Chemistry
1. What would be the EMF of the cell in which the following reaction occurs:
$$\begin{aligned}
& \mathrm{Cd}(\mathrm{S})+2 2. $$\text { Identify }[\mathrm{B}] \text { and }[\mathrm{C}] \text { formed in the reactions given below. }$$
3. Identify the 2 chemical tests which is not answered by Glucose having an open chain structure
[A] Reaction with Schiff's4. A d - block metal $$\mathrm{X}(\mathrm{Z}=26)$$ forms a compound $$[\mathrm{X}(\mathrm{CN})_2(\mathrm{CO})_4]^{+}$$. Cal5. Which one of the following compounds shows Geometrical isomerism?6. A sweet smelling organic compound $$[\mathrm{A}]\left(\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}_2\right)$$ undergoes acid 7. Arrange the following ions in the increasing order of their $$\Delta H_{(\text {hydration})}$$ values.
$$\mathrm{Cr}^{2+8. What is the final product formed when Toluene undergoes the following series of reactions?
9. The time required for $$80 \%$$ of a first order reaction is "$$y$$" times the half-life period of the same reaction. Wh10. The standard enthalpy of formation of $$\mathrm{CH}_4$$, the standard enthalpy of sublimation of Carbon and the bond dis11. From the following compounds, identify the one which is most acidic.
12. An inorganic salt comprises of atoms of elements $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$. If the oxidation numbers13. The rate constant for the reaction $$\mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$$ at $$500 \mathrm{~K}$$ is given as $14. An organic compound $$[\mathrm{A}]\left(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}\right)$$, on reaction with conc. $$\math15. For the reaction $$\mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \rightarrow 2 \mathrm{NOCl}_{(\mathrm{g})}$16. $$\mathrm{K}_{\mathrm{H}}$$ for $$\mathrm{O}_2$$ at $$293 \mathrm{~K}$$ is $$34.86 \mathrm{~kbar}$$. What should be the 17. The permanganate ion in acid medium acts as an oxidant and gets converted to its lower oxidation state. What would be th18. $$\mathrm{A}_3 \mathrm{~B}_4$$ is a sparingly soluble salt with a solubility of $$\mathrm{s} g / \mathrm{L}$$. If the Mo19. Given below are 4 graphs [A], [B], [C] and [D]
Identify the 2 graphs that represent a Zero order reaction?20. A given mass of a hydrocarbon on complete combustion produced $$176 \mathrm{~g}$$ of $$\mathrm{CO}_2$$ and $$90 \mathrm{21. An unsaturated hydrocarbon $$[\mathrm{A}]$$ reacts with $$\mathrm{HBr}$$ in presence of Benzoyl peroxide to yield [B]
Co22. Match the compounds given in Column I with their characteristic features listed in Column II
.tg {border-collapse:coll23. Choose the group of ions / molecules in which none of the species undergo Disproportionation reaction.24. What is the amount of ice that separates out on cooling a solution containing $$60 \mathrm{~g}$$ of Ethylene glycol in $25. $$\text { If a compound } \mathrm{X}_3 \mathrm{Y} \text { is } 60 \% \text { ionised in aqueous medium, what is its van'26. A Coordination compound is represented by the formula $$[\mathrm{CoBr}_3(e n) x]$$. This compound required one mole of $27. Propane in presence of $$\mathrm{O}_2$$ gas undergoes complete combustion to produce $$\mathrm{CO}_2$$ and $$\mathrm{H}_28. Arrange the following compounds in the decreasing order of reactivity towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction.
29.
Above figure represents Vapour pressure versus Temperature graphs of 2 pure volatile liquids and a solution formed by t30. Which one of the following statements is incorrect regarding acetal and ketal formation when Propanal and Propanone are 31. Choose the incorrect statement from the following.32. $$0.1 \mathrm{M}$$ solution of $$\mathrm{AgNO}_3$$ is taken in a Conductivity cell and a potential difference of $$40 \m33. A statement of Assertion followed by a statement of Reason is given.
