Let a computer program generate only the digits
Question: Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$. Then the probability that ' 10 ' is followed by '01' is equal to :(1) $\frac{1}{18}$(2) $\frac{1}{3}$(3) $\frac{1}{6}$(4) $\frac{1}{9}$Correct Option: , 4 Solution: $\begin{array}{cccc}1 0 0 1 \\ \text { odd place even place } \text { odd place } \text { even p...
Read More →The ore that contains the metal in
Question: The ore that contains the metal in the form of fluoride is:cryolitemalachitemagnetitesphaleriteCorrect Option: 1 Solution:...
Read More →If the equation
Question: If the equation $x^{2}+5 k x+16=0$ has no real roots, then (a) $k\frac{8}{5}$ (b) $k\frac{-8}{5}$ (c) $\frac{-8}{5}k\frac{8}{5}$ (d) none of these Solution: (c) $\frac{-8}{5}k\frac{8}{5}$ It is given that the equation $\left(x^{2}+5 k x+16=0\right)$ has no real roots. $\therefore\left(b^{2}-4 a c\right)0$ $\Rightarrow(5 k)^{2}-4 \times 1 \times 160$ $\Rightarrow 25 k^{2}-640$ $\Rightarrow k^{2}\frac{64}{25}$ $\Rightarrow \frac{-8}{5}k\frac{8}{5}$...
Read More →The Mond process is used for the :
Question: The Mond process is used for the :purification of $\mathrm{Ni}$extraction of Mopurification of $\mathrm{Zr}$ and $\mathrm{Ti}$extraction of $\mathrm{Zn}$Correct Option: 1 Solution:...
Read More →If the roots of
Question: If the roots of $5 x^{2}-k x+1=0$ are real and distinct, then (a) $-2 \sqrt{5}k2 \sqrt{5}$ (b) $k2 \sqrt{5}$ only (c) $k-2 \sqrt{5}$ only (d) either $k2 \sqrt{5}$ or $k-2 \sqrt{5}$ Solution: (d) either $k2 \sqrt{5}$ or $k-2 \sqrt{5}$ It is given that the roots of the equation $\left(5 x^{2}-k x+1=0\right)$ are real and distinct. $\therefore\left(b^{2}-4 a c\right)0$ $\Rightarrow(-k)^{2}-4 \times 5 \times 10$ $\Rightarrow k^{2}-200$ $\Rightarrow k^{2}20$ $\Rightarrow k\sqrt{20}$ or $k-\...
Read More →Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force
Question: Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $F$ at $a$ point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu=0.4$, the maximum possible value of $100 x$ $\frac{b}{a}$ for box not to topple before moving is_______ Solution: (50) For the box to be slide $F=\mu m g=0.4 \mathrm{mg}$ For no toppling $F\left(\frac{a}{2}+b\right) \leq m g \frac{a}{2}$ $\Rightarrow 0.4 m g\left(\frac{a}{2}+b\...
Read More →With respect to an ore,
Question: With respect to an ore, Ellingham diagram helps to predict the feasibility of itsElectrolysisZone refiningVapour phase refiningThermal reductionCorrect Option: , 4 Solution: Ellingham diagram is a graph showing the temperature dependence of the stability for compounds. It is used to select reducing agent so it helps to predict feasibility of its thermal reduction....
Read More →The roots of the equation
Question: The roots of the equation $2 x^{2}-6 x+3=0$ are (a) real, unequal and rational(b) real, unequal and irrational(c) real and equal(d) imaginary Solution: (b) real, unequal and irrational $\because D=\left(b^{2}-4 a c\right)$ $=(-6)^{2}-4 \times 2 \times 3$ $=36-24$ $=12$ 12 is greater than 0 and it is not a perfect square; therefore, the roots of the equation are real, unequal and irrational....
Read More →According to the following diagram,
Question: According to the following diagram, $\mathrm{A}$ reduces $\mathrm{BO}_{2}$ when the temperature is: $1400^{\circ} \mathrm{C}$$1400^{\circ} \mathrm{C}$$1200^{\circ} \mathrm{C}$ but $1400^{\circ} \mathrm{C}$$1200^{\circ} \mathrm{C}$Correct Option: , 2 Solution: $\mathrm{A}+\mathrm{BO}_{2} \longrightarrow \mathrm{B}+\mathrm{AO}_{2}$ $\Delta \mathrm{G}=-\mathrm{ve}$ when the temperature is above $1400^{\circ} \mathrm{C}$, A reduces $\mathrm{BO}_{2}$....
