Chemistry
1. What is the total number of electrons that can have the values $$n=2, l=1, s=1 / 2$$ in the electronic configuration $$1 2. Calculate the wavelength associated with an electron moving with a velocity of $$10^6 \mathrm{~m} / \mathrm{s}$$ (mass o 3. Which of the following pairs is not correctly matched? 4. The orbital diagram in which Aufbau principle is violated is 5. How does electron affinity change when we move from left to right in a period in the Periodic Table? 6. Which of the following statements is not correct? 7. Which of the following statements is correct? 8. Which of the following oxides of group 16 has the highest boiling point? 9. Specify the coordination number of cobalt in $$\left[\mathrm{Co}(\mathrm{CN})\left(\mathrm{H}_2 \mathrm{O}\right)(\mathr 10. Which of the following complexes is square planar and diamagnetic? 11. Which type of isomerism is exhibited by $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$$ ? 12. When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal 13. In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called 14. If $$\Delta H$$ and $$\Delta S$$ are positive for a reaction, the reaction will be spontaneous only when 15. A catalyst is a substance which 16. Consider the reaction,
$$2 \mathrm{~N}_2 \mathrm{O}_5(g) \longrightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$
The rate l 17. The $$[\mathrm{OH}]^{-}$$ in a solution is $$1 \mathrm{~mol} \mathrm{~L}^{-1}$$. The $$\mathrm{pH}$$ of the solution is 18. The solubility of $$\mathrm{Fe}(\mathrm{OH})_3$$ is $$x \mathrm{~mol} \mathrm{~L}^{-1}$$. Its $$K_{\mathrm{sp}}$$ would 19. When an electrolytic solution conducts electricity, the current is carried by 20. An electrochemical cell has two half cell reactions as,
$$\begin{aligned}
A^{2+}+2 e^{-} & \longrightarrow A ; E_{A^{2+} 21. The number of optical isomers of the compound $$\mathrm{CH}_3 \mathrm{CHBrCHBrCOOH}$$ is 22. Which of the following compounds will exhibit cis-trans (geometrical) isomerism? 23. The hybridization of carbon atoms in $$\mathrm{C}-\mathrm{C}$$ single bond of $$\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH 24. Which of the following groups is ortho and para directing? 25. Phenol on treatment with conc. $$\mathrm{HNO}_3$$ gives 26. Which of the following compounds will be formed when methoxy benzene is reacted with $$\mathrm{HBr}$$ ? 27. When ethanol and $$\mathrm{I}_2$$ are heated in the presence of $$\mathrm{Na}_2 \mathrm{CO}_3$$, the yellow crystals obt 28. Identify B in the following series of reaction
$$\mathrm{CH}_3 \mathrm{CHO} \xrightarrow{\mathrm{CH}_3 \mathrm{MgX}} A \ 29. Among the following, the least reactive aldehyde is 30. Propanal on reaction with lithium aluminium hydride gives 31. Identify Z in the following sequence
$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{I} \xrightarrow{\mathrm{KCN}} X \xrightarrow{ 32. Treatment of aniline with bromine water produces 33. Which of the following compounds has maximum acidic character? 34. $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl} \xrightarrow{\mathrm{NH}_3} X \xrightarrow{\mathrm{P}_2 \mathrm{O}_5} Y \xrigh 35. Chlorobenzene can be prepared by reacting aniline with 36. Electrolysis of an aqueous solution of sodium ethanoate gives 37. The reaction given below is an example of which of the following?
$$2 \mathrm{CH}_3 \mathrm{Br}+2 \mathrm{Na} \xrightarr 38. Which of the following is least reactive to nitration? 39. Nucleic acids are polymers of 40. Which of the following enzymes helps in digestion of proteins?
English
1. I can write with .............. hand. 2. Your friend ............. too much. 3. We bought ............. books. 4. Select the antonym for the word 'Bane'. 5. Pick out the correct synonym of the word 'Treason'.
