{"id":15580,"date":"2024-02-21T09:42:28","date_gmt":"2024-02-21T04:12:28","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=15580"},"modified":"2024-02-22T17:04:59","modified_gmt":"2024-02-22T11:34:59","slug":"tamil-nadu-11th-maths-previous-year-question-paper-march-2019-english-medium","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/tamil-nadu-11th-maths-previous-year-question-paper-march-2019-english-medium\/","title":{"rendered":"Tamil Nadu 11th Maths Previous Year Question Paper March 2019 English Medium"},"content":{"rendered":"

Students can Download Tamil Nadu 11th Maths Previous Year Question Paper March 2019 English Medium Pdf, Tamil Nadu 11th Maths Model Question Papers<\/a>\u00a0helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.<\/p>\n

TN State Board 11th Maths Previous Year Question Paper March 2019 English Medium<\/h2>\n

General Instructions:<\/p>\n

    \n
  1. The question paper comprises of four parts<\/span>.<\/li>\n
  2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.<\/li>\n
  3. All questions of Part I, II, III and IV are to be attempted separately.<\/li>\n
  4. Question numbers 1<\/span> to 20<\/span> in Part I<\/span> are Multiple Choice Questions of one mark<\/span> each.
    \nThese are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer<\/li>\n
  5. Question numbers 21<\/span> to 30<\/span> in Part II<\/span> are two-mark<\/span> questions. These are to be answered in about one or two sentences.<\/li>\n
  6. Question numbers 31<\/span> to 40<\/span> in Part III<\/span> are three-mark<\/span> questions. These are to be answered in above three to five short sentences.<\/li>\n
  7. Question numbers 41<\/span> to 47<\/span> in Part IV<\/span> are five-mark<\/span> questions. These are to be answered in detail Draw diagrams wherever necessary.<\/li>\n<\/ol>\n

    Time: 2.30 Hours
    \nMaximum Marks: 90<\/p>\n

    PART – I<\/span><\/p>\n

    I. Choose the correct answer. Answer all the questions. [20 \u00d7 1 = 20]<\/span><\/p>\n

    Question 1.
    \nThe value of x, for which the matrix A = \\(\\left[\\begin{array}{cc} e^{x-2} & e^{7+x} \\\\ e^{2+x} & e^{2 x+3} \\end{array}\\right]\\) is singular, is…………..
    \n(a) 7
    \n(b) 6
    \n(c) 9
    \n(d) 8
    \nAnswer:
    \n(d) 8<\/p>\n

    Question 2.
    \nThe nth term of the sequence 2, 7, 14, 23 …. is …………..
    \n(a) n\u00b2 + 2n + 1
    \n(b) n\u00b2 + 2n – 1
    \n(c) n\u00b2 – 2n – 1
    \n(d) n\u00b2 – 2n + 1
    \nAnswer:
    \n(b) n\u00b2 + 2n – 1<\/p>\n

    Question 3.
    \n\\(\\int \\frac{\\sec x}{\\sqrt{\\cos 2 x}} d x=\\)
    \n(a) tan-1<\/sup> (tan x) + c
    \n(b) sin-1<\/sup> (tan x) + c
    \n(c) tan-1<\/sup> (sin x) + c
    \n(d) 2 sin-1<\/sup> (tan x) + c
    \nAnswer:
    \n(b) sin-1<\/sup> (tan x) + c<\/p>\n

    \"Tamil<\/p>\n

    Question 4.
    \nThe line \\(\\frac{x}{a}\\) – \\(\\frac{y}{b}\\) = 0 has the slope 1, if ………..
    \n(a) a = b
    \n(b) only for a = 1, b = 1
    \n(c) a > b
    \n(d) a < b
    \nAnswer:
    \n(a) a = b<\/p>\n

    Question 5.
    \nThe number of five digit numbers in which all digits are even, is
    \n(a) 4 \u00d7 54<\/sup>
    \n(b) 4 \u00d7 55<\/sup>
    \n(c) 55<\/sup>
    \n(d) 5 \u00d7 5
    \nAnswer:
    \n(a) 4 \u00d7 54<\/sup><\/p>\n