Choose the correct answer out of the following opti34. $$300 \mathrm{ml}$$ of an aqueous solution of $$\mathrm{NaOH}$$ with $$\mathrm{pH}$$ value of 10 is mixed with $$200 \ma35. Aniline undergoes reactions with reagents given in the order shown
(i) Aqueous $$\mathrm{Br}_2$$
(ii) $$\mathrm{NaNO}_2 36. Which one of the following shows the correct increasing order of basic nature of the given compounds?
A: Phenylmethanami37. Given: $$\Delta \mathrm{G}^0{ }_{\mathrm{f}}$$ of $$\mathrm{C}_2 \mathrm{H}_2$$ is $$2.09 \times 10^5 \mathrm{~J} / \mat38. A Carbonyl compound $$\mathrm{X}$$ when reacted with Methyl magnesium bromide followed by hydrolysis gave product $$\mat39. Identify the Reagents I and II to be used in the course of the given reactions.
40. Given below are 4 species with one odd electron on the Carbon atom.
$$\begin{array}{ll}
\mathrm{A}=\left(\mathrm{CH}_3\r41. Which one of the following compounds when reacted with $$\mathrm{NaOH}$$ (aq) undergoes Substitution Nucleophilic Bimole42. A statement of Assertion followed by a statement of Reason is given. Choose the correct answer out of the following opti43. Match the Hormones listed in Column I with their characteristics listed in Column II
.tg {border-collapse:collapse;bor44. Identify the product [D] formed when Reactant [A] $$(M M 78 \mathrm{~g} / \mathrm{mol})$$ undergoes the series of reacti45. The boiling point of a $$4 \%$$ aqueous solution of a non-volatile solute $$\mathrm{P}$$ is equal to the boiling point o46. Given below are 4 statements about Insulin. Which of these statement/(s) is/are correct?
[A] Insulin is a globular prote47. Given below are 4 subatomic particles travelling with the same velocity "v". Which of them will have the shortest wavele48. The mass number of an element $$\mathrm{X}$$ is 175 with 104 neutrons in its nucleus. Into which one of the following or49. What is the number of mono-chloro derivatives of Ethyl cyclohexane possible?50. Which one of the following is the correct IUPAC name of the given compound?
51. An aromatic hydrocarbon $$[\mathrm{A}]\left(\mathrm{Molecular}\right.$$ formula $$\left.\mathrm{C}_9 \mathrm{H}_{12}\rig52. A given chemical reaction is represented by the following stoichiometric equation.
$$3 X+2 Y+\frac{5}{2} Z \rightarrow P53. Match the chemical reactions taking place at the Anode of the cell with the correct cell in which the reaction occurs.
54. If the enthalpy of formation of a diatomic molecule $$\mathrm{AB}$$ is $$-400 \mathrm{~kJ} / \mathrm{mol}$$ and the bond55. Choose the incorrect statement from the following56. Given below are 4 equations showing Molar conductivities at infinite dilution of various electrolytes. Which one of them57. On the basis of VSEPR theory, match the molecules listed in Column I with their shapes given in Column II.
.tg {border58. Match the compounds given in column I with the corresponding most stable Carbocations formed by each, as given in Column59. Identify the pair of molecules, both of which have positive values of Dipole moment.60. Given below are 4 molecular species/ions. Identify the species/ion which exhibits diamagnetic nature.