Mathematics
1. The value of $$\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left\{\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+ 2. If $$\theta=\frac{\pi}{2^n+1}$$, then the value of $$2^n \cos \theta \cos 2 \theta \cos 2^2 \theta \ldots \cos 2^{n-1} \ 3. Using the principal values, the value of $$\sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}+\tan ^{-1}\left\{\tan \frac{\pi 4. Find the value of $$\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{3}{5}\right)$$. 5. If $$A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$$, then $$\left(A-A^{\prime}\right)$$ is equal to (wher 6. If $$A^{-1}=\left[\begin{array}{rr}5 & -2 \\ -7 & 3\end{array}\right]$$ and $$B^{-1}=\frac{1}{2}\left[\begin{array}{rr}9 7. $$\lim _\limits{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}$$ is equal to 8. The value of $$\lim _\limits{n \rightarrow \infty}\left\{\frac{1+2+3+\ldots+n}{n+2}-\frac{n}{2}\right\}$$ is 9. If $$y=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots$$, then $$\frac{d y}{d x}$$ is equal to 10. The value of $$\frac{d}{d x}\left(x^n \log _a x e^x\right)$$ is 11. The interval in which the function $$f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi$$ is strictly decreasing, is 12. The slope of normal to the curve $$y=x^3+2 x+6$$ which is parallel to line $$x+14 y+4=0$$ is 13. If $$f(x)=\left\{\begin{array}{cc}\frac{(1-\cos 4 x)}{x^2}, & \text { if } x 0\end{array}\right.$$ then $$f(x)$$ is con 14. The value of $$\int\limits_0^{\pi / 2} \frac{d x}{1+\tan x}$$ is 15. Evaluate $$\int \frac{3 x-2}{(x+3)(x+1)^2} d x$$. 16. The general solution of the linear differential equation $$\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \fra 17. On solving the differential equation $$x^2 y d x-\left(x^3+y^3\right) d y=0$$, the value of $$\log y$$ is 18. The particular solution of the differential equation $$\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x$$, such that $$y(\pi / 2) 19. The area bounded by the circle $$x^2+y^2=16$$ and the line $$y=x$$ in the first quadrant is 20. The focal distance of the point $$(x, y)$$ from the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$$ is 21. The equation of a straight line which cuts off intercept on $$X$$-axis which is twice that on $$Y$$-axis and is at a uni 22. The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpen 23. The radius of the circle $$(x \cos \theta+y \sin \theta-a)^2+(x \sin \theta-y \cos \theta-b)^2=k^2$$ is 24. The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to it 25. The eccentricity of the ellipse $$25 x^2+9 y^2-150 x-90 y+225=0$$ is 26. A bag contains 50 tickets numbered $$1,2,3, ..., 50$$ of which five are drawn at random and arranged in ascending order 27. Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently 28. If $$(3,4,-1)$$ and $$(-1,2,3)$$ be end points of the diameter of a sphere, then the radius of the sphere is 29. The following lines are
$$\begin{aligned}
\mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathb 30. The position vector of a point $$R$$ which divides the line joining $$P(6,3,-2)$$ and $$Q(3,1,-4)$$ in the ratio $$2 : 1 31. The angle between the lines $$\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0}, \frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}$$ is 32. The cartesian product $$A \times A$$ has 9 elements among which are found $$(-1,0)$$ and $$(0,1)$$, then set $$A$$ is eq 33. If $$S=\{(a, b): b=|a-1|, a \in Z$$ and $$|a| 34. The quotient of the identity function by the reciprocal function is given by 35. Which of the following is not a function?
36. If $$(1+i)(2 i+1)(1+3 i) \ldots(1+n i)=x+i y$$, then $$2 \cdot 5 \cdot 10 \ldots\left(1+n^2\right)$$ is equal to 37. The non-zero solutions of the equation $$z^2+|z|=0$$, where $$z$$ is a complex number, are 38. The coefficient of the term independent of $$x$$ in the expansion $$\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x 39. Which of the following is the correct principle of Mathematical induction? 40. The negation of $$\sim s \vee(\sim r \wedge s)$$ is equivalent to
Physics
1. The Young's modulus of a rope of $$10 \mathrm{~m}$$ length and having diameter of $$2 \mathrm{~cm}$$ is $$200 \times 10^ 2. The zeroth law of thermodynamics for three systems $$A, B$$ and $$C$$ in contact demands that 3. The velocity of sound in a gas is $$1300 \mathrm{~m} / \mathrm{s}$$ at STP and specific heat at constant pressure is $$6 4. The net electric force on a charge of $$+3 \mu \mathrm{C}$$ at the mid-point on the line joining two charges of magnitud 5. A parallel plate capacitor of capacitance $$5 \mu \mathrm{F}$$ is charged to $$120 \mathrm{~V}$$ and then connected to a 6. 