    Question 6.
    \n\"Tamil
    \n(a) f (x) is continuous for all x in R
    \n(b) f(x) is differentiable for all x > a
    \n(c) f(x) is not differentiable at x = a
    \n(d) f (x) is discontinuous at x = a
    \nAnswer:
    \n(c) f(x) is not differentiable at x = a<\/p>\n

    Question 7.
    \nA number is selected from the set {1, 2, 3, 20}. The probability that the selected number is divisible by 3 or 4 is………..
    \n(a) \\(\\frac{1}{2}\\)
    \n(b) \\(\\frac{2}{3}\\)
    \n(c) \\(\\frac{2}{5}\\)
    \n(d) \\(\\frac{1}{8}\\)
    \nAnswer:
    \n(a) \\(\\frac{1}{2}\\)<\/p>\n

    Question 8.
    \nWhich of the following is not a periodic function with period 2\u03c0?
    \n(a) tan x
    \n(b) cos x
    \n(c) sin x
    \n(d) cosec x
    \nAnswer:
    \n(a) tan x<\/p>\n

    Question 9.
    \nThe straight line joining the points (2, 3) and (-1, 4) passes through (\u03b1, \u03b2) if………..
    \n(a) \u03b1 + 3\u03b2 = 11
    \n(b) 3\u03b1 + \u03b2 = 11
    \n(c) \u03b1 + 2\u03b2 = 7
    \n(d) 3\u03b1 + \u03b2 = 9
    \nAnswer:
    \n(a) \u03b1 + 3\u03b2 = 11<\/p>\n

    Question 10.
    \nThe minimum and the maximum values of |cos x| -2 are respectively………..
    \n(a) 0 and 2
    \n(b) -2 and 0
    \n(c) -2 and -1
    \n(d) -1 and 1
    \nAnswer:
    \n(c) -2 and -1<\/p>\n

    \"Tamil<\/p>\n

    Question 11.
    \nIf A = {(x, y) \/ y – ex<\/sup>, x \u2208 [0, \u221e)} and B = {(x, y) \/ y = sin x, x \u2208 [0, \u221e)} then n(A \u2229 B) is………..
    \n(a) \u221e
    \n(b) 1
    \n(c) \u03c6
    \n(d) 0
    \nAnswer:
    \n(d) 0<\/p>\n

    Question 12.
    \n\"Tamil
    \n(a) \\(\\underset { x\\rightarrow { 2 }^{ – } }{ lim } \\) f(x) = -1
    \n(b) \\(\\underset { x\\rightarrow { 0 } }{ lim } \\) f(x) does not exist
    \n(c) \\(\\underset { x\\rightarrow { 0 }^{ – } }{ lim } \\) f(x) = -1
    \n(d) \\(\\underset { x\\rightarrow { 0 }^{ + } }{ lim } \\) f(x) = 1
    \nAnswer:
    \n(b) \\(\\underset { x\\rightarrow { 0 } }{ lim } \\) f(x) does not exist<\/p>\n

    Question 13.
    \nIf f(x) = x\u00b2 – 3x, then the points at which f(x) =f'(x) are…………
    \n(a) both irrational
    \n(b) one rational and another irrational
    \n(c) both positive integers
    \n(d) both negative integers
    \nAnswer:
    \n(a) both irrational<\/p>\n

    Question 14.
    \nThe unit vector parallel to the resultant of the vectors \\(\\hat { i }\\) + \\(\\hat { j }\\) – \\(\\hat { k }\\) and \\(\\hat { i }\\) – 2\\(\\hat { j }\\) + \\(\\hat { k }\\) is …………
    \n(a) \\(\\frac{2 \\hat{i}-\\hat{j}+\\hat{k}}{\\sqrt{5}}\\)
    \n(b) \\(\\frac{2 \\hat{i}-\\hat{j}}{\\sqrt{5}}\\)
    \n(c) \\(\\frac{\\hat{i}-\\hat{j}+\\hat{k}}{\\sqrt{5}}\\)
    \n(d) \\(\\frac{2 \\hat{i}+\\hat{j}}{\\sqrt{5}}\\)
    \nAnswer:
    \n(d) \\(\\frac{2 \\hat{i}+\\hat{j}}{\\sqrt{5}}\\)<\/p>\n

