{"id":1766,"date":"2025-01-28T10:53:05","date_gmt":"2025-01-28T05:23:05","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=1766"},"modified":"2025-01-29T09:53:05","modified_gmt":"2025-01-29T04:23:05","slug":"tamil-nadu-12th-maths-model-question-paper-1-english-medium","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/tamil-nadu-12th-maths-model-question-paper-1-english-medium\/","title":{"rendered":"Tamil Nadu 12th Maths Model Question Paper 1 English Medium"},"content":{"rendered":"

Students can Download Tamil Nadu 12th Maths Model Question Paper 1 English Medium Pdf, Tamil Nadu 12th Maths Model Question Papers<\/a> helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n

TN State Board 12th Maths Model Question Paper 1 English Medium<\/h2>\n

Instructions:<\/p>\n

    \n
  1. \u00a0The question paper comprises of\u00a0four<\/span>\u00a0parts.<\/li>\n
  2. \u00a0You are to attempt all the parts. An internal choice of questions is provided wherever applicable.<\/li>\n
  3. questions of Part I, II. III and IV are to be attempted separately<\/li>\n
  4. Question numbers\u00a01 to 20 in Part I\u00a0<\/span>are objective type questions of\u00a0one -mark<\/span>\u00a0each. These 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\u00a021 to 30 in Part II\u00a0<\/span>are\u00a0two-marks<\/span>\u00a0questions. These are to be answered in about one or two sentences.<\/li>\n
  6. Question numbers\u00a031 to 40 in Parr III<\/span>\u00a0are\u00a0three-marks<\/span>\u00a0questions, These are to be answered in about three to five short sentences.<\/li>\n
  7. Question numbers\u00a041 to 47 in Part IV<\/span>\u00a0are\u00a0five-marks<\/span>\u00a0questions. These are to be answered) in detail. Draw diagrams wherever necessary.<\/li>\n<\/ol>\n

    Time: 3 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.
    \nIf A is a non-singular matrix such that A-1<\/sup>\u00a0= \\(\\left[\\begin{array}{rr}
    \n5 & 3 \\\\
    \n-2 & -1
    \n\\end{array}\\right]\\), Then (AT<\/sup>)-1<\/sup> = _________.
    \n\"Tamil
    \n\"Tamil
    \nAnswer:
    \n(d) \\(\\left[\\begin{array}{ll}
    \n5 & -2 \\\\
    \n3 & -1
    \n\\end{array}\\right]\\)<\/p>\n

    Question 2.
    \nIf \u0394 \u2260 0 then the system is ________.
    \n(a) Consistent and has unique solution
    \n(b) Consistent and has infinitely many solutions
    \n(c) Inconsistent
    \n(d) Either consistent or inconsistent
    \nAnswer:
    \n(a) Consistent and has unique solution<\/p>\n

    \"Tamil<\/p>\n

    Question 3.
    \nThe solution of the equation |z| – z = 1 + 2i is _______.
    \n(a) \\(\\frac{3}{2}\\) – 2i
    \n(b) \\(-\\frac{3}{2}\\) + 2i
    \n(c) 2 – \\(\\frac{3}{2}\\) i
    \n(d) 2 + \\(\\frac{3}{2}\\) i
    \nAnswer:
    \n(a) \\(\\frac{3}{2}\\) – 2i<\/p>\n

    Question 4.
    \nThe value of ei\u03b8<\/sup> + e-i\u03b8<\/sup>\u00a0is _________.
    \n(a) 2 cos \u03b8
    \n(b) cos \u03b8
    \n(c) 2 sin \u03b8
    \n(d) sin \u03b8
    \nAnswer:
    \n(a) 2 cos \u03b8<\/p>\n

    Question 5.
    \nThe polynomial x3<\/sup> – kx2<\/sup> + 9x has three real zeros if and only if, k satisfies __________.
    \n(a) |k| \u2264 6
    \n(b) k = 0
    \n(c) |k| > 6
    \n(d) |k| \u2265 6
    \nAnswer:
    \n(d) |k| \u2265 6<\/p>\n

