Mathematics, Chemistry, and Physics Question Booklet 2018 PDF

Okay, here is the transcription of the document in markdown format. # Roll Number, Time and Marks * Roll No.: (space) * Time allowed: 2 Hrs. 30 Min. * Max. Marks: 150 ### Question Booklet 2018 * Question Booklet Set: D * Question Booklet No.: 201156 ### General Instructions Examinee i...

Okay, here is the transcription of the document in markdown format. # Roll Number, Time and Marks * Roll No.: (space) * Time allowed: 2 Hrs. 30 Min. * Max. Marks: 150 ### Question Booklet 2018 * Question Booklet Set: D * Question Booklet No.: 201156 ### General Instructions Examinee is directed to read carefully the following instructions: 1. Examinee must write his/her Roll Number in the specified box on the top left hand corner of this page. Answers are required to be marked only on the Computerised O.M.R. Answer sheet which is being provided to the examinee. 2. Besides filling in the Roll Number, the examinee has to put his/her signature on the Answer-Sheet and also fill other required details like Name, Roll Number, Question Booklet code, etc. as indicated on the Answer OMR Sheet. If these details are not filled in by the examinee, his/her Answer Sheet will not be evaluated. 3. For each question, there are four alternative answers, out of which only one is correct. Examinee must darken the circle of correct option in the Answer Sheet by Black Ball Pen only. 4. There are 48 (44+4) pages in this Question-Booklet including 1 page for General Instructions and three blank pages for Rough Work in the last. In case an examinee receives an incomplete or defective Question Booklet, he/she should make a request to the Room Invigilator to change the same within 10 minutes of start of the exam. 5. This Question Booklet contains 150 questions from following subjects: | Subject | Q. Nos. | | :---------- | :-------- | | (1) Maths | 1-50 | | (2) Chemistry | 51-100 | | (3) Physics | 101-150 | 6. Each question carries 1 mark and 1/4 mark will be deducted for each wrong answer. 7. Possession and use of electronic devices such as Calculator, Cellular Phone, Digital Diary, Log Table, Pager, etc., are restricted during the examination. 8. Any leaf from the Question Booklet should not be detached. After the Examination, Question-Booklet and Answer-Sheet must be handed over to the Room Invigilator. 9. During examination the examinee will not be allowed to leave the examination hall till the END of the Examination. ## Mathematics 1. The corner points of the feasible region determined by the following system of linear inequalities $2x + y \le 10$, $x + 3y \le 15$, $x, y \ge 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px + qy$, $p, q > 0$ condition on p and q so that the maximum of z occurs at both (3, 4) and (0, 5) is A) $p = q$ B) $p = 2q$ C) $p = 3q$ D) $q = 3p$ 2. The probability that A speaks truth is $\frac{4}{5}$, B speaks truth is $\frac{3}{4}$. Then the probability they contradict each other is A) $\frac{7}{20}$ B) $\frac{5}{2}$ C) $\frac{19}{20}$ D) $\frac{12}{20}$ 3. A discrete random variable X has the probability distribution as given below: | X | 0.5 | 1 | 1.5 | 2 | | :---- | :-- | :---- | :---- | :- | | P(X) | K | K^2 | 2K^2 | K | then $P(X < 1)$ is A) $\frac{1}{3}$ B) -1 C) $\frac{2}{3}$ D) $\frac{1}{5}$ 4. The maximum value of $△ = \begin{vmatrix} 1 & 1 & 1 \\\ 1& 1+sine& 1\\\ 1& 1& 1+cose \end{vmatrix}$ is (θ is a real number) A) 1/2 B) $\frac{\sqrt{3}}{2}$ C) $\sqrt{2}$ D) $2\frac{\sqrt{3}}{4}$ 5. If A, B are matrices of order 3 and $|A| = 5$, $|B| = 3$ then $|3AB| =$ A) 27 x 5 x 3 B) $27^2 \times 5 \times 3$ C) 3 x 5 x 3 D) 9 x 5 x 3 6. Let $\begin{vmatrix} a & p & x \\\ b & q & y \\\ c & r & z \end{vmatrix} = 16$ then the value of $\begin{vmatrix} p+x& a+x & a+p \\\ q+y & b+y & b+q \\\ r+z& c+z & c+r \end{vmatrix} =$ A) 32 B) 0 C) 16 D) - 16 7. If $x^my^n = (x + y)^{m+n}$ then $\frac{dy}{dx}$ = A) $\frac{x}{y}$ B) $-\frac{x}{y}$ C) $\frac{y}{x}$ D) 1 8. If $x = t^2$, $y = t^3$ then $\frac{d^2y}{dx^2}$ is A) $\frac{3}{2}$ B) $\frac{3}{4t}$ C) $\frac{3t}{2}$ D) $\frac{3}{2}$ 9. The slope of tangent to the curve $x = t^2 + 3t - 8$, $y = 2t^2 - 2t - 5$ at the point (2, -1) is A) 22/7 B) 6/7 C) -6/7 D) -6 10. The function $f(x) = 4sin^3x - 6sin^2x + 12sinx + 100$ is A) increasing in $(\frac{π}{2}, π)$ B) decreasing in $(π/2, π)$ C) decreasing in $(-\frac{π}{2}, \frac{π}{2})$ D) increasing in $(π, \frac{π}{2})$ 11. Area bounded between $y= cosx$ and $y = sinx, 0 \le x \le \frac{\pi}{2}$ and y axis is (in square units) A) $2(\sqrt{2} - 1)$ B) $\sqrt{2} + 1$ C) $\sqrt{2} - 1$ D) 3 12. Area of the region bounded by $xy=1, x=1, x=2$ and $x$ axis is A) 1 B) $\log 2$ C) $\log 4$ D) 0 13. Area of the smaller region bounded by the ellipse $\frac{x2}{9} + \frac{y2}{4} = 1$ and the line $\frac{x}{3} + \frac{y}{2} = 1$ is A) $3(\frac{\pi}{2} - 1)$ B) $\frac{3\pi}{2}$ C) $6\pi$ D) $\frac{3\pi}{2} -2$ 14. The degree of the differential equation $(\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^2 + sin(\frac{dy}{dx}) + 1 = 0$ A) 3 B) 2 C) not defined D) 6 15. If $y = sin^{-1}(x\sqrt{1-x} - \sqrt{x}\sqrt{1-x2})$, $0<x<1$ then $\frac{dy}{dx}$ is A) $\frac{1}{\sqrt{1-x^2}} - \frac{1}{2\sqrt{x-x^2}}$ B) $\frac{1}{\sqrt{1-x}} - \frac{1}{\sqrt{1-x2}}$ C) $\frac{1}{2\sqrt{1-x2}}$ D) $\frac{1}{1-x2}$ 16. The value of $c$ in mean value theorem for the function $f(x) = x(x - 2)$, $x \epsilon [1, 2]$ is A) 1/2 B) 3/2 C) 2/3 D) 4/3 17. The function $f(x) = \frac{4-x2}{4x-x3}$ is A) discontinuous at only one point B) discontinuous at 3 points C) discontinuous at 2 points D) continuous for all real values of x 18. If $y = \sqrt{sinx} + y$, then $\frac{dy}{dx} = $ A) $\frac{cosx}{2y-1}$ B) $\frac{cosx}{1-2y}$ C) $\frac{sinx}{1-2y}$ D) $\frac{sinx}{2y-1}$ 19. If $f(x) = f(a – x), g(x) + g(a – x) = 4$ then $\int_0^a f(x)g(x)dx =$ A) $\int_0^a f(x) dx$ B) $2\int_0^a f(x) dx$ C) $\int_0^a f(x) + g(x) dx$ D) 0 20. $\int \frac{dx}{x9 + x} =$ A) $\frac{1}{8}log(\frac{x8}{1+x8}) + c$ B) $\frac{1}{9}log(\frac{x9}{1+x9})+c$ C) $\log(x9 + x)+c$ D) 0 21. $\int_0^1 (x2+x−1)10 (2x + 1) dx =$ A) 2/11 B) 1/2 C) 7/11 D) -2/ 11 22. The angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is A) $0°$ B) $30°$ C) $Cos^{-1} (\frac{-2}{3})$ D) 90° 23. A plane which passes through the points (2,0,0), (0,3,0) and [(0,0,4) is A) $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 0$ B) $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1$ C) 2x + 3y + 4z = 1 D) 6x + 4y + 3z = -1 24. The coordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8=0. A) (0, -8/5, 0) B) (0, 5/8, 0) C) (0, -5/8, 0) D) (1, 0, 0) 25. The distance between two parallel planes $2x+y+2z = 8$ and $4x+2y+4z+5 = 0$ is A) 2/7 B) 7/2 C) 1 D) 10 26. Let $A = {1, 2, 3}$ and consider the relation $R = {(1, 1), (2, 2), (3, 3), (1, 3)}$ then $R$ is A) reflexive but not transitive B) reflexive but not symmetric C) symmetric and transitive D) neither symmetric nor transitive 27. Which of the following functions from $Z$ to $Z$ are bijections? A) f(x) = $x^2$ B) f(x) = $x + 2$ C) f(x) = $2x + 