Read More →Let there be three independent events
Question: Let there be three independent events $\mathrm{E}_{1}, \mathrm{E}_{2}$ and $\mathrm{E}_{3}$. The probability that only $\mathrm{E}_{1}$ occurs is $\alpha$, only $\mathrm{E}_{2}$ occurs is $\beta$ and only $\mathrm{E}_{3}$ occurs is $\gamma$. Let ' $\mathrm{p}$ ' denote the probability of none of events occurs that satisfies the equations $(\alpha-2 \beta) \mathrm{p}=\alpha \beta$ and $(\beta-3 \gamma) \mathrm{p}=2 \beta \gamma .$ All the given probabilities are assumed to lie in the in...
Read More →The roots of the equation
Question: The roots of the equation $2 x^{2}-6 x+7=0$ are (a) real, unequal and rational(b) real, unequal and irrational(c) real and equal(d) imaginary Solution: (d) imaginary $\because D=\left(b^{2}-4 a c\right)$ $=(-6)^{2}-4 \times 2 \times 7$ $=36-56$ $=-200$ Thus, the roots of the equation are imaginary....
Read More →An elevator in a building can carry a maximum of 10 persons,
Question: An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68 \mathrm{~kg}$. The mass of the elevator itself is $920 \mathrm{~kg}$ and it moves with a constant speed of $3 \mathrm{~m} / \mathrm{s}$. The frictional force opposing the motion is $6000 \mathrm{~N}$. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ must be at least:(1) $56300 \m...
Read More →Two dices are rolled. If both dices
Question: Two dices are rolled. If both dices have six faces numbered $1,2,3,5,7$ and 11 , then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :(1) $\frac{4}{9}$(2) $\frac{17}{36}$(3) $\frac{5}{12}$(4) $\frac{1}{2}$Correct Option: , 2 Solution: $n(E)=5+4+4+3+1=17$ So, $P(E)=\frac{17}{36}$...
Read More →Among the reactions (a) - (d),
Question: Among the reactions (a) - (d), the reaction(s) that does/do not occur in the blast furnace during the extraction of iron is/are: (a) $\mathrm{CaO}+\mathrm{SiO}_{2} \rightarrow \mathrm{CaSiO}_{3}$ (b) $3 \mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{CO} \rightarrow 2 \mathrm{Fe}_{3} \mathrm{O}_{4}+\mathrm{CO}_{2}$ (c) $\mathrm{FeO}+\mathrm{SiO}_{2} \rightarrow \mathrm{FeSiO}_{3}$ (d) $\mathrm{FeO} \rightarrow \mathrm{Fe}+\frac{1}{2} \mathrm{O}_{2}$(a)(a) and (d)(c) and $(\mathrm{d})$(d)Correct...
Read More →Let A denote the event that a 6 -digit integer
Question: Let A denote the event that a 6 -digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by 3 . Then probability of event A is equal to :(1) $\frac{9}{56}$(2) $\frac{4}{9}$(3) $\frac{3}{7}$(4) $\frac{11}{27}$Correct Option: , 2 Solution: Total cases : $\underline{6} \cdot \underline{6} \cdot \underline{5} \cdot \underline{4} \cdot \underline{3} \cdot \underline{2}$ $\mathrm{n}(\mathrm{s})=6 \cdot 6 !$ Favourable cases : Number divisible by $3 \equiv$ Sum of digits mus...
Read More →A mass of 10 kg is suspended by a rope of length 4 m,
Question: A mass of $10 \mathrm{~kg}$ is suspended by a rope of length $4 \mathrm{~m}$, from the ceiling. A force $\mathrm{F}$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $F$ equals: (Take $g=10 \mathrm{~ms}^{-2}$ and the rope to be massless)(1) $100 \mathrm{~N}$(2) $90 \mathrm{~N}$(3) $70 \mathrm{~N}$(4) $75 \mathrm{~N}$Correct Option: 1 Solution: (1) From the free body diagram $T \cos 45^{\circ}=...
