Objective Questions (MCQ)
Question: Objective Questions (MCQ) The roots of the quadratic equation $2 x^{2}-x-6=0$ are (a) $-2, \frac{3}{2}$ (b) $2, \frac{-3}{2}$ (c) $-2, \frac{-3}{2}$ (d) $2, \frac{3}{2}$ Solution: The given quadratic equation is $2 x^{2}-x-6=0$. $2 x^{2}-x-6=0$ $\Rightarrow 2 x^{2}-4 x+3 x-6=0$ $\Rightarrow 2 x(x-2)+3(x-2)=0$ $\Rightarrow(x-2)(2 x+3)=0$ $\Rightarrow x-2=0$ or $2 x+3=0$ $\Rightarrow x=2$ or $x=\frac{-3}{2}$ Thus, the roots of the given equation are 2 and $\frac{-3}{2}$. Hence, the corre...
Read More →The correct statement regarding the given Ellingham diagram is:
Question: The correct statement regarding the given Ellingham diagram is: At $1400^{\circ} \mathrm{C}, \mathrm{Al}$ can be used for the extraction of $\mathrm{Zn}$ from $\mathrm{ZnO}$At $500^{\circ} \mathrm{C}$, coke can be used for the extraction of $\mathrm{Zn}$ from $\mathrm{ZnO}$Coke cannot be used for the extraction of $\mathrm{Cu}$ from $\mathrm{Cu}_{2} \mathrm{O}$.At $800^{\circ} \mathrm{C}, \mathrm{Cu}$ can be used for the extraction of $\mathrm{Zn}$ from $\mathrm{ZnO}$Correct Option: 1 ...
Read More →Objective Questions (MCQ)
Question: Objective Questions (MCQ)The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m2. The breadth of the field is(a) 20 m (b) 30 m (c) 12 m (d) 16 m Solution: Let the breadth of the rectangular field bexm. Length of the rectangular field = (x+ 8) mArea of the rectangular field = 240 m2 $\therefore(x+8) \times x=240 \quad$ (Area = Length $\times$ Breadth) $\Rightarrow x^{2}+8 x-240=0$ $\Rightarrow x^{2}+20 x-12 x-240=0$ $\Rightarrow x(x+20)-12(x+20)=...
Read More →A hairpin like shape as shown in figure is made by bending a long current carrying wire.
Question: A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $\mathrm{P}$ which lies on the centre of the semicircle? (1) $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}}(2-\pi)$(2) $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}}(2+\pi)$(3) $\frac{\mu_{0} \mathrm{I}}{2 \pi_{\mathrm{r}}}(2+\pi)$(4) $\frac{\mu_{0} \mathrm{I}}{2 \pi_{\mathrm{r}}}(2-\pi)$Correct Option: , 2 Solution: (2) $B=2 \times B_{\text {st.wire }...
Read More →The ore that contains both iron and copper is:
Question: The ore that contains both iron and copper is:copper pyritesmalachitedolomiteazuriteCorrect Option: 1 Solution: Amongst the given ores, copper pyrite $\left(\mathrm{CuFeS}_{2}\right)$, dolomite $\left(\mathrm{MgCO}_{3} \cdot \mathrm{CaCO}_{3}\right)$, malachite $\left[\mathrm{CuCO}_{3} \cdot \mathrm{Cu}(\mathrm{OH})_{2}\right]$, azurite $\left[2 \mathrm{CuCO}_{3} \cdot \mathrm{Cu}(\mathrm{OH})_{2}\right]$, copper pyrite contains both copper and iron....
Read More →Let A be a set of all 4 -digit natural
Question: Let $A$ be a set of all 4 -digit natural numbers whose exactly one digit is 7 . Then the probability that a randomly chosen element of $A$ leaves remainder 2 when divided by 5 is:(1) $\frac{1}{5}$(2) $\frac{2}{9}$(3) $\frac{97}{297}$(4) $\frac{122}{297}$Correct Option: , 3 Solution: Total cases $(4 \times 9 \times 9 \times 9)-(3 \times 9 \times 9)$ Probability $=\frac{(3 \times 9 \times 9)-(2 \times 9)+(8 \times 9 \times 9)}{\left(4 \times 9^{3}\right)-\left(3 \times 9^{2}\right)}$ $=\...
Read More →The correct statement is :
Question: The correct statement is :leaching of bauxite using concentrated $\mathrm{NaOH}$ solution gives sodium aluminate and sodium silicate.the Hall-Heroult process is used for the production of aluminium and iron.pig iron is obtained from cast iron.the blistered appearance of copper during the metallurgical process is due to the evolution of $\mathrm{CO}_{2}$.Correct Option: 1 Solution: During metallurgy of aluminium, when bauxite (powdered ore) is treated with $\mathrm{NaOH}$ (conc), sodium...
