Chemistry
1. Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine? 2. Product of the following reaction is
3. Acetophenone when reacted with a base, $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{ONa}$$, yields a stable compound which has th 4. Gabriel's synthesis is used frequency for the preparation of which of the following? 5. The product P in the reaction,
6. Pick out the incorrect statement(s) from the following.
1. Glucose exists in two different crystalline forms, $$\alpha$$ 7. Which of the following is incorrect? 8. Rank the following compounds in order of increasing basicity.
9. Ammoniacal silver nitrate forms a white precipitate easily with 10. Consider the following equilibrium,
$$\begin{aligned}
& 2 \mathrm{No}(g) \rightleftharpoons \mathrm{N}_2+\mathrm{O}_2 ; 11. Which of the following is incorrect regarding Henry's law? 12. $$t$$-butyl chloride preferably undergo hydrolysis by 13. Which of these represents the correct order of decreasing bond order? 14. In a $$0.2 \mathrm{~M}$$ aqueous solution, lactic acid is $$6.9 \%$$ dissociated. The value of dissociation constant is 15. Pick up the correct statement. 16. Total number of $$\sigma$$ and $$\pi$$ bonds in ethene molecule is 17. A buffer solution has equal volumes of $$0.1 \mathrm{~M} \mathrm{~NH}_4 \mathrm{OH}$$ and $$0.01 \mathrm{~M} \mathrm{~NH 18. Assuming no change in volume, the time required to obtain solution of $$\mathrm{pH}=4$$ by electrolysis of $$100 \mathrm 19. Which of the following compounds would not be expected to decarboxylate when heated? 20. Which of these molecules have non-bonding electron pairs on the cental atom?
$$\mathrm{I}: \mathrm{SF}_4 : \mathrm{II}: 21. For a cell reaction, $$A(s)+B^{2+}(a q) \longrightarrow A^{2+}(a q)+B(s)$$; the standard emf of the cell is $$0.295 \mat 22. Which of the following shows negative deviation from Raoult's law? 23. $$5 \mathrm{~g}$$ of non-volatile water soluble compound $$X$$ is dissolved in $$100 \mathrm{~g}$$ of water. The elevati 24. The correct decreasing order of negative electron gain enthalpy for $$\mathrm{C}, \mathrm{Ca}, \mathrm{Al}, \mathrm{F}$$ 25.
I and II are 26. $$\mathrm{Ti}^{2+}$$ is purple while $$\mathrm{Ti}^{4+}$$ is colourless because 27. In Friedal-Crafts alkylation reaction of phenol with chloromethane, the product formed will be 28. Which among the following is diamagnetic? 29. Which one of the following is an important component of chlorophyll? 30. A volatile compound is formed by carbon monoxide and 31. The complex $$\left[\mathrm{PtCl}_2(\mathrm{en})_2\right]^{2+}$$ ion shows 32. $$15 \mathrm{~g}$$ of $$\mathrm{CaCO}_3$$ completely reacts with 33. Bohr's radius of 2 nd orbit of $$\mathrm{Be}^{3+}$$ is equal to that of 34. How much faster would a reaction proceed at $$25^{\circ} \mathrm{C}$$ than at $$0^{\circ} \mathrm{C}$$ if the activation 35. The blue colouration obtained from the Lassaigne's test of nitrogen is due to the formation of 36. The ion that is isoelectronic with $$\mathrm{CO}$$ is 37. At $$300 \mathrm{~K}$$, the half-life period of a gaseous reaction at an initial pressure of $$40 \mathrm{~kPa}$$ is 350 38. If 2 moles of $$\mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})$$ are completely burnt $$4100 \mathrm{~kJ}$$ of heat is liberated 39. Abnormal colligative properties are observed only when the dissolved non-volatile solute in a given dilute solution 40. Aqueous $$\mathrm{CuSO}_4$$ changes its colour from sky blue to deep blue on addition of $$\mathrm{NH}_3$$ because 41.
Identify A, B and C. 42. For a reaction, $$2 A+B \longrightarrow$$ products,
If concentration of $$B$$ is kept constant and concentration of $$A$ 43. For an adiabatic change in a system, the condition which is applicable is 44. In dilute alkaline solution $$\mathrm{MnO}_4^{-}$$ changes to 45. Which of the following complex show optical isomerism?