$$[\mathrm{A}]=\ma
Mathematics
1. The side of an equilateral triangle expands at the rate of $$\sqrt{3} \mathrm{~cm} / \mathrm{sec}$$. When the side is $$2. $$
\text { If } P=\left[\begin{array}{lll}
1 & \alpha & 3 \\
1 & 3 & 3 \\
2 & 4 & 4
\end{array}\right] \text { is the ad3. $$
\text { If } f(x)=\left\{\begin{array}{cc}
\frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \4. $$\begin{aligned}
&\begin{aligned}
& \text { A, B, C are subsets of the Universal set U } \\
& \text { If } \mathrm{A}=\5. The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is6. In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are neve7. $$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to8. A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. The9. If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$10. The probability that a randomly chosen number from one to twelve is a divisor of twelve is11. Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]12. If $$f(x)=f^{\prime}(x)$$ and $$f(1)=2$$, then $$f(3)$$ is13. The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadr14. If $$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$ then the inverse of $$(A I)^t$$ 15. $$
\text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll}
x & 0 & 016. If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$17. If $$\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c$$ then the value of $$k$$ is18. $$P$$ is a point on the line segment joining the points $$(3,2,-1)$$ and $$(6,2,-2)$$. If $$x$$ coordinate of $$\mathrm{19. A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms20. The particular solution of $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$, when $$x=0, y=\frac{1}{2}$$ is21. If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ 22. The mean of the numbers $$a, b, 8,5,10$$ is 6 and the variance is 6.80 , then which of the following gives possible valu23. If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, the24. $$\int \sqrt{x^2-4 x+2} d x=$$25. $$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \26. The minimum value of $$Z=150 x+200 y$$ for the given constraints
$$\begin{aligned}
& 3 x+5 y \geq 30 \\
& x+y \geq 8 ; x27. The vector equation of two lines are
$$\begin{aligned}
& \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \28. $$
\text { If the matrix } A=\left(\begin{array}{cc}
1 & -1 \\
-1 & 1
\end{array}\right) \text { then } A^{n+1}=
$$29. $$
\text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \ca30. If $$
\left[\begin{array}{lll}
1 & x & 1
\end{array}\right]\left[\begin{array}{ccc}
1 & 3 & 2 \\
2 & 5 & 1 \\
15 & 3 & 231. $$
\int \frac{x}{x^4-16} d x=
$$32. Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection 33. An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Ot34. The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$.
The equation of the line is35. Given $$a, b, c$$ are three unequal numbers such that $$\mathrm{b}$$ is arithmetic mean of $$a$$ and $$c$$ and $$(b-a),(36. $$
\text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to }
$$37. The equation of a circle passing through the origin is $$x^2+y^2-6 x+2 y=0$$. The equation of one of its diameter is38. The particular solution of the differential equation $$\cos x \frac{d y}{d x}+y=\sin x$$ at $$y(0)=1$$39. A random variable X with probability distribution is given below
.tg {border-collapse:collapse;border-spacing:0;}
.tg 40. $$
\text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is }
$$41. $$
\text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is }
$$42. $$
\text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is }
$$43. The area (in sq units) of the minor segment bounded by the circle $$x^2+y^2=a^2$$ and the line $$x=\frac{a}{\sqrt{2}}$$ 44. Let $$f: R \rightarrow R$$ be a function defined by $$f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}$$ then45. $$
\lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals }
$$46. $$
\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0
$$47. The vector $$(\vec{r})$$ whose magnitude is $$3 \sqrt{2}$$ units which makes an angle of $$\frac{\pi}{4}$$ and $$\frac{\48. $$
\text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{1249. For a given curve $$y=2 x-x^2$$, when $$x$$ increases at the rate of 3 units/sec, then how does the slope of the curve c50. The coefficient of the third term in the expansion of $$\left(x^2-\frac{1}{4}\right)^n$$, when expanded in the descendin51. $$
\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=
$$52. $$
\text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in 53. $$
\int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is }
$$54. $$
\text { If } \frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6), x \in R \text { then }
$$55. $$
\text { The area (in sq units) enclosed by the parabola } y^2=8 x \text {, its latus-rectum and the } x \text {-axis 56. The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side th57. Express the set $$A=\{1,7,17,31,49\}$$ in set builder form58. $$
(32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to }
$$59. $$
\text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is }
$$60. Which of the following is not a homogenous function of $$x$$ and $$y$$
Physics
1. The resistance of the galvanometer and shunt of an ammeter are $$90 \mathrm{~ohm}$$ and $$10 \mathrm{~ohm}$$ respectivel2. A glass of hot water cools from $$90^{\circ} \mathrm{C}$$ to $$70^{\circ} \mathrm{C}$$ in 3 minutes when the temperature3. When two objects are moving along a straight line in the same direction, the distance between them increases by $$6 \mat4. In the Young's double slit experiment $$n^{\text {th }}$$ bright for red coincides with $$(n+1)^{\text {th }}$$ bright f5. A metal ball of $$20 \mathrm{~g}$$ is projected at an angle $$30^{\circ}$$ with the horizontal with an initial velocity 6. The threshold frequency for a metal surface is '$$n_0$$'. A photo electric current '$$I$$' is produced when it is expose7. A $$500 \mathrm{~W}$$ heating unit is designed to operate on a $$400 \mathrm{~V}$$ line. If line voltage drops to $$160 8. Current flows through uniform, square frames as shown in the figure.