24 cells of emf $$1.5 \mathrm{~V}$$ each having internal resistance of $$1 \mathrm{~ohm}$$ are connected to an external 7. Two straight wires each $$10 \mathrm{~cm}$$ long are parallel to one another and separated by $$2 \mathrm{~cm}$$. When t 8. The alternating current in a circuit is given by $$I=50 \sin 314 t$$. The peak value and frequency of the current are 9. A bar magnet of pole strength $$10 \mathrm{~Am}$$ is cut into two equal parts breadthwise. The pole strength of each mag 10. A $$50 \mathrm{~Hz}$$ $$\mathrm{AC}$$ signal is applied in a circuit of inductance of $$(1 / \pi) \mathrm{H}$$ and resis 11. The magnetic field at a point on the axis of a long solenoid having 5 turns per $$\mathrm{cm}$$ length when a current of 12. An object is $$8 \mathrm{~cm}$$ high. It is desired to form a real image $$4 \mathrm{~cm}$$ high at $$60 \mathrm{~cm}$$ 13. When an object is placed $$40 \mathrm{~cm}$$ from a diverging lens, its virtual image is formed $$20 \mathrm{~cm}$$ from 14. Polonium has a half-life of 140 days. If we take $$20 \mathrm{~g}$$ of polonium initially then the amount of it that rem 15. According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition 16. Einstein's photoelectric equation is 17. The Brewster's law is given by the expression 18. If two slits in Young's experiment are $$0.4 \mathrm{~mm}$$ apart and fringe width on a screen $$200 \mathrm{~cm}$$ away 19. The distance of moon form the earth is $$3.8 \times 10^5 \mathrm{~km}$$. Supposing that the eye is most sensitive to the 20. Which of the following logic gates are also known as the Universal gates? 21. Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in 22. The demodulator or detector circuit consists of a 23. The power $$(P)$$ of an engine lifting a mass of $$100 \mathrm{~kg}$$ upto a height of $$10 \mathrm{~m}$$ in $$1 \mathrm 24. A silver wire of radius $$0.1 \mathrm{~cm}$$ carries a current of $$2 \mathrm{~A}$$. If the charge density in silver is 25. An electron revolves in a circle at the rate of $$10^{19}$$ rounds per second. The equivalent current is $$\left(e=1.6 \ 26. A hollow sphere of radius $$0.1 \mathrm{~m}$$ has a charge of $$5 \times 10^{-8} \mathrm{C}$$. The potential at a distan 27. The efficiency of a Carnot engine kept at the temperatures of $$27^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$ i 28. According to equipartition law of energy each particle in a system of particles have thermal energy $$E$$ equal to 29. An electric charge does not have which of the following properties? 30. Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is 31. The horizontal and vertical components of earth's magnetic field at a place are $$0.3 \mathrm{G}$$ and $$0.52 \mathrm{G} 32. A long straight wire is carrying a current of $$12 \mathrm{~A}$$. The magnetic field at a distance of $$8 \mathrm{~cm}$$ 33. The temperature coefficient of the resistance of a wire is 0.00125 per $${ }^{\circ} \mathrm{C}$$. At $$300 \mathrm{~K}$ 34. Which component of electromagnetic spectrum have maximum wavelength? 35. The induced emf in a coil of $$10 \mathrm{H}$$ inductance in which current varies from $$9 \mathrm{~A}$$ to $$4 \mathrm{ 36. If the alternating current $$I=I_1 \cos \omega t+ I_2 \sin \omega t$$ then the rms current is given by 37. A conductor of length $$5 \mathrm{~cm}$$ is moved parallel to itself with a speed of $$2 \mathrm{~m} / \mathrm{s}$$, per 38. The Rutherford scattering experiment proves that an atom consists of 39. Unpolarised light falls on two polarising sheets placed one on top of other. If the intensity of transmitted light is on 40. A person has a minimum distance of distinct vision as $$50 \mathrm{~cm}$$. The power of lenses required to read a book a
1
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0
If $$f(x)=\left\{\begin{array}{cc}\frac{(1-\cos 4 x)}{x^2}, & \text { if } x < 0 \\ a, & \text { if } x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & \text { if } x > 0\end{array}\right.$$ then $$f(x)$$ is continuous at $$x=0$$, for $$a$$
A
4
B
$$\sqrt{32}$$
C
8
D
16
2
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0
The value of $$\int\limits_0^{\pi / 2} \frac{d x}{1+\tan x}$$ is
A
$$\frac{\pi}{2}$$
B
0
C
$$\frac{\pi}{4}$$
D
$$\frac{\pi}{8}$$
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0
Evaluate $$\int \frac{3 x-2}{(x+3)(x+1)^2} d x$$.
A
$$\frac{11}{4} \log [|x+1||x+3|]+\frac{5}{2(x+1)}+C$$
B
$$\frac{11}{4} \log \left|\frac{x+3}{x+1}\right|+\frac{1}{x+1}+C$$
C
$$\frac{11}{4} \log |x+2|+\frac{5}{2}(x+3)+\frac{1}{x+1}+C$$
D
$$\frac{11}{4} \log \left|\frac{x+1}{x+3}\right|+\frac{5}{2(x+1)}+C$$
4
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0
The general solution of the linear differential equation $$\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \frac{\pi}{2}\right)$$ is
A
$$y=-x(\sec x+\tan x)^{-1}+\frac{c}{\sec x+\tan x}+1$$
B
$$y=x+\frac{C}{\sec x+\tan x}+\frac{1}{\tan x}$$
C
$$y=\frac{x+1}{\sec x+\tan x}+C$$
D
$$y=x+\sec x+\tan x+C$$
Paper analysis
Total Questions
Chemistry
40
English
5
Mathematics
40
Physics
40
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