A modern grand-prix racing car of mass
Question: A modern grand-prix racing car of mass $\mathrm{m}$ is travelling on a flat track in a circular arc of radius $\mathrm{R}$ with a speed $\mathrm{v}$. If the coefficient of static friction between the tyres and the track is $\mu_{s}$, then the magnitude of negative lift $F_{L}$ acting downwards on the car is: (Assume forces on the four tyres are identical and $g=$ acceleration due to gravity) (1) $\mathrm{m}\left(\frac{\mathrm{v}^{2}}{\mu_{s} \mathrm{R}}+\mathrm{g}\right)$(2) $\mathrm{m...
Read More →The number of words
Question: The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is__________. Solution: For vowels not together Number of ways to arrange $\mathrm{L}, \mathrm{T}, \mathrm{T}, \mathrm{R}=\frac{4 !}{2 !}$ Then put both $\mathrm{E}$ in 5 gaps formed in ${ }^{5} C_{2}$ ways. $\therefore$ No. of ways $=\frac{4 !}{2 !} \cdot{ }^{5} C_{2}=120$...
Read More →Which of the following ore is concentrated using
Question: Which of the following ore is concentrated using group 1 cyanide salt?SphaleriteSideriteMalachiteCalamineCorrect Option: 1 Solution: Conc. of sphalerite, first by cyanide salt as a depressant to remove the impurity of galena $\mathrm{Zns}+\mathrm{Pbs}+\mathrm{NaCN} \longrightarrow \mathrm{Na}_{2}\left[\mathrm{Zn}(\mathrm{CN})_{4}\right]+\mathrm{PbS} \uparrow$...
Read More →Two families with three members each and
Question: Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?(1) $2 ! 3 ! 4 !$(2) $(3 !)^{3} \cdot(4 !)$(3) $(3 !)^{2} \cdot(4 !)$(4) $3 !(4 !)^{3}$Correct Option: , 2 Solution: Number of arrangement $=(3 ! \times 3 ! \times 4 !) \times 3 !=(3 !)^{3} 4 !$...
Read More →The sum of the roots of the equation
Question: The sum of the roots of the equation $x^{2}-6 x+2=0$ is (a) 2(b) 2(c) 6(d) 6 Solution: (c) 6 Sum of the roots of the equation $x^{2}-6 x+2=0$ is $\alpha+\beta=\frac{-b}{a}=\frac{-(-6)}{1}=6$, where $\alpha$ and $\beta$ are the roots of the equation....
Read More →A body of mass 2 kg moves under a force
Question: A body of mass $2 \mathrm{~kg}$ moves under a force of $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. It starts from rest and was at the origin initially. After $4 \mathrm{~s}$, its new coordinates are $(8, b, 20)$. The value of $b$ is______ (Round off to the Nearest Integer) Solution: (12) $\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{2}$ $=\hat{\mathrm{i}}+1.5 \hat{...
Read More →Match list-I with list-II :
Question: Match list-I with list-II : Choose the most appropriate answer from the option given below :$a-i, b-i v, c-i i, d-i i i$a-ii, b-iii, c $-\mathrm{i}, \mathrm{d}-\mathrm{iv}$$a-i i, b-i i i, c-i v, d-i$$a-i i, b-i v, c-i i i, d-i$Correct Option: , 3 Solution: (a) Mercury $\rightarrow$ Distillation refining (b) Copper $\rightarrow$ Electrolytic refining (c) Silicon $\rightarrow$ Zone refining (d) Nickel $\rightarrow$ Vapour phase refining...
Read More →There are 3 sections in a question paper and each
Question: There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:(1) 3000(2) 1500(3) 2255(4) 2250Correct Option: , 4 Solution: (4) Since, each section has 5 questions. $\therefore$ Total number of selection of 5 questions $=3 \times{ }^{5} C_{1} \times{ }^{5} C_{1} \times{ }^{5} C_{3}+3 \times{ }^...
Read More →If one root of the equation
Question: If one root of the equation $2 x^{2}+a x+6=0$ is 2 , then $a=?$ (a) 7 (b) $-7$ (c) $\frac{7}{2}$ (d) $\frac{-7}{2}$ Solution: (b) 7 It is given that one root of the equation $2 x^{2}+a x+6=0$ is 2 . $\therefore 2 \times 2^{2}+a \times 2+6=0$ $\Rightarrow 2 a+14=0$ $\Rightarrow a=-7$...