In which case is the magnetic field at the centre o9. A transformer which steps down $$330 \mathrm{~V}$$ to $$33 \mathrm{~V}$$ is to operate a device having impedance $$110 \10. A cell of emf E and internal resistance r is connected to two external resistances $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$11. Select the unit of the coefficient of mutual induction from the following.12. Steel is preferred to soft iron for making permanent magnets because,13. A particle executes a simple harmonic motion of amplitude $$\mathrm{A}$$. The distance from the mean position at which i14. A body of mass $$5 \mathrm{~kg}$$ at rest is rotated for $$25 \mathrm{~s}$$ with a constant moment of force $$10 \mathrm15. In the normal adjustment of an astronomical telescope, the objective and eyepiece are $$32 \mathrm{~cm}$$ apart. If the 16. In a given semiconductor, the ratio of the number density of electron to number density of hole is $$2: 1$$. If $$\frac{17. If $$\mathrm{A}$$ is the areal velocity of a planet of mass $$\mathrm{M}$$, then its angular momentum is18. When a particular wave length of light is used the focal length of a convex mirror is found to be $$10 \mathrm{~cm}$$. I19. The mass of a particle $$\mathrm{A}$$ is double that of the particle $$\mathrm{B}$$ and the kinetic energy of $$\mathrm{20. A coil of inductance $$1 \mathrm{H}$$ and resistance $$100 \Omega$$ is connected to an alternating current source of fre21. The current through a conductor is '$$\mathrm{a}$$' when the temperature is $$0^{\circ} \mathrm{C}$$. It is '$$\mathrm{b22. Which of the following graph shows the variation of velocity with mass for the constant momentum?
23. For a $$30^{\circ}$$ prism when a ray of light is incident at an angle $$60^{\circ}$$ on one of its faces, the emergent 24. A coil offers a resistance of $$20 \mathrm{~ohm}$$ for a direct current. If we send an alternating current through the s25. A square shaped aluminium coin weighs $$0.75 \mathrm{~g}$$ and its diagonal measures $$14 \mathrm{~mm}$$. It has equal a26. If the earth has a mass nine times and radius four times that of planet X, the ratio of the maximum speed required by a 27. Two similar coils $A$ and $B$ of radius '$$r$$' and number of turns '$$N$$' each are placed concentrically with their pl28. An ideal diode is connected in series with a capacitor. The free ends of the capacitor and the diode are connected acros29. Which of the following statement is true regarding the centre of mass of a system?30. A ray of light travelling through a medium of refractive index $$\frac{5}{4}$$ is incident on a glass of refractive inde31. The ratio of the radii of the nucleus of two element $$\mathrm{X}$$ and $$\mathrm{Y}$$ having the mass numbers 232 and 232. When light wave passes from a medium of refractive index '$$\mu$$' to another medium of refractive index '$$2 \mu$$' the33. On increasing the temperature of a conductor, its resistance increases because34. The difference in energy levels of an electron at two excited levels is $$13.75 \mathrm{~eV}$$. If it makes a transition35. A string of length $$25 \mathrm{~cm}$$ and mass $$10^{-3} \mathrm{~kg}$$ is clamped at its ends. The tension in the stri36. A cubical box of side $$1 \mathrm{~m}$$ contains Boron gas at a pressure of $$100 \mathrm{~Nm}^{-2}$$. During an observa37. Around the central part of an air cored solenoid of length $$20 \mathrm{~cm}$$ and area of cross section $$1.4 \times 1038. A circular coil