    Question 15.
    \nIt is given that the events A and B are such that P(A) = \\(\\frac{1}{4}\\), P(A\/B) = \\(\\frac{1}{2}\\) and P(B\/A) = \\(\\frac{2}{3}\\). The P(B) is………..
    \n(a) \\(\\frac{2}{3}\\)
    \n(b) \\(\\frac{1}{2}\\)
    \n(c) \\(\\frac{1}{6}\\)
    \n(d) \\(\\frac{1}{3}\\)
    \nAnswer:
    \n(d) \\(\\frac{1}{3}\\)<\/p>\n

    Question 16.
    \nIf \\(\\vec { a }, \\vec { b }\\) are the position vectors of A and B, then which one of the following points whose position vector lies on AB?
    \n(a) \\(\\frac{2 \\vec{a}+\\vec{b}}{2}\\)
    \n(b) \\(\\frac{\\vec{a}-\\vec{b}}{3}\\)
    \n(c) \\(\\vec { a } + \\vec { b }\\)
    \n(d) \\(\\frac{2 \\vec{a}-\\vec{b}}{2}\\)
    \nAnswer:
    \n(a) \\(\\frac{2 \\vec{a}+\\vec{b}}{2}\\)<\/p>\n

    Question 17.
    \nIf |x + 2| \u2264 8, then x belongs to…………
    \n(a) (6, 10)
    \n(b) (-10, 6)
    \n(c) [6, 10]
    \n(d) [-10, 6]
    \nAnswer:
    \n(d) [-10, 6]<\/p>\n

    \"Tamil<\/p>\n

    Question 18.
    \nThe expansion of (1 – x)-2<\/sup> is ………..
    \n(a) 1 – x + x\u00b2 – ……
    \n(b) 1 + x + x\u00b2 + ……
    \n(c) 1 – 2x + 3x\u00b2 – ….
    \n(d) 1 + 2x + 3x\u00b2 + ……
    \nAnswer:
    \n(d) 1 + 2x + 3x\u00b2 + ……<\/p>\n

    Question 19.
    \nIf f : R \u2192 R is defined by f(x) = |x| – 5, then the range of f is………..
    \n(a) (-\u221e, -5)
    \n(b) (-\u221e, 5)
    \n(c) [-5, \u221e)
    \n(d) (-5, \u221e)
    \nAnswer:
    \n(c) [-5, \u221e)<\/p>\n

    Question 20.
    \nWhich one of the following is not true about the matrix \"Tamil
    \n(a) an upper triangular matrix
    \n(b) lower triangular matrix
    \n(c) a scalar matrix
    \n(d) a diagonal matrix
    \nAnswer:
    \n(c) a scalar matrix<\/p>\n

    PART-II<\/span><\/p>\n

    II. Answer any seven questions. Question No. 30 is compulsory. [7 \u00d7 2 = 14]<\/span><\/p>\n

    Question 21.
    \nWrite the use of horizontal line test.
    \nAnswer:
    \nHorizontal line test is used to check whether a function is one-one, onto or not.<\/p>\n

    Question 22.
    \nWrite the relationship between Permutation and Combination.
    \nAnswer:
    \nPermutation means selection followed by arrangement.
    \nCombination means selection only now selcting Y from ‘n’ things can be done in n<\/sup>Cr<\/sub> ways ….(1) (r \u2264 n)
    \nSelecting and arranging r from n things can be done in n<\/sup>Pr<\/sub> ways ……(2)
    \n‘r’ things can be arranged in r! ways …… (3)
    \nNow (2) = (1) \u00d7 (3)
    \n(i.e.,) n<\/sup>Pr<\/sub> = n<\/sup>Cr<\/sub> \u00d7 r!
    \n\u21d2 n<\/sup>Cr<\/sub> = \\(\\frac{^{n}P_r}{r!}\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 23.
    \nCount the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digits are repeated.
    \nAnswer:
    \nThe required numbers is = 1 \u00d7 8 \u00d7 7 \u00d7 2
    \n= 112<\/p>\n