Read More →A solenoid of 1000 turns per metre has a core with relative permeability
Question: A solenoid of 1000 turns per metre has a core with relative permeability 500 . Insulated windings of the solenoid carry an electric current of $5 \mathrm{~A}$. The magnetic flux density produced by the solenoid is: (permeability of free space $=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )(1) $\pi \mathrm{T}$(2) $2 \times 10^{-3} \pi \mathrm{T}$(3) $\frac{\pi}{5} \mathrm{~T}$(4) $10^{-4} \pi \mathrm{T}$Correct Option: Solution: (1) $\mathrm{B}=\mu \mathrm{nI}=\mu_{0} \mu_{\mathrm{rn}...
Read More →In a group of 400 people, 160 are smokers and
Question: In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35 \%, 20 \%$ and $10 \%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:(1) $\frac{7}{45}$(2) $\frac{8}{45}$(3) $\frac{14}{45}$(4) $\frac{28}{45...
Read More →The idea of froth floatation method came from a person X
Question: The idea of froth floatation method came from a person X and this method is related to the process $Y$ of ores, $X$ and $Y$, respectively, are :fisher woman and concentrationwasher woman and concentrationfisher man and reductionwasher man and reductionCorrect Option: , 2 Solution: Froth floatation was discovered by washer women. It is a method of concentration of ores....
Read More →The perimeter of a rectangle is 82 m and its area is 400 m2.
Question: The perimeter of a rectangle is 82 m and its area is 400 m2. The breadth of the rectangle is(a) 25 m(b) 20 m(c) 16 m(d) 9 m Solution: (c) 16 m Let the length and breadth of the rectangle be $l$ and $b$. Perimeter of the rectangle $=82 \mathrm{~m}$ $\Rightarrow 2 \times(l+b)=82$ $\Rightarrow l+b=41$ $\Rightarrow l=(41-b)$ $\ldots(\mathrm{i})$ Area of the rectangle $=400 \mathrm{~m}^{2}$ $\Rightarrow l \times b=400 \mathrm{~m}^{2}$ $\Rightarrow(41-b) b=400 \quad($ using $(\mathrm{i}))$ $...
Read More →When a missile is fired from a ship,
Question: When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:(1) $\frac{1}{8}$(2) $\frac{1}{27}$(3) $\frac{3}{4}$(4) $\frac{3}{8}$Correct Option: 1 Solution: Probability of not getting intercepted $=\frac{2}{3}$ Probability of missile hitti...
Read More →The correct statement is :
Question: The correct statement is :aniline is a froth stabilizer.zincite is a carbonate ore.sodium cyanide cannot be used in the metallurgy of silver.zone refining process is used for the refining of titanium.Correct Option: 1 Solution: Ti is refined by van Arkel method. Silver is leached by dilute solution of $\mathrm{NaCN}$. Zincite is oxide ore of zinc i.e. ZnO. Aniline is a froth stabilizer....
Read More →The probability that two randomly
Question: The probability that two randomly selected subsets of the set $\backslash\{1,2,3,4,5 \backslash\}$ have exactly two elements in their intersection, is:(1) $\frac{65}{2^{7}}$(2) $\frac{135}{2^{9}}$(3) $\frac{65}{2^{8}}$(4) $\frac{35}{2^{7}}$Correct Option: , 2 Solution: Required probability $=\frac{{ }^{5} C_{2} \times 3^{3}}{4^{5}}$ $=\frac{10 \times 27}{2^{10}}=\frac{135}{2^{9}}$...
Read More →Match the refining methods (Column I) with metals (Column II).
Question: Match the refining methods (Column I) with metals (Column II). (I) - (c); (II) - (a); (III) - (b); (IV) - (d)(I) - (b); (II) - (c); (III) - (d); (IV) - (a)(I) - (c); (II) - (d); (III) - (b); (IV) - (a)(I) - (b); (II) - (d); (III) - (a)I (IV) - (c)Correct Option: , 3 Solution: Liquation is used for $\mathrm{Sn}$, zone refining is used for $\mathrm{Ga}$, mond's process is used for refining of Ni and van Arkel method is used for $\mathrm{Zr}$, So, correct match is (I) - (c); (II)-(d); (II...
Read More →The magnetic field in a region is given by
Question: The magnetic field in a region is given by $\vec{B}=B_{0}\left(\frac{x}{a}\right) \hat{k}$. A square loop of side $\mathrm{d}$ is placed with its edges along the $x$ and $\mathrm{y}$ axes. The loop is moved with a constant velocity $\vec{v}=v_{0} \hat{i}$. The emf induced in the loop is : (1) $\frac{\mathrm{B}_{0} \mathrm{v}_{0}^{2} \mathrm{~d}}{2 \mathrm{a}}$(2) $\frac{\mathrm{B}_{0} \mathrm{v}_{0} \mathrm{~d}}{2 \mathrm{a}}$(3) $\frac{\mathrm{B}_{0} \mathrm{v}_{0} \mathrm{~d}^{2}}{\m...
