8<\/sup> is ………………
\n(a) 81
\n(b) 27
\n(c) 9
\n(d) 3
\nAnswer:
\n(a) 81<\/p>\n
<\/p>\n
Question 10.
\nA line perpendicular to the line 5x -y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5sq.units, then its equation is …………………..
\n(a) x + 5y \u00b1 5\\(\\sqrt{2}\\) = 0
\n(b) x – 5y \u00b1 5\\(\\sqrt{2}\\) = 0
\n(c) 5x + y \u00b1 5\\(\\sqrt{2}\\) = 0
\n(d) 5x – y \u00b1 5\\(\\sqrt{2}\\) = 0
\nAnswer:
\n(a) x + 5y \u00b1 5\\(\\sqrt{2}\\) = 0<\/p>\n
Question 11.
\nA factor of the determinant \\(\\left|\\begin{array}{ccc}
\nx & -6 & -1 \\\\
\n2 & -3 x & x-3 \\\\
\n-3 & 2 x & x+2
\n\\end{array}\\right|\\) is ……………….
\n(a) x + 3
\n(b) 2x – 1
\n(c) x – 2
\n(d) x – 3
\nAnswer:
\n(a) x + 3<\/p>\n
<\/p>\n
Question 12.
\nIf \u03bb\\(\\vec { a } \\) + 2\u03bb\\(\\vec { j } \\) + 2\u03bb\\(\\vec { k } \\) is a unit vector then the value of \u03bb is ………………
\n(a) \\(\\frac{1}{3}\\)
\n(b) \\(\\frac{1}{4}\\)
\n(c) \\(\\frac{1}{9}\\)
\n(d) \\(\\frac{1}{2}\\)
\nAnswer:
\n(a) \\(\\frac{1}{3}\\)<\/p>\n
Question 13.
\nOne of the diagonals of parallelogram ABCD with \\(\\vec { a } \\) and \\(\\vec { b } \\) are adjacent sides is \\(\\vec { a } \\) + \\(\\vec { b } \\). The other diagonal BD is ………………….
\n(a) \\(\\vec { a } \\) – \\(\\vec { b } \\)
\n(b) \\(\\vec { a } \\) – \\(\\vec { b } \\)
\n(c) \\(\\vec { a } \\) + \\(\\vec { b } \\)
\n(d) \\(\\frac{\\vec{a}+\\vec{b}}{2}\\)
\nAnswer:
\n(b) \\(\\vec { a } \\) – \\(\\vec { b } \\)<\/p>\n
<\/p>\n
Question 14.
\nIf (1, 2, 4) and (2, -3\u03bb, -3) are the initial and terminal points of the vector \\(\\vec { i } \\) + 5\\(\\vec { j } \\) – 7\\(\\vec { k } \\) then the value of \u03bb …………………..
\n(a) \\(\\frac{7}{3}\\)
\n(b) –\\(\\frac{7}{3}\\)
\n(c) \\(\\frac{5}{3}\\)
\n(d) \\(\\frac{-5}{3}\\)
\nAnswer:
\n(b) –\\(\\frac{7}{3}\\)<\/p>\n
Question 15.
\nIf y = mx + c and f(0) =f'(0) = 1 then f(2) = …………………..
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nAnswer:
\n(c) 3<\/p>\n
<\/p>\n
Question 16.
\nThe derivative of (x + \\(\\frac{1}{x}\\))2<\/sup> w.r.to. x is ………………..
\n(a) 2x – \\(\\frac { 2 }{ x^{ 3 } } \\)
\n(b) 2x + \\(\\frac { 2 }{ x^{ 3 } } \\)
\n(c) 2(x + \\(\\frac{1}{x}\\))
\n(d) 0
\nAnswer:
\n(a) 2x – \\(\\frac { 2 }{ x^{ 3 } } \\)<\/p>\nQuestion 17.
\nIf f(x) is \\(\\left\\{\\begin{array}{cc}
\na x^{2}-b, & -1<x<1 \\\\
\n\\frac{1}{|x|}, & \\text { elsewhere }
\n\\end{array}\\right.\\) is differentiable at x = 1, then …………………
\n(a) a = \\(\\frac{1}{2}\\), b = \\(\\frac{-3}{2}\\)
\n(b) a = \\(\\frac{-1}{2}\\), b = \\(\\frac{3}{2}\\)
\n(c) a = \\(\\frac{-1}{2}\\), b = \\(\\frac{-3}{2}\\)
\n(d) a = \\(\\frac{1}{2}\\), b = \\(\\frac{3}{2}\\)
\nAnswer:
\n(c) a = \\(\\frac{-1}{2}\\), b = \\(\\frac{-3}{2}\\)<\/p>\n
<\/p>\n
Question 18.