of radius $$0.1 \mathrm{~m}$$ is placed in the $$\mathrm{X}-\mathrm{Y}$$ plane and a current $$2 \mathrm39. A body is moving along a circular path of radius '$$r$$' with a frequency of revolution numerically equal to the radius 40. Which of the given dimensional formula represents heat capacity41. If potential (in volt) in a region is expressed as $$\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathr42. The closest approach of an alpha particle when it make a head on collision with a gold nucleus is $$10 \times 10^{-14} \43. A one $\mathrm{kg}$ block of ice at $$-1.5^{\circ} \mathrm{C}$$ falls from a height of $$1.5 \mathrm{~km}$$ and is found44. 64 rain drops of the same radius are falling through air with a steady velocity of $$0.5 \mathrm{~cm} \mathrm{~s}^{-1}$$45. The capacitance of a parallel plate capacitor is $$400 \mathrm{~pF}$$. It is connected to an ac source of $$100 \mathrm{46. Though $$\mathrm{Sn}$$ and $$\mathrm{Si}$$ are $$4^{\text {th }}$$ group elements, $$\mathrm{Sn}$$ is a metal while $$\m47. Five charges, '$$q$$' each are placed at the comers of a regular pentagon of side '$$a$$' as shown in figure. First, cha48. Two circular coils of radius '$$a$$' and '$$2 a$$' are placed coaxially at a distance ' $$x$$ and '$$2 x$$' respectively49. A metallic rod of $$2 \mathrm{~m}$$ length is rotated with a frequency $$100 \mathrm{~Hz}$$ about an axis passing throug50. The power of a gun which fires 120 bullet per minute with a velocity $$120 \mathrm{~ms}^{-1}$$ is : (given the mass of e51. The width of the fringes obtained in the Young's double slit experiment is $$2.6 \mathrm{~mm}$$ when light of wave lengt52. An electric bulb of volume $$300 \mathrm{~cm}^3$$ was sealed off during manufacture at a pressure of $$1 \mathrm{~mm}$$ 53. Find the binding energy of the tritium nucleus:
[Given: mass of $$1 \mathrm{H}^3=3.01605 \mathrm{~u} ; \mathrm{~m}_{\mat54. In a single slit diffraction experiment, for slit width '$$\alpha$$' the width of the central maxima is '$$\beta$$'. If 55. Two charges '$$-q$$' each are fixed, separated by distance '$$2 d$$'. A third charge '$$q$$' of mass '$$m$$' placed at t56. Two metal spheres, one of radius $$\frac{R}{2}$$ and the other of radius $$2 \mathrm{R}$$ respectively have the same sur57. Find the value of '$$n$$' in the given equation $$P=\rho^n v^2$$ where '$$P$$' is the pressure, '$$\rho$$' density and '58. A stone of mass $$2 \mathrm{~kg}$$ is hung from the ceiling of the room using two strings. If the strings make an angle 59. A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as 60. If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are $$\mathrm{a}, \mathrm{b}$$
1
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is
A
$$(-4,-1,-3)$$
B
$$(4,-1,-3)$$
C
$$(-4,-1,3)$$
D
$$(-4,1,-3)$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?
A
$$8!\times \frac{9}{2}$$
B
$$8!\times \frac{7}{2}$$
C
$$7!\times \frac{9}{2}$$
D
$$9!\times \frac{7}{2}$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to
A
$$a^{-\frac{3}{2}}$$
B
$$\frac{1}{2 a^{\frac{3}{2}}}$$
C
$$\frac{1}{2}$$
D
$$2 a^{-\frac{3}{2}}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability that the two numbers are equal is
A
$$\frac{5}{64}$$
B
$$\frac{1}{5}$$
C
$$\frac{1}{16}$$
D
$$\frac{1}{8}$$
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Chemistry
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Mathematics
60
Physics
60
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