TS EAMCET 2020 (Online) 10th September Morning Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. The degeneracy of the level of hydrogen atoms that contain the energy of $\left(\frac{-R_{\mathrm{H}}}{16}\right)$ is 2. Wavelength of $\mathrm{H}^{+}$ion with kinetic energy 1.65 eV is (mass of proton $=1.6726 \times 10^{-27} \mathrm{~kg}$ 3. Assertion (A) $\mathrm{Mg}^{2+}$ and $\mathrm{Al}^{3+}$ are isoelectronic but the magnitude of ionic radius of $\mathrm{ 4. The successive ionisation energy values for an element ' $X$ ' are given below : (i) 1st ionisation energy $=410 \mathrm 5. $$ \text { Match the following : } $$ List-I List-II A. <mrow data-mjx-texclass="ORD"> <mi 6. Which of the following molecules does not exist according to molecular orbital theory? 7. Root mean square ( rms ) speed of $\mathrm{O}_2$ is $500 \mathrm{~m} / \mathrm{s}$ at a constant temperature. Calculate 8. Which of the following describes an ideal gas? (i) The volume occupied by a gas molecule is negligible. (ii) The collisi 9. What is the $\%$ strength of 22.4 volume of $\mathrm{H}_2 \mathrm{O}_2$ solution? 10. $\mathrm{KMnO}_4$ oxidises $\mathrm{C}_2 \mathrm{H}_2 \mathrm{O}_4$ to form $\mathrm{CO}_2$. In which of the following, 11. $\Delta H$ and $\Delta S$ for a reaction are $+30.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and 0.06 $\mathrm{kJK}^{-1} \mathrm 12. The vapour density of $\mathrm{N}_2 \mathrm{O}_4$ in $\mathrm{N}_2 \mathrm{O}_4 \rightleftharpoons 2 \mathrm{NO}_2$ is 4 13. What is the equilibrium constant $\left(K_C\right)$ for the given reaction? $$ \mathrm{N}_2+\mathrm{O}_2 \rightleftharpo 14. Hard water contains ion of 15. Predict the feasibility of the given reactions in aqueous solution (i) $\mathrm{Be}(\mathrm{OH})_2+2 \mathrm{OH}^{-} \lo 16. What is the nature of the bonding in anhydrous $\mathrm{AlCl}_3$ and hydrated $\mathrm{AlCl}_3$ respectively? 17. Which of the following elements reacts with water? 18. Biochemical oxygen demand (BOD) is a measure of organic materials present in water, BOD value less than 5 ppm indicates 19. Sodium fusion extract of aniline when heated with ferrous sulphate solution and then acidified with concentrated $\mathr 20. Ethyl phenyl acetylene (1-phenyl-1-butyne) on reduction with partially deactiveated palladised charcoal (Lindlar's catal 21. Which one of the following methods is suitable to generate aromatic compound(s) from linear aliphatic saturated hydrocar 22. Copper crystallises in ccp arrangement and accepted value of metal ion radius was found to be $1.14 \mathop {\rm{A}}\lim 23. $A^{2+}, B^{2+}$ and $C^{-}$form an ionic complex like $A_{x-2}\left[B(C)_x\right]_2$. If the complex is $75 \%$ dissoci 24. The freezing point of equimolal aqueous solution will be highest for 25. The standard electrode potentials of $\mathrm{Ag}^{+} / \mathrm{Ag}$ is +0.80 V and $\mathrm{Cu}^{+} / \mathrm{Cu}$ is + 26. For a zero order reaction, the plot of concentration of reactant vs time is (Hint: Consider the intercept on the concent 27. The gold numbers of gelatin, haemoglobin and sodium acetate are $5 \times 10^{-3}, 5 \times 10^{-2}$ and $7 \times 10^{- 28. Which one of the following ores does not contain iron? 29. When copper metal is treated with cold and dilute nitric acid, it forms 30. Which one of the following is not a colourless compound? 31. Which of the following statement is not true about interstitial complexes? 32. Which of the following molecules is colourless? 33. Which of the following vinyl derivatives is the most reactive towards anionic polymerisation? 34. Amino acids containing heterocyclic ring are (i) Histidine (ii) Valine (iii) Arginine (iv) Proline 35. Which among the following is an arsenic based antibiotic drug, for which Paul Ehrlich was awarded Noble prize in 1908. 36. $$ \text { The major product in the following reaction sequence is } $$ 37. $$ \text { Which of the following gives alcohol/phenol products? } $$ 38. $$ \text { The major products } P \text { and } Q \text { in the following reactions are } $$ 39. $$ \text { In the following reactions, } P, Q \text { and } R \text { are } $$ 40. $$ \text { Following transformation can be accomplished by } $$

