathrm{ii})$$(\mathrm{a})-(\mathrm{ii}),(\mathrm{b})-(\mathrm{iv}),(\mathrm{c})-(\mathrm{iii}),(\mathrm{d})-(\mathrm{i})$$(\mathrm{a})-(\mathrm{i} v),(\mathrm{b})-(\mathrm{iii}),(\mathrm{c})-(\mathrm{i}),(\mathrm{d})-(\mathrm{ii})$Correct Option: , 4 Soluti...
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