\n\u222b\\(\\frac { \\sqrt { tanx } }{ sin2x } \\) dx is ………………
\n(a) \\(\\sqrt{tanx}\\) + c
\n(b) 2\\(\\sqrt{tanx}\\) + c
\n(c) \\(\\frac{1}{2}\\) \\(\\sqrt{tanx}\\) + c
\n(d) \\(\\frac{1}{4}\\) \\(\\sqrt{tanx}\\) + c
\nAnswer:
\n(a) \\(\\sqrt{tanx}\\) + c<\/p>\n
Question 19.
\nAn urn contains 5 red and 5 black balls. A balls is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be ………………….
\n(a) \\(\\frac{5}{12}\\)
\n(b) \\(\\frac{1}{2}\\)
\n(c) \\(\\frac{7}{12}\\)
\n(d) \\(\\frac{1}{4}\\)
\nAnswer:
\n(b) \\(\\frac{1}{2}\\)<\/p>\n
<\/p>\n
Question 20.
\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}\\) then
\nP(B) = ………………….
\n(a) \\(\\frac{1}{6}\\)
\n(b) \\(\\frac{1}{3}\\)
\n(c) \\(\\frac{2}{3}\\)
\n(d) \\(\\frac{1}{2}\\)
\nAnswer:
\n(b) \\(\\frac{1}{3}\\)<\/p>\n
PART – II<\/span><\/p>\nII. Answer any seven questions. Question No. 30 is compulsory. [7 \u00d7 2 = 14]<\/span><\/p>\nQuestion 21.
\nIf n(P(A)) = 1024, n(A\u222aB) = 15 and n(P(B)) = 32 then find n(A\u2229B)
\nAnswer:
\nn(P(A)) = 1024 = 210<\/sup> \u21d2 n(A) = 10
\nn(A\u222aB) = 15
\nn(P(B)) = 32 = 25<\/sup> \u21d2 n(B) = 5
\nWe know n(A\u222aB) = n(A) + n(B) – n(A\u2229B)
\n(i.e) 15 = 10 + 5 – n(A\u2229B)
\n\u21d2 n(A\u2229B) = 15 – 15 = 0<\/p>\n
<\/p>\n
Question 22.
\nSimplify (343)2\/3<\/sup>
\nAnswer:
\n(343)2\/3<\/sup> = (73<\/sup>)2\/3<\/sup> = 73\u00d72\/3<\/sup> = 72<\/sup> = 49<\/p>\nQuestion 23.
\nShow that cos36\u00b0 cos 72\u00b0 cos 108\u00b0 cos 144\u00b0 = \\(\\frac{1}{16}\\)
\nAnswer:
\nLHS = cos36\u00b0 cos(90\u00b0 – 18\u00b0) cos(90\u00b0 – 18\u00b0) cos(90\u00b0 + 18\u00b0) cos(180\u00b0 – 36\u00b0)
\n= sin2<\/sup> 18\u00b0 cos2<\/sup> 36\u00b0
\n= (\\(\\frac { \\sqrt { 5-1 } }{ 4 } \\))2<\/sup> (\\(\\frac { \\sqrt { 5+1 } }{ 4 } \\))2<\/sup> = \\(\\frac{1}{16}\\) = RHS<\/p>\n
<\/p>\n
Question 24.
\nFind the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour?
\nAnswer:
\nThere are 6 red balls, 5 white balls and 5 blue balls.
\nWe have to select 3 balls of each colour.
\n\u2234Number of ways of selection = 6<\/sup>C3<\/sub> \u00d7 5<\/sup>C3<\/sub> \u00d7 5<\/sup>C3<\/sub>
\n= \\(\\frac { 6! }{ 3!3! } \\) \u00d7 \\(\\frac { 5! }{ 3!2! } \\) \u00d7 \\(\\frac { 5! }{ 3!2! } \\)
\n= 20 \u00d7 10 \u00d7 10 = 2000<\/p>\nQuestion 25.
\nFind |A| if A = \\(\\left[\\begin{array}{ccc}
\n0 & \\sin \\alpha & \\cos \\alpha \\\\
\n\\sin \\alpha & 0 & \\sin \\beta \\\\
\n\\cos \\alpha & -\\sin \\beta & 0
\n\\end{array}\\right]\\)
\nAnswer:
\n\\(\\left[\\begin{array}{ccc}
\n0 & \\sin \\alpha & \\cos \\alpha \\\\
\n\\sin \\alpha & 0 & \\sin \\beta \\\\
\n\\cos \\alpha & -\\sin \\beta & 0
\n\\end{array}\\right]\\)
\n= 0M11<\/sub> – sin \u03b1M12<\/sub> + cos \u03b1M13<\/sub>
\n= 0 – sin \u03b1(0 – cos \u03b1 sin \u03b2) + cos \u03b1 (-sin \u03b1 sin \u03b2 – 0) = 0<\/p>\n
<\/p>\n
Question 26.