Mathematics

1. Let $f:[0,10] \rightarrow[1,20]$ be a function defined as $$ f(x)=\left\{\begin{array}{ll} \frac{60-5 x}{3}, & 0 \leq x 2. The domain of the function, $f(x)=\sqrt{\log _{10}\left(\frac{5 x-x^2}{4}\right)}$ is 3. Let the greatest common divisor of $m, n$ be 1 . If $\frac{1}{1 \cdot 7}+\frac{1}{7 \cdot 13}+\frac{1}{13 \cdot 19}+\ldo 4. If $A, B$ are two non singular matrices of order $3,|B|=k$, a positive integer, then match the items of list-I with the 5. All the real values of $p, q$ so that the system of equations $$ 2 x+p y+6 z=8, x+2 y+q z=5 $$ and $\quad x+y+3 z=4$ may 6. If $p$ and $q$ are two distinct real values of $\lambda$ for which the system of equations $$ \begin{array}{r} (\lambda- 7. Let $z=x+i y$ be a complex number, $A=\{z /|z| \leq 2\}$ and $B=\{z /(1-i) z+(1+i) \bar{z} \geq 4\}$ Then which one of t 8. The solutions of the equation $z^2\left(1-z^2\right)=16, z \in \mathbf{C}$, lie on the curve 9. If $z, \bar{z},-z,-\bar{z}$ forms a rectangle of area $2 \sqrt{3}$ square units, then one such $z$ is 10. $$ \left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^8+\left(\frac{1+\cos \theta-i \sin \theta}{1 11. Let $S$ be the set of all possible integral values of $\lambda$ in the interval $(-3,7)$ for which the roots of the quad 12. $\alpha$ is the maximum value of $1-2 x-5 x^2$ and $\beta$ is the minimum value of $x^2-2 x+r$. If $5 \alpha x^2+\beta x 13. For the equation $x^4+x^3-4 x^2+x-1=0$ the ratio of the sum of the squares of all the roots to the product of the distin 14. If $\alpha_1, \beta_1, \gamma_1, \delta_1$ are the roots of the equation $a x^4+b x^3+c x^2+d x+e=0$ and $\alpha_2, \bet 15. The total number of three digit and five digit integers which can be formed by using the digits $0,1,2,3,4,5$ but using 16. At an election a voter may vote for any number of candidates not exceeding the number to be elected. If 4 candidates are 17. Let $x \in \mathbf{R}$ be so small that the powers of $x$ beyond two are insignificant and negligibly small. For such $x 18. For $0 19. If $\frac{4 x^2+5 x^4+7}{\left(x^2+1\right)\left(x^4+x^2+1\right)}=\frac{A x+B}{x^2+1} +\frac{C x^3+D x^2+E x+F}{x^4+x^2 20. $$ \begin{aligned} \sin ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}-\sin ^4 \frac{3 \pi}{8} & +\sin ^4 \frac{5 \pi}{8} +\c 21. $$ \operatorname{cosec}^{-1}\left[\left(\frac{\tan ^2\left(\frac{\alpha-\pi}{4}\right)-1}{\tan ^2\left(\frac{\alpha-\pi} 22. Assertion (A) If $A=15^{\circ}, B=17^{\circ}$ and $C=13^{\circ}$, then $\cot 2 A+\cot 2 B+\cot 2 C=\cot 2 A \cot 2 B \co 23. The solution set of the trigonometric equation $\tan \theta+5 \cot \theta=\sec \theta$ is 24. If $\tan ^{-1} \frac{1}{5}+\frac{1}{2} \sec ^{-1} x+\tan ^{-1} \frac{1}{8}=\frac{\pi}{8}$, then $x^2=$ 25. Assertion $(\mathrm{A}) \operatorname{cosech}^{-1}(3)=\log \left(\frac{1+\sqrt{10}}{3}\right)$ Reason (R) $e^{\operatorn 26. In a $\triangle A B C$ if $\angle A=3 \angle B, C A=9$ and $B C=16$, then the length of $A B$ is 27. In $\triangle A B C, \frac{1+\cos C}{r_1+r_2}+\frac{1+\cos A}{r_2+r_3}+\frac{1+\cos