Read More →The chemical that is added to reduce the melting point
Question: The chemical that is added to reduce the melting point of the reaction mixture during the extraction of aluminium is :CryoliteBauxiteCalamineKaolite OfficialCorrect Option: 1 Solution: To reduce the melting point of reaction mixture, cryolite is added....
Read More →The number of words,
Question: The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is__________. Solution: $S \rightarrow 2, L \rightarrow 2, A, B, Y, U$ $\therefore$ Required number of ways $={ }^{2} C_{1} \times{ }^{5} C_{2} \times \frac{4 !}{2 !}=240$...
Read More →Statement I : A cyclist is moving on an unbanked road with a speed
Question: Statement I : A cyclist is moving on an unbanked road with a speed of $7 \mathrm{kmh}^{-1}$ and takes a sharp circular turn along a path of radius of $2 \mathrm{~m}$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ Statement II : If the road is banked at an angle of $45^{\circ}$, cyclist can cross the curve of $2 \mathrm{~m}$ radius with the speed of $18.5 \mathr...
Read More →If x = 3 is a solution of the equation
Question: If $x=3$ is a solution of the equation $3 x^{2}+(k-1) x+9=0$, then $k=?$ (a) 11(b) 11(c) 13(d) 13 Solution: (b) 11 It is given that $x=3$ is a solution of $3 x^{2}+(k-1) x+9=0$; therefore, we have: $3(3)^{2}+(k-1) \times 3+9=0$ $\Rightarrow 27+3(k-1)+9=0$ $\Rightarrow 3(k-1)=-36$ $\Rightarrow(k-1)=-12$ $\Rightarrow k=-11$...
Read More →Match List-I and List-II :
Question: Match List-I and List-II : Choose the correct answer from the options given below :-(ii),(b)-(iii),(c)-(i),(d)-(iv)(a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)(a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)(a)-(ii), (b)-(1), (c)-(iv), (d)-(iii)Correct Option: , 4 Solution:...
Read More →A test consists of 6 multiple choice questions,
Question: A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is____________. Solution: Select any 4 correct questions in ${ }^{6} C_{4}$ ways. Number of ways of answering wrong question $=3$ $\therefore$ Required number of ways $={ }^{6} C_{4}(1)^{4} \times 3^{2}=135$....
Read More →The total number of 3 -digit numbers,
Question: The total number of 3 -digit numbers, whose sum of digits is 10 , is________. Solution: Let $x y z$ be the three digit number $x+y+z=10, x \leq 1, y \geq 0, z \geq 0$ $x-1=t \Rightarrow x=1+t$ $x-1 \geq 0, t \geq 0$ $t+y+z=10-1=9$ $0 \leq t, z, z \leq 9$ $\therefore$ Total number of non-negative integral solution $={ }^{9+3-1} C_{3-1}={ }^{11} C_{2}=\frac{11 \cdot 10}{2}=55$ But for $t=9, x=10$, so required number of integers $=55-1=54$...
Read More →Which of the following is not a quadratic equation?
Question: Which of the following is not a quadratic equation? (a) $3 x-x^{2}=x^{2}+5$ (b) $(x+2)^{2}=2\left(x^{2}-5\right)$ (c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$ (d) $(x-1)^{2}=3 x^{2}+x-2$ Solution: (c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$ $\because(\sqrt{2} x+3)^{2}=2 x^{2}+6$ $\Rightarrow 2 x^{2}+9+6 \sqrt{2} x=2 x^{2}+6$ $\Rightarrow 6 \sqrt{2} x+3=0$, which is not a quadratic equation...
Read More →Which of the following is a quadratic equation?
Question: Which of the following is a quadratic equation? (a) $\left(x^{2}+1\right)=(2-x)^{2}+3$ (b) $x^{3}-x^{2}=(x-1)^{3}$ (c) $2 x^{2}+3=(5+x)(2 x-3)$ (d) None of these Solution: (b) $x^{3}-x^{2}=(x-1)^{3}$ $\because x^{3}-x^{2}=(x-1)^{3}$ $\Rightarrow x^{3}-x^{2}=x^{3}-3 x^{2}+3 x-1$ $\Rightarrow 2 x^{2}-3 x+1=0$, which is a quadratic equation...