    Question 24.
    \nFind the separate equations from a combined equation of a straight line 2x\u00b2 + xy- 3y\u00b2 = 0
    \nAnswer:
    \nThe combined equation is 2x\u00b2 +xy – 3y\u00b2 = 0
    \n\"Tamil
    \nFactorizing (2) (-3) = -6
    \n2x\u00b2 + xy – 3y\u00b2 = 2x\u00b2 – 2xy + 3xy – 3y\u00b2
    \n= 2x(x – y) + by (x – y) = (2x + by) (x – y)
    \n\u2234 2x\u00b2 + xy – by\u00b2 = 0 \u21d2 (2x + 3y) (x – y) = 0
    \nSo the separate equations are 2x + 3y = 0; x – y = 0<\/p>\n

    Question 25.
    \nDefine diagonal and scalar matrices.
    \nAnswer:
    \nA square matrix A = [aij<\/sub>]n \u00d7 n<\/sub> is called a diagonal matrix
    \nIf aij<\/sub> = 0 whenever i \u2260 j
    \nA square matrix A = [aij<\/sub>]n \u00d7 n<\/sub> is called a scalar matrix
    \n\"Tamil<\/p>\n

    Question 26.
    \nFind a unit vector along the direction of the vector \\(5 \\hat{i}-3 \\hat{j}+4 \\hat{k}\\)
    \nAnswer:
    \nLet \\(\\hat{a}\\) = \\(5 \\hat{i}-3 \\hat{j}+4 \\hat{k}\\)
    \n\"Tamil<\/p>\n

    Question 27.
    \nDefine a continuous function on the closed interval [a, b]
    \nAnswer:
    \nA function f : [a, b] \u2192 R is said to be continuous on the closed interval [a, b] if it continuous on the open interval (a, b) and
    \n\\(\\underset { x\\rightarrow { a }^{ + } }{ lim } \\) f(x) = f(a) and \\(\\underset { x\\rightarrow { b }^{ – } }{ lim } \\) f(x) = 1 f(x) = f(b)<\/p>\n

    Question 28.
    \nConsider the function f(x) = \u221ax, x \u2265 0. Does \\(\\underset { x\\rightarrow { 0 }}{ lim } \\) f(x) exist?
    \nAnswer:
    \n\\(\\underset { x\\rightarrow { 0 }^{ – } }{ lim } \\) \u221ax is does not exist
    \n\\(\\underset { x\\rightarrow { 0 }^{ + } }{ lim } \\) \u221ax = 0
    \n\\(\\underset { x\\rightarrow { 0 } }{ lim } \\) \u221ax is does not exist<\/p>\n

    Question 29.
    \nAn integer is chosen at random from the first ten positive integers. Find the probability that it is multiple of three.
    \nAnswer:
    \nS = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
    \nA = {3, 6, 9}
    \nn(S) = 10; n(A) = 3
    \nP(A) = \\(\\frac{n(A)}{n(S)}\\) = \\(\\frac{3}{10}\\)<\/p>\n

    Question 30.
    \nIs it correct to say A \u00d7 A = {(a, a): a \u2208 A}? Justify your answer.
    \nAnswer:
    \nIt is not correct
    \nSince A \u00d7 A = {(a, b); a, b \u2208 A} is true<\/p>\n

    \"Tamil<\/p>\n

    PART-III<\/span><\/p>\n

    Answer any seven questions. Question no. 40 is compulsory [7 \u00d7 3]<\/span><\/p>\n

    Question 31.
    \nA football player can kick a football from ground level with an initial velocity (u) of 80 ft\/second. Find the maximum horizontal distance the football travels and at what angle
    \nTake R = \\(\\frac{u\u00b2 sin 2\u03b1}{g}\\), and g = 32
    \nAnswer:
    \n\"Tamil
    \nMaximum distance = 200ft
    \nThe required angle is \\(\\frac{\u03c0}{4}\\)<\/p>\n