1$ D) f(x) = $x^2 + 1$ 28. Let f : R - {$\frac{3}{5}$} $\rightarrow$ R be defind by $f(x) = 2-A, g (x) = b. In which of following case for A = B ? (a = 2h, b = 3k) , a, b != 0 (A) $\sqrt{e}$ (B) 2 (b) Let H.C.F of A and B then H= k . Value of k ? (A) 2 (B) 5 (C) $\frac{3x + 2}{5x - 3}$ then 5 (D) None (A) $f^{-1} (x) = \frac{3x + 2}{5x - 3}$ \ -x (D) $f^{-1}(x)=\frac{x-3}{5-x}$> (B) II / A, g 1B / C Are one one func then g lOf : AC is also one 5 (D) 8:2C (LE) ECE 39. If = 2 + 200 + 200 + "Which of 1e folowing is not rue2 D If Of is on2 then g must be on2 and f nee4 not be on D (A) If/ AB ,g BC are on func then gc CIs also 52/ is C If Of is oneone func then boh D (A) (2 B) 32 (C) 2 8 C) of=log8 D) 4 e relabve bovering of vapour in o 4 0 12 0 2 log88 g+ c the solubon y/11e folowing baw the solubon of 2 22 + log8 x + c 5 C) log (x8 + x) + c 8log 914 The bmber de86766 equ1516 the sole fraebon of solute presehb the solo e)log8x+x8)+ c. is sobve 1his47a7776 6 If + + 6(4 = If 5a557 6 (C)7/11 D 344 Isb 8 2 + 20. lo9 8 g 2 + + (h24eanglebeweenthelhnes2 -4) 444 5 (C)45 " 9447 e A "s plane whzcb passes hrough 4he 7/00 50125(44 54 4 87 ) If Of is bne onC func then 5h h 163 C C / 617 C 46 8 :56145+ : 6) /A4 58964 440 7// 9 A 5: (4 :4 4) If /(4 5 g /(4 = 6( 4 5 : 867664:5 17 6:867460/(4 5/ ( B5 4: : 4 118, What volbmber bmbmber08 : 4 86/C4) : 1 27 ( :7666- 1.56111 D) 87 1 567s40 12 ## Chemistry 1. The largest bond angle is in A) $AsH_3$ B) $NH_3$ C) $H_2O$ D) $PH_3$ 2. Which of the following ions having the following electronic structures would have maximum magnetic moment? A) $1s^2 2s^2 2p^6 3s^2 3p^6 3d^3$ B) $1s^2 2s^2 2p^6 3s^2 3p^6 3d^5$ C) $1s^2 2s^2 2p^6 3s^2 3p^6 3d^7$ D) $1s^2 2s^2 2p^6 3s^2 3p^6 3d^9$ 3. Which of the following does not give Cannizzaro's reaction? A) $CCl_3CHO$ B) $C_6H_5CHO$ C) HCHO D) $CH_3CHO$ 4. Which one of the following is a tridentate ligand? A) Ethylene diamine B) Ammonia C) Oxalato D) 1, 2,3 - triamino propane 5. In the compound $CoCl.5NH_3$ A) All the Cl show primary valency only. B) All the Cl show primary valency and one Cl shows secondary valency. C) One Cl shows primary valency and two Cl shows primary valency as well as secondary valency. D) All the Cl show secondary valency. 6. In Dow's process, the starting raw material is A) phenol B) chlorobenzene C) aniline D) diazobenzene 7. Which of the following oxidation state is common for all lanthanoids? A) +2 B) +3 C) +4 D) +5 8. The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation of such a reaction will be (R = 8.314 JK-1 and log 2 = 0.301) A) 53.6 kJ mol-1 B) 48.6 kJ mol-1 C) 58.5 kJ mol-1 D) 60.5 kJ mol-1 9. The molarity of a solution obtained by mixing 750 mL of 0.5(M)HCI with 250 mL of 2(M)HCI will be A) 1.75 M B) 1.00 M C) 0.875 M D) 0.975 M 10. A compound with molecular mass 180 is acylated with $CH_3COCI$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is A) 2 B) 5 C) 4 D) 6 11. What volume of oxygen necessary for the complete combustion of 20 L of propane is? A) 40 L B) 60 L C) 80 L D) 100 L 12. The total number of electrons in 18 mL of water (density = 1 g mL-1) is A) 6.02 x $10^{25}$ B) 6.02 x $10^{24}$ C) 6.02 x 18 x $10^{23}$ D) 6.02 x $10^{23}$ 13. Which one of the following is a correct set with respect to molecule, hybridization and shape? A) $BeCl_2$, $sp^2$, linear B) $BeCl_2$, $sp^2$, triangular planar C) $BCl_3$, $sp^2$, triangular planar D) $BCI_3$, $sp^3$, tetrahedral 14. Two identical vessels separately contain equal masses of Hydrogen and Helium at the same temperature. Then