    \"Tamil<\/p>\n

    Question 6.
    \nThe domain of the function defined by f (x) = sin-1<\/sup> \\(\\sqrt{x-1}\\) is ________.
    \n(a) [1, 2]
    \n(b) [-1, 1]
    \n(c) [0, 1]
    \n(d)[-1, 0]
    \nAnswer:
    \n(a) [1, 2]<\/p>\n

    Question 7.
    \ntan-1<\/sup> (\\(\\frac{1}{4}\\)) + tan-1<\/sup> (\\(\\frac{2}{9}\\)) is equal to ________.
    \n\"Tamil
    \nAnswer:
    \n\\(\\tan ^{-1}\\left(\\frac{1}{2}\\right)\\)<\/p>\n

    Question 8.
    \n8. The equation of the latus rectum of y2<\/sup> = 4x is _______.
    \n(a) x = 1
    \n(b) y = 1
    \n(c) x = 4
    \n(d) y = -1
    \nAnswer:
    \n(a) x = 1<\/p>\n

    Question 9.
    \nThe circle passing through (1, -2) and touching the axis of x at (3, 0) passing through the point _______.
    \n(a) (-5, 2)
    \n(b) (2, -5)
    \n(c) (5, -2)
    \n(d) (-2, 5)
    \nAnswer:
    \n(c) (5, -2)<\/p>\n

    Question 10.
    \nIf the length of the perpendicular from the origin to the plane 2x + 3y + \u03bbz = 1, \u03bb > 0 is \\(\\frac{1}{5}\\), then the value of \u03bb is _______.
    \n(a) 2\\(\\sqrt{3}\\)
    \n(b) 3\\(\\sqrt{2}\\)
    \n(c) 0
    \n(d) 1
    \nAnswer:
    \n(a) 2\\(\\sqrt{3}\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 11.
    \nThe tangent to the curve y2<\/sup> – xy + 9 = 0 is vertical when ________.
    \n(a) y = 0
    \n(b) y = \u00b1 \\(\\sqrt{3}\\)
    \n(c) y = \\(\\frac{1}{2}\\)
    \n(d) y = \u00b1 \\(\\sqrt{3}\\)
    \nAnswer:
    \n(b) y = \u00b1 \\(\\sqrt{3}\\)<\/p>\n

    Question 12.
    \nThe volume of a sphere is increasing in volume at the rate of 3\u03c0 cm3<\/sup>\/sec. The rate of change of its radius when radius \\(\\frac{1}{2}\\) cm _______.
    \n(a) 3 cm\/s
    \n(b) 2 cm\/s
    \n(c) 1 cm\/s
    \n(d) \\(\\frac{1}{2}\\) cm\/s
    \nAnswer:
    \n(a) 3 cm\/s<\/p>\n

    Question 13.
    \nIf we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is _______.
    \n(a) 0.4 cu.cm
    \n(b) 0.45 cu.cm
    \n(c) 2 cu.cm
    \n(d) 4.8 cu.cm
    \nAnswer:
    \n(d) 4.8 cu.cm<\/p>\n

    Question 14.
    \nIf v (x, y) = log (ex<\/sup> + ey<\/sup> ), then \\(\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\) is equal to _____.
    \n(a) ex<\/sup> + ey<\/sup>
    \n(b) \\(\\frac{1}{e^{x}+e^{y}}\\)
    \n(c) 2
    \n(d) 1
    \nAnswer:
    \n(d) 1<\/p>\n

    Question 15.
    \nThe value of \\(\\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\sin ^{2} x \\cos x d x\\) is _______.
    \n(a) \\(\\frac{3}{2}\\)
    \n(b) \\(\\frac{1}{2}\\)
    \n(c) 0
    \n(d) \\(\\frac{2}{3}\\)
    \nAnswer:
    \n(d) \\(\\frac{2}{3}\\)<\/p>\n

    Question 16.
    \nThe general solution of the differential equation log \\(\\left(\\frac{d y}{d x}\\right)\\) = x + y is ______.
    \n(a) ex<\/sup> + ey<\/sup> = c
    \n(b) ex<\/sup> + e-y<\/sup> = c
    \n(c) e–<\/sup>x<\/sup> + ey<\/sup> = c
    \n(d) e–<\/sup>x<\/sup> + e-y<\/sup> = c
    \nAnswer:
    \n(b) ex<\/sup> + e-y<\/sup>\u00a0= c<\/p>\n