    Question 32.
    \nFind the coefficient of x3 in the expansion of (2 – 3x)7<\/sup>.
    \nAnswer:
    \nThe general term is (2 – 3x)7<\/sup> is tr + 1<\/sub> = 7<\/sup>Cr<\/sub> (2)7 – r<\/sup> (-3x)r<\/sup>
    \n= 7<\/sup>Cr<\/sub> (2)7 – r<\/sup> (-3x)r<\/sup> (x)r<\/sup>
    \nSo the co-efficient of xr<\/sup> is 7<\/sup>Cr<\/sub> (2)7 – r<\/sup> (-3)r<\/sup>
    \nTo find co-efficient of x\u00b3
    \nequate r to 3 (i.e.,) r = 3
    \n\u2234 co-efficient of x\u00b3 is 7<\/sup>Cr<\/sub> (2)7 – 3<\/sup> (-3)3<\/sup>
    \n= \\(\\frac{7\u00d76\u00d75}{3\u00d72\u00d71}\\) (2)4<\/sub> (-27)
    \n= 7 \u00d7 5 \u00d7 (16) (-27)
    \n= -15120<\/p>\n

    Question 33.
    \nFind the nearest point on the line x – 2y – 5 from the origin.
    \nAnswer:
    \n\"Tamil
    \nx = 1, y = -2
    \nNearest point is (x1<\/sub>, y1<\/sub>) = (1, -2)<\/p>\n

    Question 34.
    \nProve that square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.
    \nAnswer:
    \nLet A be a square matrix. Then A = \\(\\frac{1}{2}\\)(A + AT<\/sup>) + \\(\\frac{1}{2}\\)(A – AT<\/sup>)
    \nWe know that, (A + AT<\/sup>) is a symmetric, (A – AT<\/sup>) is a skew-symmetric
    \nA can be written as sum of a symmetric skew symmetric matrices.<\/p>\n

    \"Tamil<\/p>\n

    Question 35.
    \nIf \\(\\vec { a }\\) , \\(\\vec { b }\\), \\(\\vec { c }\\) are three vectors such that \\(\\vec { a }\\) + 2\\(\\vec { b }\\) + \\(\\vec { c }\\) = 0, and |\\(\\vec { a }\\)|=3, |\\(\\vec { b }\\)| =4, |\\(\\vec { c }\\)| =7, find the angle between \\(\\vec { a }\\) and \\(\\vec { b }\\).
    \nAnswer:
    \n\\(\\vec { a }\\) + 2\\(\\vec { b }\\) + \\(\\vec { c }\\) = 0
    \n\u2234 \\(\\vec { a }\\) + 2\\(\\vec { b }\\) = \\(\\vec { c }\\)
    \nsquaring on both sides
    \n(\\(\\vec { a }\\) + 2\\(\\vec { b }\\))\u00b2 = c\u00b2
    \na\u00b2 + 4b\u00b2 + 4\\(\\vec { a }\\)\\(\\vec { b }\\) = c\u00b2
    \n3\u00b2 + 4(4\u00b2) + 4 \\(\\vec { a }\\) \\(\\vec { b }\\) = 7\u00b2
    \n9 + 64 + 4\\(\\vec { a }\\) \\(\\vec { b }\\) = 49
    \n4\\(\\vec { a }\\) \\(\\vec { b }\\) = 49 – 73 = -24
    \n\\(\\vec { a }\\) \\(\\vec { b }\\) = –\\(\\frac {24}{4}\\) = -6
    \n|\\(\\vec { a }\\)| |\\(\\vec { b }\\)| cos \u03b8 = -6 \u21d2 (3) (4) cos \u03b8 = -6
    \n\u21d2 cos \u03b8 = –\\(\\frac {6}{12}\\) = –\\(\\frac {1}{2}\\) \u21d2 \u03b8 = \u03c0 – \\(\\frac {\u03c0}{3}\\) = \\(\\frac {2\u03c0}{3}\\)<\/p>\n

    Question 36.
    \nExamine the continuity of the function cot x + tan x.
    \nAnswer:
    \nLet f (x) = cot x + tan x
    \ncot x is continuous in R – n\u03c0
    \ntan x is continuous in R – (n + 1) \\(\\frac {\u03c0}{2}\\)
    \n\u2234 f(x) is continuous in R – \\(\\frac {n\u03c0}{2}\\), (n\u2208Z)<\/p>\n