Read More →A block of 200 g mass moves with a uniform speed in a horizontal circular groove
Question: A block of $200 \mathrm{~g}$ mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius $20 \mathrm{~cm}$. If the block takes $40 \mathrm{~s}$ to complete one round, the normal force by the side walls of the groove is :(1) $0.0314 \mathrm{~N}$(2) $9.859 \times 10^{-2} \mathrm{~N}$(3) $6.28 \times 10^{-3} \mathrm{~N}$(4) $9.859 \times 10^{-4} \mathrm{~N}$Correct Option: , 4 Solution: (4) $\mathrm{N}=\mathrm{m} \omega^{2} \mathrm{R}$ $\mathrm{N}=\...
Read More →The point of intersection and sudden increase in the slope,
Question: The point of intersection and sudden increase in the slope, in the diagram given below, respectively, indicates: $\Delta G=0$ and melting or boiling point of the metal oxide$\Delta \mathrm{G}0$ and decomposition of the metal oxide$\Delta \mathrm{G}0$ and decomposition of the metal oxide$\Delta \mathrm{G}=0$ and reduction of the metal oxideCorrect Option: 1 Solution: At intersection point $\Delta \mathrm{G}=0$ and sudden increase in slope is due to melting or boiling point of the metal....
Read More →The value of
Question: The value of $\left(2 \cdot{ }^{1} P_{0}-3 \cdot{ }^{2} P_{1}+4 \cdot{ }^{3} P_{2}-\ldots\right.$ up to $51^{\text {th }}$ term $)$ $+\left(1 !-2 !+3 !-\ldots\right.$ up to $51^{\text {th }}$ term $)$ is equal to :(1) $1-51(51) !$(2) $1+(51) !$(3) $1+(52) !$(4) 1Correct Option: , 3 Solution: We know, $(r+1) \cdot{ }^{r} P_{r-1}=(r+1) \cdot \frac{r !}{1 !}=(r+1) !$ So, $\left(2 \cdot{ }^{1} P_{0}-3 \cdot{ }^{2} P_{1}+\ldots . .51\right.$ terms $)+$ $(1 !-2 !+3 !-\ldots$ upto 51 terms) $...
Read More →Let n>2 be an integer. Suppose that there are
Question: Let $n2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of $n$ is :(1) 201(2) 200(3) 101(4) 199Correct Option: 1 Solution: (1) Number of two consecutive stations (Bl...
Read More →Which of the following is a quadratic equation?
Question: Which of the following is a quadratic equation? (a) $x^{2}-3 \sqrt{x}+2=0$ (b) $x+\frac{1}{x}=x^{2}$ (c) $x^{2}+\frac{1}{x^{2}}=5$ (d) $2 x^{2}-5 x=(x-1)^{2}$ Solution: (d) $2 x^{2}-5 x=(x-1)^{2}$ A quadratic equation is the equation with degree 2 . $\because 2 x^{2}-5 x=(x-1)^{2}$ $\Rightarrow 2 x^{2}-5 x=x^{2}-2 x+1$ $\Rightarrow 2 x^{2}-5 x-x^{2}+2 x-1=0$ $\Rightarrow x^{2}-3 x-1=0$, which is a quadratic equation...
Read More →A block of mass m slides along a floor while a force of magnitude
Question: A block of mass $m$ slides along a floor while a force of magnitude $F$ is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is $\mu_{\mathrm{K}}$. Then, the block's acceleration ' $\mathrm{a}$ ' is given by : ( $\mathrm{g}$ is (1) $-\frac{\mathrm{F}}{\mathrm{m}} \cos \theta-\mu_{\mathrm{K}}\left(\mathrm{g}-\frac{\mathrm{F}}{\mathrm{m}} \sin \theta\right)$(2) $\frac{\mathrm{F}}{\mathrm{m}} \cos \theta-\mu_{\mathrm{K}}\left(\mathrm{g}-\frac{\math...
Read More →which of the following reduction reaction CANNOT
Question: which of the following reduction reaction CANNOT be carried out with coke?$\mathrm{Al}_{2} \mathrm{O}_{3} \rightarrow \mathrm{Al}$$\mathrm{ZnO} \rightarrow \mathrm{Zn}$$\mathrm{Fe}_{2} \mathrm{O}_{3} \rightarrow \mathrm{Fe}$$\mathrm{Cu}_{2} \mathrm{O} \rightarrow \mathrm{Cu}$Correct Option: 1 Solution: Reduction of $\mathrm{Al}_{2} \mathrm{O}_{3} \rightarrow \mathrm{Al}$ is carried out by electrolytic reduction of its fused salts. $\mathrm{ZnO}, \mathrm{Fe}_{2} \mathrm{O}_{3} \ \mathrm...
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