(i) $$c i s-\left[\mathrm{COCl}(\mathrm{en})_2\left(\mathrm{NH}_3 46. 47. Mohr's salt has the formula
Mathematics
1. The value of $$a^{\log _b c}-c^{\log _b a}$$, where $$a, b, c>0$$ but $$a, b, c \neq 1$$, is 2. The slope of the tangent to the curve, $$y=x^2-x y$$ at $$\left(1, \frac{1}{2}\right)$$ is 3. The value of $$\lim _\limits{x \rightarrow 0} \frac{e^{a x}-e^{b x}}{2 x}$$ is equal to 4. The points of intersection of circles $$(x+1)^2+y^2=4$$ and $$(x-1)^2+y^2=9$$ are $$(a, \pm b)$$, then $$(a, b)$$ equals 5. The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7 x^2+10$$ 6. The circle $$x^2+y^2+3 x-y+2=0$$ cuts an intercept on $$X$$-axis of length 7. Let $$f(x)=a+(x-4)^{\frac{4}{9}}$$, then minima of $$f(x)$$ is 8. If $$f(x) = \left\{ {\matrix{
{2\sin x} & ; & { - \pi \le x \le {{ - \pi } \over 2}} \cr
{a\sin x + b} & ; & { 9. The value of $$\lim _\limits{x \rightarrow \infty}\left(\frac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}$$ is 10. $$S \equiv x^2+y^2-2 x-4 y-4=0$$ and $$S^{\prime} \equiv x^2+y^2-4 x-2 y-16=0$$ are two circles the point $$(-2,-1)$$ li 11. A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a squar 12. The feasible region for the inequations $$x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0$$ is 13. The maximum value of $$Z=10 x+16 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 12,2 x+y \leq 20$$ is 14. If $$A=\left[\begin{array}{ll}2 & 2 \\ 3 & 4\end{array}\right]$$, then $$A^{-1}$$ equals to 15. If $$A$$ is a matrix of order $$4 \operatorname{such}$$ that $$A(\operatorname{adj} A)=10 \mathrm{~I}$$, then $$|\operat 16. If $$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$ is a singular matrix, then possible values of $$\ma 17. The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\ha 18. If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \ha 19. The maximum value of $$Z=12 x+13 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 5$$ and $$3 x+y \leq 9$$ is 20. $$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$ 21. The place $$x-2 y+z=0$$ is parallel to the line 22. $$\int \frac{x d x}{2(1+x)^{3 / 2}}$$ is equal to 23. $$\int \frac{4^x}{\sqrt{1-16^x}} d x$$ is equal to 24. $$\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x$$ is equal to 25. The lines $$\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}$$ and $$\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}$$ are perpendicu 26. If two lines $$L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$L_2: \frac{x-3}{1}=\frac{y-k}{2}=z$$ intersect at 27. A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1 28. If a number $n$ is chosen at random from the set $$\{11,12,13, \ldots \ldots, 30\}$$. Then, the probability that $$n$$ i 29. Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form t 30. If $$A, B$$ and $$C$$ are mutually exclusive and exhaustive events of a random experiment such that $$P(B)=\frac{3}{2} P 31. Using mathematical induction, the numbers $$a_n \delta$$ are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n, (n \geq 0)$$. Then 32. If $$49^n+16^n+k$$ is divisible by 64 for $$n \in N$$, then the least negative integral value of $$k$$ is 33. $$2^{3 n}-7 n-1 \text { is divisible by }$$ 34. The sum of $$n$$ terms of the series, $$\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$$ is 35. The value of $$\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}$$ is equal to 36. If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an $$\mathrm{AP}$$ is 37. The differential equation of all non-vertical lines in a plane is 38. The general solution of $$\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2$$ is 39. The solution of the differential equation $$\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)$$ is 40. $$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$ 41. In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most tw 42. If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ 43. The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as 44. The general solution of $$2 \cos 4 x+\sin ^2 2 x=0$$ is 45. If $$2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}$$, then $$f\left(x^8\right)$$ is equ 46. If $$A=\{a, b, c\}, B=\{b, c, d\}$$ and $$C=\{a, d, c\}$$ then $$(A-B) \times(B \cap C)$$ is equal to 47. If $$n(A)=p$$ and $$n(B)=q$$, then the numbers of relations from the set $$A$$ to the set $$B$$ is 48. If $$z=\sqrt{3}+i$$, then the argument of $$z^2 e^{z-i}$$ is equal to 49. If $$i=\sqrt{-1}$$ and $$n$$ is a positive integer, then $$i^n+i^{n+1}+i^{n+2}+i^{n+3}$$ is equal to 50. If $$\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$$, where $$x$$ and $$y$$ are real, then the ordere 51. There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any 52. The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition a 53. A polygon of n sides has 105 diagonals, then n is equal to 54. Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\righ 55. The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is e 56. The slope of lines which makes an angle $$60^{\circ}$$ with the line $$y-3 x+18=0$$ 57. 3 and 5 are intercepts of a line $$L=0$$, then the distance of $$L=0$$ from $$(3,7)$$ is 58. The total number of terms in the expansion of $$(x+y)^{60}+(x-y)^{60}$$ is 59. The coefficient of $$x^{29}$$ in the expansion of $$\left(1-3 x+3 x^2-x^3\right)^{15}$$ is 60. In the expansion of $$\left(1+3 x+3 x^2+x^3\right)^{2 n}$$, the term which has greatest binomial coefficient, is
Physics
1. The mean energy per molecule for a diatomic gas is 2. The phase difference between displacement and velocity of a particle in simple harmonic motion is 3. The mass density of a nucleus varies with mass number $$A$$ as 4. A capacitor of capacity $$2 ~\mu \mathrm{F}$$ is charged upto a potential $$14 \mathrm{~V}$$ and then connected in paral 5. The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in va 6. A particle is projected at an angle $$30^{\circ}$$ with horizontal having kinetic energy $$K$$. The kinetic energy of th 7. An air bubble in water $$\left(\mu=\frac{4}{3}\right)$$ is shown in figure. The apparent depth of the image of the bubbl 8. A transistor is connected in CE configuration. The collector supply is $$10 \mathrm{~V}$$ and the voltage drop across a 9. One end of the string of length $l$ is connected to a particle of mass $$m$$ and the other end is connected to a small p 10. A thin circular ring of mass ,$$M$$ and radius $$R$$ rotates about an axis through its centre and perpendicular to its p 11. Two wire of same material having radius in ratio 2 : 1 and lengths in ratio 1: 2. If same force is applied on them, then 12. In the figure, pendulum bob on left side is pulled a side to a height $$h$$ from its initial position. After it is relea 13. A gas is taken through the cycle $$A \rightarrow B \rightarrow C \rightarrow A$$, as shown in figure. What is the net wo 14. The gases carbon monoxide $$(\mathrm{CO})$$ and nitrogen at the same temperature have kinetic energies $$E_1$$ and $$E_2 15. Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $$A$$ and the 16. Starting from the centre of the earth having radius $$R$$, the variation of $$g$$ (acceleration due to gravity) is shown 17. A long spring, when stretched by a distance $$x$$, has potential energy $$U$$. On increasing the stretching to $$n x$$, 18. With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should 19. A dielectric of dielectric constant $$K$$ is introduced such that half of its area of a capacitor of capacitance $$C$$ i 20. Two very long straight parallel wires carry currents $$i$$ and $$2 i$$ in opposite directions. The distance between the 21. The magnetic flux linked with a coil satisfies the relation $$\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}$$, where $$t$$ i 22. The instantaneous values of alternating current and voltages in a circuit given as
$$\begin{aligned}
& i=\frac{1}{\sqrt{ 23. A car is moving towards a high cliff. The car driver sounds a horn of frequency $$f$$. The reflected sound heard by the 24. If escape velocity on earth surface is $$11.1 \mathrm{~kmh}^{-1}$$, then find the escape velocity on moon surface. If ma 25. An ideal gas goes from state $$A$$ to state $$B$$ via three different processes as indicated in the $$p$$-$$V$$ diagram. 26. In the series L-C-R circuit shown, the impedance is
27. In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio 28. The wavelength of the first line of Lyman series for $$\mathrm{H}$$ - atom is equal to that of the second line of Balmer 29. If $$150 \mathrm{~J}$$ of heat is added to a system and the work done by the system is $$110 \mathrm{~J}$$, then change 30. In the figure below, the capacitance of each capacitor is $$3 \mu \mathrm{F}$$. The effective capacitance between $$A$$ 31. The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of 32. In Young's double slit experiment, the ratio of maximum and minimum intensities in the fringe system is $$9: 1$$. The ra 33. In the case of an inductor 34. The height vertically above the earth's surface at which the acceleration due to gravity becomes $$1 \%$$ of its value a 35. If $$C$$ be the capacitance and $$V$$ be the electric potential, then the dimensional formula of $$\mathrm{CV}^2$$ is 36. Which logic gate is represented by the following combination logic gates?