    Question 37.
    \nDifferentiate y = sin-1<\/sup> (\\(\\frac {1-x\u00b2}{1+x\u00b2}\\))
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 38.
    \nfind \\(\\frac {dy}{dx}\\) if x = a (t – sin t), y = a(1 – cos t)
    \nAnswer:
    \nx = a (t – sin t) \u21d2 \\(\\frac {dy}{dx}\\) = a(1 – cos t)
    \ny = a(1 – cos t) \u21d2 \\(\\frac {dy}{dt}\\) = a(sin t)
    \n\"Tamil<\/p>\n

    Question 39.
    \nEvaluate \\(\\int { (x+3) } \\sqrt { x+2 }\\) dx
    \nAnswer:
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 40.
    \nConstruct a suitable domain X such that f : X \u2192 N defined by\/(n) = n + 3 to be one to one and onto.
    \nAnswer:
    \nf : X \u2192 N is defined by f(x) = n + 3
    \nSince f is one-one and onto function
    \nsuitable Domain is (-2, 1,0} \u222a N (or) {-2, -1, 0, 1, 2}<\/p>\n

    PART- IV<\/span><\/p>\n

    IV. Answer all the questions. [7 x 5 = 35]<\/span><\/p>\n

    Question 41 (a).
    \nFor the given base curve y = sin x, draw y = \\(\\frac {1}{2}\\) sin 2x
    \nAnswer:
    \n\"Tamil<\/p>\n

    [OR]<\/p>\n

    (b) Write any five different forms of an equation of a straight line.
    \nAnswer:
    \n(i) Slope intercept form : y = mx + c, c \u2260 0
    \n(ii) Point and slope form : y – y1<\/sub> = m (x – x1<\/sub>)
    \n(iii) Two Point form : \\(\\frac {y – y_1}{y_{2}-y_1}\\) \\(\\frac {x – x_1}{x_{2}-x_1}\\)
    \n(iv) Intercept form : \\(\\frac {x}{a}\\) + \\(\\frac {y}{b}\\) = 1
    \n(v) Normal form : x cos \u03b1 + y sin \u03b1<\/p>\n

    Question 42 (a).
    \nSolve the equation \\(\\sqrt {6-4x-x\u00b2}\\) = x + 4
    \nAnswer:
    \nSquaring both sides
    \n6 – 4x – x\u00b2 = (x + 4)\u00b2
    \n(i.e.,) x\u00b2 + 6x + 5 = 0 \u21d2 (x + 1) (x + 5) = 0
    \n\u21d2 x = -1, x = -5
    \nBut x \u2265 – 4
    \n\u21d2 x = -1<\/p>\n

    [OR]<\/p>\n

    (b) Prove that in any \u0394ABC, \u0394 = \\(\\sqrt{s(s-a)(s-b)(s-c)}\\), where s is the semi-perimeter of \u0394ABC.
    \nAnswer:
    \n\u0394 = \\(\\frac {1}{2}\\) ab sin C = \\(\\frac {1}{2}\\) ab (2sin \\(\\frac {C}{2}\\) cos \\(\\frac {C}{2}\\))
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 43 (a).
    \nState and prove any one of the Napier’s formulae.
    \nAnswer:
    \n\"Tamil<\/p>\n

    [OR]<\/p>\n

    (b) Do the limit of the function \\(\\frac {sin(x-\\left\\lfloor x \\right\\rfloor)}{x – \\left\\lfloor x \\right\\rfloor}\\) exist as x \u2192 0? State the reasons for your answer.
    \nAnswer:
    \n\"Tamil
    \nSo, the limit does not exist.<\/p>\n