B}{r_1+r_3}=$ 28. In a triangle $A B C$, if $\cos A \cos B+\sin A \sin B \sin C=1$, then $a: b: c=$ 29. Let $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$ be two non collinear vectors, $\mathbf{O P}=x_1 \mathbf{a}+y_1 \m 30. The position vector of a point $P$ is $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{a}=-\hat{\ma 31. In a quadrilateral $A B C D$, the point $P$ divides $D C$ in the ratio $1: 3$ internally and $Q$ is the mid-point of $A 32. $\mathbf{p}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{q}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\m 33. Let $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=7 \hat{\mathbf{i}}+2 \hat{\mathbf{j 34. The shortest distance between the line $\mathbf{r}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(\hat 35. For the following frequency distribution, the variance is approximately equal to $$ \begin{array}{cccccc} \hline \begin{ 36. If the mean of the discrete distribution $8,9,6,5, x, 4$, 6, 5 is 6 , then its standard deviation (nearest to two decima 37. If $A$ and $B$ are events of a sample space such that $P(A \cup B)=\frac{3}{4}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A}) 38. Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}, P(X / Y)=\frac{1}{2}$ and $P(Y / X)=\frac{2 39. Let $A$ and $B$ be not mutually exclusive events. If $P(A)=\frac{4}{9}, P(A \cap \bar{B})=\frac{3}{7}$ then $P\left(\fra 40. If $20 \%$ of the bolts produced by a machine are defective then the probability that out of 4 bolts chosen at random, l 41. In a book consisting of 600 pages, there are 60 typographical errors. The probability that a randomly chosen page will c 42. If $M$ is the foot of the perpendicular drawn from the origin $O$ on to the variable line $L$, passing through a fixed p 43. When the origin is shifted to the point $\left(\frac{3}{2}, \frac{3}{2}\right)$ by the translation of coordinate axes, t 44. A line $L_1$ passing through $A(3,4)$ and having slope 1 cuts another line $L_2$ passing through $C$ at $B$, such that $ 45. Angles made with the $X$-axis by the two lines passing through the point $P(1,2)$ and cutting the line $x+y=4$ at a dist 46. The straight lines $x+3 y-9=0,4 x+5 y-1=0$, $p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the 47. The straight lines $x+3 y-9=0,4 x+5 y-1=0$, $p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the 48. The centroid of the triangle formed by the lines $x+y=1$ and $2 y^2-x y-6 x^2=0$ is 49. Two points from the set of concyclic points of the circle passing through $(1,1),(2,-1),(3,2)$ is 50. If the polar of a point $P$ with respect to a circle of radius $r$ which touches the coordinate axes and lies in the fir 51. If the circles $x^2+y^2-2 x-2(3+\sqrt{7}) y+8+6 \sqrt{7}=0$ and $x^2+y^2-8 x-6 y+k^2=0, k \in \mathbf{Z}$, have exactly 52. The circle $S=0$ cuts the circles $C_1=x^2+y^2-8 x-2 y+16=0$ and $C_2=x^2+y^2-4 x-4 y-1=0$ orthogonally. If the common c 53. The equation of the circle passing through the points of intersection of the two orthogonal circles $S_1=x^2+y^2+k