Read More →Solve the following
Question: Let $\mathrm{B}_{\mathrm{i}}(\mathrm{i}=1,2,3)$ be three independent events in a sample space. The probability that only $\mathrm{B}_{1}$ occur is $\alpha$, only $\mathrm{B}_{2}$ occurs is $\beta$ and only $\mathrm{B}_{3}$ occurs is $\gamma$. Let $\mathrm{p}$ be the probability that none of the events $B_{i}$ occurs and these 4 probabilities satisfy the equations $(\alpha-2 \beta) \mathrm{p}=\alpha \beta$ and $(\beta-3 \gamma) \mathrm{p}=2 \beta \gamma($ All the probabilities are assum...
Read More →The sum of a number and its reciprocal is
Question: The sum of a number and its reciprocal is $2 \frac{1}{20}$. The number is (a) $\frac{5}{4}$ or $\frac{4}{5}$ (b) $\frac{4}{3}$ or $\frac{3}{4}$ (c) $\frac{5}{6}$ or $\frac{6}{5}$ (d) $\frac{1}{6}$ or 6 Solution: (a) $\frac{5}{4}$ or $\frac{4}{5}$ Let the required number be $x$. According to the question: $x+\frac{1}{x}=\frac{41}{20}$ $\Rightarrow \frac{x^{2}+1}{x}=\frac{41}{20}$ $\Rightarrow 20 x^{2}-41 x+20=0$ $\Rightarrow 20 x^{2}-25 x-16 x+20=0$ $\Rightarrow 5 x(4 x-5)-4(4 x-5)=0$ $...
Read More →A charge Q is moving
Question: A charge $Q$ is moving $\overrightarrow{\mathrm{dI}}$ distance in the magnetic field $\overrightarrow{\mathrm{B}}$. Find the value of work done by $\overrightarrow{\mathrm{B}}$.(1) 1(2) Infinite(3) Zero(4) $-1$Correct Option: , 3 Solution: (3) Since force on a point charge by magnetic field is always perpendicular to $\vec{v}[\vec{F}=q \vec{V} \times \vec{B}] \therefore$ Work by magnetic force on the point charge is zero....
Read More →The one that is not a carbonate ore is:
Question: The one that is not a carbonate ore is:malachitecalaminesideritebauxiteCorrect Option: , 4 Solution:...
Read More →An ordinary dice is rolled for a
Question: An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :(1) $\frac{3}{16}$(2) $\frac{1}{2}$(3) $\frac{5}{16}$(4) $\frac{1}{32}$Correct Option: , 2 Solution: $\mathrm{P}$ (odd no. twice ) $=\mathrm{P}$ ( even no. thrice ) $\Rightarrow{ }^{n} C_{2}\left(\frac{1}{2}\right)^{n}={ }^{n} C_{3}\left(\frac...
Read More →For what values of k, the equation
Question: For what values of $k$, the equation $k x^{2}-6 x-2=0$ has real roots? (a) $k \leq \frac{-9}{2}$ (b) $k \geq \frac{-9}{2}$ (c) $k \leq-2$ (d) None of these Solution: (b) $k \geq \frac{-9}{2}$ It is given that the roots of the equation $\left(k x^{2}-6 x-2=0\right)$ are real. $\therefore D \geq 0$ $\Rightarrow\left(b^{2}-4 a c\right) \geq 0$ $\Rightarrow(-6)^{2}-4 \times k \times(-2) \geq 0$ $\Rightarrow 36+8 k \geq 0$ $\Rightarrow k \geq \frac{-36}{8}$ $\Rightarrow k \geq \frac{-9}{2}$...
Read More →Assertion: For the extraction of iron,
Question: Assertion: For the extraction of iron, haematite ore is used. Reason: Haematite is a carbonate ore of iron.Only the reason is correctBoth the assertion and reason are correct, but the reason is not the correct explanation for the assertion.Both the assertion and reason are correct and the reason is the correct explanation for the assertion.Only the assertion is correct.Correct Option: , 4 Solution: For the extraction of iron, haematite ore $\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)$ ...
Read More →Let in a Binomial distribution,
Question: Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be $0.4096$ and $0.2048$ respectively. Then the probability of getting exactly 3 successes is equal to:(1) $\frac{32}{625}$(2) $\frac{80}{243}$(3) $\frac{40}{243}$(4) $\frac{128}{625}$Correct Option: 1 Solution: $\mathrm{P}(\mathrm{X}=1)={ }^{5} \mathrm{C}_{1} \cdot \mathrm{p} \cdot \mathrm{q}^{4}=0.4096$ $\mathrm{P}(\mathrm{X}=2)={ }^{5} \mathrm{C}_{2} \cdot \mathrm{p}^{2} \c...
Read More →If the equation
Question: If the equation $x^{2}-k x+1=0$ has no real roots, then (a)k 2(b)k 2(c) 2 k 2(d) none of these Solution: (c) 2 k 2 It is given that the equation $x^{2}-k x+1=0$ has no real roots. $\therefore\left(b^{2}-4 a c\right)0$ $\Rightarrow(-k)^{2}-4 \times 1 \times 10$ $\Rightarrow k^{2}4$ $\Rightarrow-2k2$...
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