Read More →The refining method used when the metal and the impurities have low and high melting temperatures,
Question: The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is:liquationvapour phase refiningzone refiningdistillationCorrect Option: 1 Solution: Liquation method is used for purification of metals having low melting point....
Read More →The purest form of commercial iron is:
Question: The purest form of commercial iron is:pig ironwrought ironcast ironscrap iron and pig ironCorrect Option: , 2 Solution: Wrought iron is purest form of commercial iron....
Read More →A pack of cards has one card missing.
Question: A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :(1) $\frac{3}{4}$(2) $\frac{52}{867}$(3) $\frac{39}{50}$(4) $\frac{22}{425}$Correct Option: , 3 Solution: $\mathrm{E}_{1}$ : Event denotes spade is missing $\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{1}{4} ; \mathrm{P}\left(\overline{\mathrm{E}}_{1}\right)=\frac{3}{4}$ A: Event drawn two cards are spade $\mathrm{P}(\mathrm{A})=\frac{\...
Read More →The element that can be refined by
Question: The element that can be refined by distillation is :nickelzinctingalliumCorrect Option: , 2 Solution: $\mathrm{Zn}, \mathrm{Cd}$ and $\mathrm{Hg}$ are purified by fractional distillation process....
Read More →A 60 HP electric motor lifts an elevator having a maximum total load capacity
Question: A 60 HP electric motor lifts an elevator having a maximum total load capacity of $2000 \mathrm{~kg}$. If the frictional force on the elevator is $4000 \mathrm{~N}$, the speed of the elevator at full load is close to: $\left(1 \mathrm{HP}=746 \mathrm{~W}, \mathrm{~g}=10 \mathrm{~ms}^{-2}\right)$(1) $1.7 \mathrm{~ms}^{-1}$(2) $1.9 \mathrm{~ms}^{-1}$(3) $1.5 \mathrm{~ms}^{-1}$(4) $2.0 \mathrm{~ms}^{-1}$Correct Option: , 2 Solution: (2) Total force required to lift maximum load capacity ag...
Read More →The INCORRECT statement is :
Question: The INCORRECT statement is :bronze is an alloy of copper and tin.cast iron is used to manufacture wrought iron.german silver is an alloy of zinc, copper and nickel.brass is an alloy of copper and nickel.Correct Option: , 4 Solution: (a) Bronze contains $88-96 \% \mathrm{Cu}$ and 4-12\% Sn. (b) Cast iron is used to make wraught iron. (c) German silver contains $50 \% \mathrm{Cu}, 30 \% \mathrm{Zn} \ 20 \% \mathrm{Ni}$. (d) Brass contains $70 \% \mathrm{Cu}$ and $30 \% \mathrm{Zn}$....
Read More →Boron and silicon of very high purity can
Question: Boron and silicon of very high purity can be obtained through:liquationzone refiningvapour phase refiningelectrolytic refiningCorrect Option: , 2 Solution: Germanium (Ge), silicon (Si), boron (B), gallium (Ga) and indium (In) can be obtained in pure state by zone refining process....
Read More →A particle moving in the x y plane experiences a velocity
Question: A particle moving in the $x y$ plane experiences a velocity dependent force $\overrightarrow{\mathrm{F}}=k\left(v_{y} \hat{i}+v_{x} \hat{j}\right)$, where $v_{x}$ and $v_{y}$ are $x$ and $y$ components of its velocity $\vec{v}$. if $\vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle?(1) quantity $\vec{v} \times \vec{a}$ is constant in time(2) $\vec{F}$ arises due to a magnetic field(3) kinetic energy of particle is constant in ...
Read More →An insect is at the bottom of a hemispherical ditch of radius
Question: An insect is at the bottom of a hemispherical ditch of radius $1 \mathrm{~m}$. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is $0.75$, then $h$ is : $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$(1) $0.20 \mathrm{~m}$(2) $0.45 \mathrm{~m}$(3) $0.60 \mathrm{~m}$(4) $0.80 \mathrm{~m}$Correct Option: 1 Solution: (1) For balancing, $m g \sin \theta=f=\mu m g \cos \theta$ $h=R-R \cos \t...
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