    \"Tamil<\/p>\n

    Question 17.
    \nThe order and degree of the differential equation \\(\\frac{d^{2} y}{d x^{2}}+\\left(\\frac{d y}{d x}\\right)^{1 \/ 3}+x^{1 \/ 4}=0\\) are respectively.
    \n(a) 2, 3
    \n(b) 3, 3
    \n(c) 2, 6
    \n(d) 2, 4
    \nAnswer:
    \n(a) 2, 3<\/p>\n

    Question 18.
    \nIf X is a binomial random variable with expected value 6 and variance 2.4, Then P {X = 5} is _______.
    \n\"Tamil
    \nAnswer:
    \n(d) \\(\\left(\\begin{array}{c}
    \n10 \\\\
    \n5
    \n\\end{array}\\right)\\left(\\frac{3}{5}\\right)^{5}\\left(\\frac{2}{5}\\right)^{5}\\)<\/p>\n

    Question 19.
    \nA random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is ______.
    \n(a) 6
    \n(b) 4
    \n(c) 3
    \n(d) 2
    \nAnswer:
    \n(d) 2<\/p>\n

    Question 20.
    \nIf a*b = \\(\\sqrt{a^{2}+b^{2}}\\) on the real numbers then * is ________.
    \n(a) commutative but not associative
    \n(b) associative but not commutative
    \n(c) both commutative and associative
    \n(d) neither commutative nor associative
    \nAnswer:
    \n(c) both commutative and associative<\/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.
    \nUsing elementary transformation find the inverse of the matrix \\(\\left[\\begin{array}{cc}
    \n3 & -1 \\\\
    \n-4 & 2
    \n\\end{array}\\right]\\)
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 22.
    \nEvaluate the zw if z = 5 – 2i and w = -1 + 3i
    \nAnswer:
    \nzw = (5 – 2i) (-1 + 3i) = -5 + 15i + 2i – 6i2<\/sup> = -5 + 17i + 6 = 1 + 17i<\/p>\n

    \"Tamil<\/p>\n

    Question 23.
    \nFind a polynomial equation of minimum degree with rational coefficients, having 2i + 3 as a root.
    \nAnswer:
    \nGiven roots is (3 + 2i), the other root is (3 – 2i); Since imaginary roots occur in with real co-efficient occurring conjugate pairs.
    \nx2<\/sup> – x(S.O.R) + P.O.R = 0 \u21d2 x2<\/sup> – x(6) + (9 + 4) = 0
    \nx2<\/sup> – 6x + 13 = 0<\/p>\n

    Question 24.
    \nIs cos-1<\/sup> (-x) = \u03c0 – cos-1<\/sup> x true? Justify your answer.
    \nAnswer:
    \nLet \u03b8 = cos-1<\/sup> (-x)
    \n\u21d2 cos \u03b8 = -x \u21d2 -cos\u03b8 = x
    \ni.e. cos(\u03c0 – \u03b8) = x
    \n\u21d2 \u03c0 – \u03b8 = cos-1<\/sup> x \u21d2 \u03c0 – cos-1<\/sup> x = \u03b8
    \ni.e. \u03c0 – cos-1<\/sup> x = cos-1<\/sup>(-x)<\/p>\n

    Question 25.
    \nUsing the Rolle\u2019s theorem, determine the values of x at which the tangent is parallel to the x – axis for the following functions: f(x) = x2<\/sup> – x, x \u2208 [0, 1]
    \nAnswer:
    \nTangent is parallel to x axis. So \\(\\frac{d y}{d x}=0\\)
    \nf (x) = x2<\/sup> -x
    \nf’ (x) = 2x – 1
    \nf'(x) = 0 \u21d2 2x – 1 = 0 \u21d2 x = \\(\\frac{1}{2}\\) \u2208[0, 1]<\/p>\n