37. An LED is constructed from a $$p$$-$$n$$ junction diode using GaAsP. The energy gap is $$1.9 \mathrm{~eV}$$. The wavelen 38. A body is projected vertically upwards. The times corresponding to height $$h$$ while ascending and while descending are 39. When a certain metal surface is illuminated with light of frequency $$\nu$$, the stopping potential for photoelectric cu 40. A fish in water (refractive index $$n$$ ) looks at a bird vertically above in the air. If $$y$$ is the height of the bir 41. A car starts from rest and accelerates uniformly to a speed of $$180 \mathrm{~kmh}^{-1}$$ in $$10 \mathrm{~s}$$. The dis 42. A plane electromagnetic wave of frequency $$20 \mathrm{~MHz}$$ travels through a space along $$x$$-direction. If the ele 43. The sides of a parallelogram are represented by vectors $$\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k 44. If $$\theta_1$$ and $$\theta_2$$ be the apparent angles of dip observed in two vertical planes at right angles to each o 45. Let $$K_1$$ be the maximum kinetic energy of photoelectrons emitted by light of wavelength $$\lambda_1$$ and $$K_2$$ cor 46. A ball is projected horizontally with a velocity of $$5 \mathrm{~ms}^{-1}$$ from the top of a building $$19.6 \mathrm{~m 47. A galvanometer having a resistance of $$8 \Omega$$ is shunted by a wire of resistance $$2 \Omega$$. If the total current 48. In the diagram shown below, $$m_1$$ and $$m_2$$ are the masses of two particles and $$x_1$$ and $$x_2$$ are their respec 49. A block of wood floats in water with $$(4 / 5)$$ th of its volume submerged. If the same block just floats in a liquid, 50. A balloon with mass $m$ is descending down with an acceleration $$a$$ (where, $$a 51. A straight wire of length $$2 \mathrm{~m}$$ carries a current of $$10 \mathrm{~A}$$. If this wire is placed in uniform m 52. Two slabs are of the thicknesses $$d_1$$ and $$d_2$$. Their thermal conductivities are $$K_1$$ and $$K_2$$, respectively 53. A square wire of each side l carries a current $$I$$. The magnetic field at the mid-point of the square
54. A cylinder of radius $$r$$ and of thermal conductivity $$K_1$$ is surrounded by a cylindrical shell of inner radius $$r$ 55. The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $$v_1$$ and $$v_2$$, respectively. 56. Two cells with the same emf $$E$$ and different internal resistances $$r_1$$ and $$r_2$$ are connected in series to an e 57. A string vibrates with a frequency of $$200 \mathrm{~Hz}$$. When its length is doubled and tension is altered, it begins 58. When $$10^{19}$$ electrons are removed from a neutral metal plate, the electric charge on it is 59. In an electrical circuit $$R, L, C$$ and $$\mathrm{AC}$$ voltage source are all connected in series. When $$L$$ is remov
1
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ is equal to
A
$$\frac{m}{m-1}$$
B
$$\frac{m+1}{m}$$
C
$$\frac{m+1}{m-1}$$
D
None of these
2
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as
A
$$\sin 2 A+\cos 2 A$$
B
$$2 \sec A \operatorname{cosec} A+2$$
C
$$\tan 2 A+\cot 2 A$$
D
$$\sec 2 A+\operatorname{cosec} 2 A$$
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of $$2 \cos 4 x+\sin ^2 2 x=0$$ is
A
$$x=\frac{n \pi}{2} \pm \sin ^{-1}\left(\frac{1}{5}\right)$$
B
$$x=\frac{n \pi}{4}+\frac{(-1)^n}{4} \sin ^{-1}\left( \pm \frac{2 \sqrt{2}}{3}\right)$$
C
$$x=\frac{n \pi}{2} \pm \cos ^{-1}\left(\frac{1}{5}\right)$$
D
$$x=\frac{n \pi}{4}+\frac{(-1)^n}{4} \cos ^{-1}\left(\frac{1}{5}\right)$$
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $$2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}$$, then $$f\left(x^8\right)$$ is equal to
A
$$\frac{\left(1-x^8\right)\left(2 x^8+3\right)}{5 x^8}$$
B
$$\frac{\left(1+x^8\right)\left(2 x^8-3\right)}{5 x^8}$$
C
$$\frac{\left(1-x^8\right)\left(2 x^8-3\right)}{5 x^8}$$
D
None of these
Paper analysis
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Chemistry
47
Mathematics
60
Physics
59
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