A) the number of molecules in the two vessels are equal B) the pressure are equal C) the pressure of Hydrogen is half of that of Helium D) the pressure of Hydrogen is twice of that of Helium 15. Human body is an example of A) Open system B) Closed system C) Isolated system D) None of these 16. The unstable intermediate dichlorocarbene [:CCI2] is formed during A) Kolbe's reaction B) Friedel Craft's reaction C) Williamson's synthesis D) Reimer-Tiemann reaction 17. Transition elements are generally used as catalysts because A) They form different intermediate compound B) They are heavy metals C) They are paramagnetic D) They possess high melting points 18. In $[NiCl_4]2-$ the type of hybridization for Ni is A) $sp^3d^2$ B) $dsp^3$ C) $sp^3$ D) $dsp^2$ 19. Number of unpaired electrons in $d^4$ low spin octahedral complex are A) 1 B) 2 C) 3 D) Zero 20. The compounds A and B respectively in the following reaction are $C_6H_5NH_2 + NaNO_2 + HCI \rightarrow C_6H_5N_2Cl \xrightarrow{CuCN} C_6H_5CN$ A) Flurobenzene and phenol B) Benzene diazonium chloride and benzonitrile C) Nitrobenzene and chlorobenzene D) Phenol and bromobenzene 21. Dialysis can be used to separate A) protein and starch B) glucose and protein C) glucose and NaCl D) glucose and fructose 22. An alkyl halide reacts with sodium in dry ether to give 2,3,4,5- tetramethylhexane. The alkyl halide is A) $(CH_0)^6C. What is one way to check if A= B ? D 44 of he + the B the 41 129C4 1: 77741/ )If45 2 7637444:: /44 A In8/m45 5(4 ::8 / +7 D- 84196 18 What h4e C +7744 84) + e)he7 (474 52/75:58/C4) the6re /I 4 the4h "n7e h876 +555= D 5C4 - the" e-9287-634 D he" - :.07 87. D 49 15 he" C) (he : he" 5: the 4e1170 (A) 3 (13Bhe 154 C) 6 (13 Che (1:3 hhe4gree of 1e 5C D4 ## PHYSICS 101. The text describes a potentiometer circuit. A cell with 2V and internal resistance 0.4Ω maintains a potential drop across a resistor wire AB. A standard cell has EMF 1.02V and gives balance point at 67cm. When a standard cell replaced with one which unknown EMF e balance point shifts to 82cm. Find the EMF of new Cell. All components are shown in the circuit diagram. A) 1.25 V B) 1.5 V C) 1.75 V D) 1.8 V 102. The text describes a early model for am atom. A) - $Ζe/4\πR^3$ B) -$3Ζe/4\πR^3$ C) - $Ζe/2\πR^3$ D) - $4\Δe/3\πR^3$ 103. Equipotentials in space show a charged object travels at constant potential. 104. What are the source dimensions with: $I_D = \frac{A}{E_{e}L}$ 105. Ground state 13.6 w is on photon electron 9 eV A) $6.4 \times 10^{-7}$ B) $4 \times 10^{-7}$ C) $12.4 \times 10^{-7}$ D) $8 \times 10^{-7}$ 106. If, $R \text{(relation)} S \text{(side)} Z \text{(size)}$. what is correct? 107. Two wire $l_1, l_2$. What is relative heat? A) 1:2 B) 2:1 C) 1:8 D) Two wires 108. Dimensions are same Material is given which is stretch? 109. Given volume of 'I. Show in final? 110. Fridge forbids with what are zero? A) Kelvin B) Class C C) 1st law D) Conservation 111. What does the frequency change to slow upwards? A) Increases B) Decrease 112. Light goes into medium μ, in medium half of light. What is angle of incidence? 113. An Idealistically efficiency is applied in kW. Secondary and primary values. A) $\frac{10^4 \cdot 8^2}{2.5} V$ B) $\frac{10^4 \cdot 8}{2.5} V$ C) $\frac{10^4}{2.5 \cdot 8^2} V$ D) V $\frac{10^4 }{2.5 8} V$ 114. What is the oscillation relationship if above a plane positive is over period? A) > I B) {1, 2, 3) and is known as list 8 D) -5 a " - b c h 702, 4 the e11t 7 / A :56 b-C, de7 ) If 7 (C 111 /:7/7 ### blank page ### blank page ### blank page