    Question 26.
    \nIn each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree g (x, y, z) = \\(\\frac{\\sqrt{3 x^{2}+5 y^{2}+z^{2}}}{4 x+7 y}\\)
    \nAnswer:
    \n\"Tamil
    \n\u2234 It is homogeneous function of degree 0.<\/p>\n

    Question 27.
    \nFind, by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = e-2x<\/sup>, y = 0, x = 0 and x = 1.
    \nAnswer:
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 28.
    \nCompute P(X = k) for the binomial distribution, B (n,p) where n = 10, p = \\(\\frac{1}{5}\\), k = 4
    \nAnswer:
    \nn = 10, p = \\(\\frac{1}{5}\\), k = 4
    \n\u2234 q = 1 – p = 1 – \\(\\frac{1}{5}=\\frac{4}{5}\\)
    \nP(X = x) =nCx<\/sub> px<\/sup>qn-x<\/sup>, x = 0, 1, 2, …….n.
    \nP (X = k) = P (X = 4)
    \n\"Tamil<\/p>\n

    Question 29.
    \n\"Tamil
    \nbe any three boolean matrices of the same type. Find A \u2227 B
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 30.
    \nThe slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve.
    \nAnswer:
    \nSlope of the tangent is the reciprocal of four times the ordinate
    \ni.e., \\(\\frac{d y}{d x}=\\frac{1}{4 y}\\)
    \n4\u222by dy = \u222b dx
    \n4\\(\\frac{y^{2}}{2}\\) = x + c \u21d2 2y2<\/sup> = x + c
    \nPasses through (2, 5)
    \n\u2234 c = 50 – 2 = 48
    \nEquation of the curve is 2y2<\/sup> = x + 48<\/p>\n

    Part – III<\/span><\/p>\n

    III. Answer any seven questions. Question No. 40 is compulsory. [7 x 3 = 21]<\/span><\/p>\n

    Question 31.
    \nA man is appointed in a job with a monthly salary of certain amount and a fixed amount of annual increment. If his salary was \u20b919,800 per month at the end of the first month after 3 years of service and \u20b923,400 per month at the end of the first month after 9 years of service, find his starting salary and his annual increment. (Use matrix inversion method to solve the problem.)<\/p>\n

    Question 32.
    \nIf the equations x2<\/sup> + px + q = 0 and x2<\/sup> + p’x + q’ = 0 have a common root, show that it must be equal to \\(\\frac{p q^{\\prime}-p^{\\prime} q}{q-q^{\\prime}} \\text { or } \\frac{q-q^{\\prime}}{p^{\\prime}-p}\\)<\/p>\n

    Question 33.
    \nFind the value of tan-1<\/sup> (-1) + \\(\\cos ^{-1}\\left(\\frac{1}{2}\\right)+\\sin ^{-1}\\left(-\\frac{1}{2}\\right)\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 34.
    \nA camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s =16t2<\/sup>\u00a0in t seconds.
    \n(i) How long does the camera fall before it hits the ground?
    \n(ii) What is the average velocity with which the camera falls during the last 2 seconds?
    \n(iii) What is the instantaneous velocity of the camera when it hits the ground?<\/p>\n

    Question 35.
    \nIf the radius of a sphere is measured as 7m with an error of 0.02 m then find the approximate error in calculating its volume.<\/p>\n

    Question 36.
    \nFind the volume of the solid that results when the ellipse \\(\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1\\) (a > b > 0) is revolved about the minor axis.<\/p>\n

    Question 37.
    \nVerify that the function y = e is a solution of the differential equation \\(\\frac{d^{2} y}{d x^{2}}+\\frac{d y}{d x}-6 y=0\\)<\/p>\n

    Question 38.
    \nFind the mean and variance of the distribution \\(f(x)=\\left\\{\\begin{array}{cc}
    \n3 e^{-3 x}, & 0<x<\\infty \\\\
    \n0, & \\text { elsewhere }
    \n\\end{array}\\right.\\)<\/p>\n

    Question 39.
    \nLet A = {a + \\(\\sqrt{5}\\) b : a, b \u2208 Z} . Check whether the usual multiplication is a binary operation on A.<\/p>\n