x-4 y 54. Consider the parabola $y^2+2 x+2 y-3=0$ and match the items of List-I with those of the List-II. $$ \begin{array}{llll} 55. The normal at a point on the parabola $y^2=4 x$ passes through $(5,0)$. If there are two more normals to this parabola w 56. The eccentricity of an ellipse passing through $(3 \sqrt{2}, \sqrt{10})$ with foci at $(-4,0)$ and $(4,0)$ is 57. If the product of the lengths of the perpendiculars drawn from the foci to the tangent $y=\frac{-3}{4} x+3 \sqrt{2}$ of 58. The equation of the hyperbola, whose eccentricity is $\sqrt{2}$ and whose foci are 16 units apart, is 59. If the points $A(-1,0,7), B(3,2, t), C(5, k,-2)$ are collinear, then the ratio in which the point $P(t, k-2 t, t+k)$ div 60. The direction cosines $l, m, n$ of two lines are satisfying $3 l+m+5 n=0$ and $6 m n-2 n l+5 l m=0$. If $\theta$ is the 61. A tetrahedron has vertices $O(0,0,0), A(1,2,1)$, $B(2,1,3), C(-1,1,2)$. If $\theta$ is the angle between the faces $O A 62. If $\log (1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots \ldots \infty$ and $\mathop {\lim }\limits_{x \to 0} \ 63. If $f(x)=\left\{\begin{array}{ll}k, & \text { for } x=1 \\ \frac{(9 x-1)(\sqrt{x}-1)}{3 x^2+2 x-5}, & \text { for } x \n 64. let $g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0$. If $F(x)=f(x) g(x), G(x)=f^{\prime}(x) g^{\p 65. If $y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}$, then $\frac{d y}{d x}=$ 66. Let $f(x)$ and $g(x)$ be twice differentiable functions such that $f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)$ and $g 67. If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec, then the rate (in units/sec) at w 68. Let $a$ be a fixed positive real number and $n$ be an arbitrary constant. For the curve $y=\frac{x^n}{a^{n-1}}$, if the 69. In each of the choices given below, a function and an interval are given. The correct choice having a function and the a 70. Let $P(x)$ be a polynomial of degree 3 having extreme value at $x=1$. If $\mathop {\lim }\limits_{x \to 0}\left(\frac{P( 71. $$ \int \frac{y^2+\sqrt[3]{y^4}+\sqrt[6]{y^2}}{y\left(1+\sqrt[3]{y^2}\right)} d y= $$ 72. For $k \in(1, \infty), \int \frac{1}{1+k \cos x} d x=$ 73. $$ \int e^{-3 x}\left(x^2+\sin 4 x\right) d x= $$ 74. If $\int \frac{2 x^{12}+5 x^9}{\left(1+x^3+x^5\right)^3} d x=\frac{x^m}{l\left(1+x^3+x^5\right)^r}+C$, then $\frac{m-l}{ 75. $$ \mathop {\lim }\limits_{x \to \infty }\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots \ldots\ 76. $$ \int_{\pi / 4}^{\pi / 2} \frac{3 d x}{1+e^{\sqrt{8} \sin \left(x-\frac{3 \pi}{8}\right)}}= $$ 77. If the area of the region bounded by $y=\cos x, y=\sin x$, $x=\pi / 4$ and $x=\pi$ is bisected by the line $x=a$, then $ 78. If the family of curves $y=a e^{4 x}+b e^{-x}$, where $a, b$ are arbitrary constants represents the general solution of 79. If the length of the sub tangent at any point $p(x, y)$ on a curve $f(x, y)=0$ is $x+7 y^2$, then $f(x, y)=$ 80. If the general solution of the differential equation $(y-x+1) d y-(y+x+2) d x=0$ is $f(x, y, c)=0$, then the value of $c