    Question 44. (a)
    \nProve that for any natural number n, an<\/sup> – bn<\/sup> is divisible by a – b, where a > b.
    \nAnswer:
    \na = a – b + b
    \nSo, an<\/sup> =[a- b + b]n<\/sup> = [(a -b) + b]n<\/sup>
    \n= n<\/sup>C0<\/sub> (a – b)n<\/sup> + n<\/sup>C1<\/sub> (a – b)n-1<\/sup>b1<\/sup> + n<\/sup>C2<\/sub>\u00a0(a – b)n-2<\/sup>b\u00b2 + ……. + n<\/sup>Cn-1<\/sub>, (a – b) bn-1<\/sup>+ n<\/sup>Cn<\/sub>(bn<\/sup>)
    \n\u21d2 an<\/sup> – bn<\/sup> = (a – b)n<\/sup> + n<\/sup>C1<\/sub> (a – b)n-1<\/sup>b + n<\/sup>C2<\/sub> (a – b)n-2<\/sup>b\u00b2) + …….. + n<\/sup>Cn-1<\/sub> (a – b) bn-1<\/sup>
    \n= (a – b) [(a – b)n-1<\/sup> + n<\/sup>C1<\/sub> (a – b)n-2<\/sup>b + n<\/sup>C2<\/sub> (a – b)n-3<\/sup>b\u00b2 + …….. + n<\/sup>Cn-1<\/sub> bn-1<\/sup>]
    \n= (a – b) [an<\/sup> integer]
    \n\u21d2 an<\/sup> – bn<\/sup> If is divisible by(a – b).<\/p>\n

    [OR]<\/p>\n

    (b) Evaluate: \\(\\int \\frac{2 x+4}{x^{2}+4 x+6}\\)
    \nAnswer:
    \nLet 2x + 4 = A \\(\\frac {d}{dx}\\) (x\u00b2 + 4x + 6) + B
    \n(i.e.,) 2x + 4 = A(2x + 4) + B
    \nEquating the coefficient of x and constant term we get
    \nA = 1, B = 0
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 45 (a).
    \nProve that \\(\\sqrt[3]{x^{3}+7}-\\sqrt[3]{x^{3}+4}\\) is approximately equal to \\(\\frac {1}{x\u00b2}\\)when x is large.
    \nAnswer:
    \n\"Tamil<\/p>\n

    [OR]<\/p>\n

    (b) Find the unit vectors perpendicular to each of the vectors \\(\\vec { a }\\) + \\(\\vec { b }\\) and \\(\\vec { a }\\) – \\(\\vec { b }\\) where \\(\\vec { a }\\) = \\(\\hat { i }\\) + \\(\\hat { j }\\) + \\(\\hat { j }\\) and \\(\\vec { b }\\) = \\(\\hat { i }\\) + 2\\(\\hat { j }\\) + 3\\(\\hat { k }\\).
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 46 (a).
    \nFind \\(\\frac {d\u00b2y}{dx}\\) if x\u00b2 + y\u00b2 = 4
    \nAnswer:
    \nwe have x\u00b2 + y\u00b2 = 4
    \n\"Tamil<\/p>\n

    [OR]<\/p>\n

    (b) The chances of X, Y and Z becoming managers of a certain company are 4 : 2 : 3. The probabilities that bonus scheme will be introduced if X, Y and Z become managers are 0.3, 0.5 and 0.4 respectively. If the bonus scheme has been introduced, what is the probability that Z was appointed as the manager?
    \nAnswer:
    \nGiven X : Y : Z = 4 : 2 : 3
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 47 (a).
    \nProve that
    \n\"Tamil
    \nAnswer:
    \n\"Tamil
    \n\u2234 (x – y) is a factor
    \nSimilarly (y – z)(z – x) are also factors.
    \nThe other factor is k(x\u00b2 + y\u00b2 + z\u00b2) + l(xy + yz + zx)
    \n\"Tamil
    \nPutting x = 0, y = 1, z = 2 \u21d2 5k + 2l = 2 …. (1)
    \nPutting x = 0, y = – 1, z = 1 \u21d2 2k – l = -1 …. (2)
    \nfrom (1) & (2) k = 0, l = -1
    \n\"Tamil<\/p>\n

    [OR]<\/p>\n

    (b) Evaluate \\(\\int \\sqrt{x^{2}+x+1}\\) dx
    \nAnswer:
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n","protected":false},"excerpt":{"rendered":"

    Students can Download Tamil Nadu 11th Maths Previous Year Question Paper March 2019 English Medium Pdf, Tamil Nadu 11th Maths Model Question Papers\u00a0helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations. TN State Board 11th Maths Previous Year Question Paper March 2019 English Medium General Instructions: …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[7],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/15580"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=15580"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/15580\/revisions"}],"predecessor-version":[{"id":60616,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/15580\/revisions\/60616"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=15580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=15580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=15580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}