    Question 40.
    \nIf \\(\\frac{z+3}{z-5 i}=\\frac{1+4 i}{2}\\) find the complex number z.<\/p>\n

    Part – IV<\/span><\/p>\n

    IV. Answer all the questions. [7 \u00d7 5 = 35]<\/span><\/p>\n

    Question 41.
    \n(a) Solve, by Cramer \u2019s rule, the system of equations
    \nx1<\/sub> – x2<\/sub> = 3, 2x1<\/sub> + 3x2<\/sub> + 4x3<\/sub> = 17,\u00a0 x2<\/sub> + 2x3<\/sub> = 7
    \n[OR]
    \n(b) A manufacturer wants to design an open box having a square base and a surface area of 108 sq.cm. Determine the dimensions of the box for the maximum volume.<\/p>\n

    \"Tamil<\/p>\n

    Question 42.
    \n(a) Solve the equation z3<\/sup> + 8i = 0, where z \u2208 C.
    \n[OR]
    \n(b) Solve (1 + 2ex\/y<\/sup>)dx + 2ex\/y<\/sup> \\(\\left(1-\\frac{x}{y}\\right)\\) dy = 0<\/p>\n

    Question 43.
    \n(a) Find the area of the region bounded between the parabola x2<\/sup> =y and the curve y = |x|.
    \n[OR]
    \n(b) Find the vector and cartesian equations of the plane containing the line \\(\\frac{x-2}{2}=\\frac{y-2}{3}=\\frac{z-1}{-2}\\) and passing through the point (-1, 1, -1).<\/p>\n

    Question 44.
    \n(a) Cross section of a Nuclear cooling tower is in the shape of a hyperbola with equation \\(\\frac{x^{2}}{30^{2}}-\\frac{y^{2}}{44^{2}}=1\\). The tower is 150 m tall and the distance from the top of the tower to the centre of the hyperbola is half the distance from the base of the tower to the centre of the hyperbola. Find the diameter of the top and base of the tower.
    \n[OR]
    \n(b) If 2 + i and 3 – \\(\\sqrt{2}\\) are roots of the equation
    \nx6<\/sup> – 13x5<\/sup> + 62x4<\/sup> – 126x3<\/sup> + 65x2<\/sup> + 127x – 140 = 0 find all roots.<\/p>\n

    Question 45.
    \n(a) If u = \\(\\sin ^{-1}\\left(\\frac{x+y}{\\sqrt{x}+\\sqrt{y}}\\right)\\) show that \\(x \\frac{\\partial u}{\\partial x}+y \\frac{\\partial u}{\\partial y}=\\frac{1}{2} \\tan u\\)
    \n[OR]
    \n(b) The cumulative distribution function of a discrete random variable is given by.
    \n\"Tamil
    \nFind (i) the probability mass function (ii) P(X < 3) and (iii) P(X \u2265 2).<\/p>\n

    Question 46.
    \n(a) Prove that: \\(\\cos \\left[\\tan ^{-1}\\left\\{\\sin \\left(\\cot ^{-1} x\\right)\\right\\}\\right]=\\sqrt{\\frac{x^{2}+1}{x^{2}+2}}\\)
    \n[OR]
    \n(b) Verify (i) closure property (ii) commutative property (iii) associative property (iv) existence of identity and (v) existence of inverse for following operation on the given set. m*n = m + n – mn ; m, n \u2208 Z<\/p>\n

    \"Tamil<\/p>\n

    Question 47.
    \n(a) Find the equation of the circle passing through the points (1, 1), (2, -1), and (3, 2).
    \n[OR]
    \n(b) Evaluate: \\(\\int_{0}^{\\pi \/ 2} \\frac{d x}{4+9 \\cos ^{2} x}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

    Students can Download Tamil Nadu 12th Maths Model Question Paper 1 English Medium Pdf, Tamil Nadu 12th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. TN State Board 12th Maths Model Question Paper 1 English …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[5],"tags":[],"class_list":["post-1766","post","type-post","status-publish","format-standard","hentry","category-class-12"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1766"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=1766"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1766\/revisions"}],"predecessor-version":[{"id":40025,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1766\/revisions\/40025"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=1766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=1766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=1766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}