Physics

1. The nuclear forces are 2. Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period $T$,which is pro 3. A car travelling at $15 \mathrm{~m} / \mathrm{s}$ overtake another car travelling at $10 \mathrm{~m} / \mathrm{s}$. Assu 4. If a body moving in a circular path maintains constant speed of $10 \mathrm{~ms}^{-1}$, then which of the following corr 5. If $0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is a unit vector, then $c$ is 6. A projectile is launched from point $A$ of the given landscape with a water body as shown in the diagram. The launching 7. When a bullet is fired from a rifle its momentum becomes $20 \mathrm{~kg}-\mathrm{ms}^{-1}$. If the velocity of the bull 8. A block is between two surfaces as shown in the figure. Find the normal reaction at both surfaces. [Assume, $g=10 \mathr 9. When a body is acted upon by a resultant force, then the work done by the resultant force is equal to 10. A force acts on a body of mass 10 kg , resulting in its displacement given as $x=\left(\frac{t^3}{25}\right) \mathrm{m}$ 11. A bullet of mass 25 g moves horizontally at a speed of $250 \mathrm{~m} / \mathrm{s}$ is fired into a wooden block of ma 12. A circular hole of radius 3 cm is cut out from a uniform circular disc of radius 6 cm . The centre of the hole is at 3 c 13. For a particle executing SHM, determine the ratio of average acceleration of the particle between extreme position and e 14. Choose the correct statement. 15. A slab of side 50 cm and thickness 10 cm is subjected to a shearing force of $10^5 \mathrm{~N}$ on its narrow edge. If t 16. A meniscus drop of radius 1 cm is sprayed into $10^6$ droplets of equal size. Calculate the energy expended if surface t 17. The specific heat of helium at constant volume is 12.6 J $\mathrm{mol}^{-1} \mathrm{~K}^{-1}$. The specific heat of heli 18. A composite slab is prepared with two different materials $A$ and $B$. The relation between their coefficient of thermal 19. Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} \mathrm{C}$ is $W$. Then, the work don 20. If a gas has $n$ degrees of freedom, then the ratio of $\frac{C_p}{C_V}$ is 21. A bus moving with an uniform speed of $72 \mathrm{~km} / \mathrm{h}$ towards a building blows a horn of frequency 1.7 kH 22. If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on th 23. On using red light $(\lambda=6600 \mathop {\rm{A}}\limits^{\rm{o}})$ in Young's double slit experiment, 60 fringes are o 24. Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe width 25. If a proton is moved against the coulomb force of an electric field, then 26. Assume each oil drop consists of a capacitance of $C$. If combine $n$ drops to form a bigger drop, then the capacitance 27. A conductor of length 100 cm and area of cross-section $1 \mathrm{~mm}^2$ carries a current of 5 A . If the resistivity 28. If the Wheatstone's bridge with four resistors $R_1, R_2$ and $R_3, R_4$ is balanced, then the correct expression is 29. A circular coil of 10 turns and radius 10 cm is placed in a uniform magnetic field of 0.1 T normal to the plane of the c 30. A 50 cm long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of inducti 31. If relative permeability of iron is 5500 , then its susceptibility is 32. A moving coil galvanometer of resistance $100 \Omega$ is used as an ammeter using a resistance $0.1 \Omega$. The maximum 33. In $C R$-circuit the growth of charge on the capacitor is 34. What is the amplitude of the electric field in a parallel beam of light intensity $\left(\frac{15}{\pi}\right) \frac{\ma 35. Photons of energy 2.4 eV and wavelength $\lambda$ fall on a metal plate and release photoelectrons with a maximum veloci 36. The ratio of maximum to minimum wavelength in Balmer series of an hydrogenic atom is 37. Alpha rays emitted from a radioactive substance are 38. Which of the following depicts the output of the full wave rectifier with capacitor filter for the following AC input? 39. The Boolean expression of the circuit given in figure is 40. A message signal of frequency 10 kHz and peak voltage of 15 V is used to modulate a carrier frequency of 1 MHz and peak

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

In $\triangle A B C, \frac{1+\cos C}{r_1+r_2}+\frac{1+\cos A}{r_2+r_3}+\frac{1+\cos B}{r_1+r_3}=$

$\frac{2}{3 R}$

$\frac{R}{2}$

$\frac{3}{2 R}$

$\frac{6 R}{5}$

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

In a triangle $A B C$, if $\cos A \cos B+\sin A \sin B \sin C=1$, then $a: b: c=$

$1: 1: \sqrt{2}$

$1: 1: 1$

$\sqrt{2}: 1: 1$

$1: \sqrt{2}: 1$

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

Let $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$ be two non collinear vectors,

$\mathbf{O P}=x_1 \mathbf{a}+y_1 \mathbf{b}, \mathbf{O Q}=x_2 \mathbf{a}+y_2 \mathbf{b}$ and $\mathbf{A}^{\prime} \mathbf{O}=\mathbf{O A}$,

$\mathbf{B}^{\prime} \mathbf{O}=\mathbf{O B}$. If $x_1=\frac{-3}{4}, x_2=\frac{1}{3}, y_1=\frac{7}{4}, y_2=\frac{5}{3}$, then

$P$ lies inside the $\triangle A^{\prime} O B$ and $Q$ lies outside the $\triangle A O B$

$P$ lies outside the $\triangle A O B^{\prime}$ and $Q$ lies on the $\triangle A^{\prime} O B^{\prime}$

$P$ lies inside the $\triangle A O B$ and $Q$ lies outside the $\triangle A O B^{\prime}$

$P$ lies on the $\triangle A^{\prime} O B$ and $Q$ lies outside the $\triangle A O B$

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

The position vector of a point $P$ is $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{a}=-\hat{\mathbf{i}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors which determine a plane $\pi$. The equation of a line through $P$ normal to $\mathbf{b}$ and lying on the plane $\pi$ is

$\mathbf{r}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(-\hat{\mathbf{i}}+5 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$

$\mathbf{r}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$

$\mathbf{r}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})$

$\mathbf{r}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(-3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})$

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