\nFor any vector prove that \\(\\vec { r } \\) = [\\(\\vec { r } \\).\\(\\vec { i } \\)) + (\\(\\vec { r } \\).\\(\\vec { j } \\))j + [\\(\\vec { r } \\).\\(\\vec { k } \\)}k
\nAnswer:
\nLet \\(\\vec { r } \\) = x\\(\\hat { i } \\) + y\\(\\hat { j } \\) + z\\(\\hat { k } \\)
\n
<\/p>\n
<\/p>\n
Question 27.
\nCalculate \\(\\lim _{x \\rightarrow-2}\\) (x3<\/sup> – 3x + 6) (-x2<\/sup> + 15)
\nAnswer:
\n
<\/p>\nQuestion 28.
\nEvaluate y = ex<\/sup> sin x
\nAnswer:
\n
<\/p>\nQuestion 29.
\nIntegrate the following with respect to x
\n\\(\\frac{4}{3+4x}\\) + (10x + 3)9<\/sup> – 3 cosec(2x + 3) cot (2x + 3)
\nAnswer:
\n
<\/p>\n
<\/p>\n
Question 30.
\nP(A) = 0.6, P (B) = 0.5 and P(A\u2229B) = 0.2 find P(A\/B)
\nAnswer:
\nGiven that P(A) = 0.6, P(B) = 0.5, and P(A\u2229B) = 0.2
\nP(A\/B) = \\(\\frac { p(A\u2229B) }{ p(B) } \\) = \\(\\frac{0.2}{0.5}\\) = \\(\\frac{2}{5}\\)<\/p>\n
PART – III<\/span><\/p>\nIII. Answer any seven questions. Question No. 40 is compulsory. [7 \u00d7 3 = 21]<\/span><\/p>\nQuestion 31.
\nA quadratic polynomial has one of its zeros 1 + \\(\\sqrt{5}\\) and it satisfies p(1) = 2. Find the quadratic polynomial?<\/p>\n
Question 32.
\nProve that<\/p>\n
\n- tan-1<\/sup> (\\(\\frac{1}{7}\\)) + tan-1<\/sup>(\\(\\frac{1}{13}\\)) = tan-1<\/sup>(\\(\\frac{2}{9}\\))<\/li>\n
- cos-1<\/sup>\\(\\frac{4}{5}\\) + tan-1<\/sup>\\(\\frac{3}{5}\\) = tan-1<\/sup>\\(\\frac{27}{11}\\)<\/li>\n<\/ol>\n
<\/p>\n
Question 33.
\nThe product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP?<\/p>\n
Question 34.
\nFind the equation of the line passing through the point (5, 2) and perpendiular to the line joining the points (2, 3) and (3, -1)?<\/p>\n
<\/p>\n
Question 35.
\nFind the area of the triangle whose vertices are (0,0), (1,2) and (4,3)?<\/p>\n
Question 36.
\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 fimd the angle between \\(\\vec { a } \\) and \\(\\vec { b } \\)<\/p>\n
Question 37.
\nEvaluate: \\({ \\underset { x\\rightarrow 0 }{ lim } }\\) \\(\\frac { 3^{ x }-1 }{ \\sqrt { 1+x-1 } } \\)<\/p>\n
<\/p>\n
Question 38.
\nFind \\(\\frac{dy}{dx}\\) for y = tan-1<\/sup> \\((\\frac { cosx+sinx }{ cosx-sinx } )\\)<\/p>\nQuestion 39.
\nEvaluate: \u222bx5<\/sup> ex2<\/sup><\/sup><\/p>\nQuestion 40.
\nHow many automobile license plates can be made, if each plate contains two different letters followed by three different digits?<\/p>\n
PART – IV<\/span><\/p>\nIV. Answer all the questions. [7 \u00d7 5 = 35]<\/span><\/p>\nQuestion 41.
\n(a) If f : R – {-1, 1} \u2192 R is defined by f(x) = \\(\\frac { x }{ x^{ 2 }-1 } \\), verify whether f is one-to-one or not?<\/p>\n
[OR]<\/p>\n
(b) Solve: log2<\/sub> x + log4<\/sub> x + log8<\/sub> x = 11<\/p>\n
<\/p>\n
Question 42.
\n(a) Prove that \\(\\frac{\\sin x+\\sin 3 x+\\sin 5 x+\\sin 7 x}{\\cos x+\\cos 3 x+\\cos 5 x+\\cos 7 x}\\) = tan 4x<\/p>\n
[OR]<\/p>\n
(b) If x + y + z = xyz, then prove that \\(\\frac { 2x }{ 1-x^{ 2 } } \\) + \\(\\frac { 2y }{ 1-y^{ 2 } } \\) + \\(\\frac { 2z }{ 1-z^{ 2 } } \\) = \\(\\frac { 2x }{ 1-x^{ 2 } } \\) \\(\\frac { 2y }{ 1-y^{ 2 } } \\) \\(\\frac { 2z }{ 1-z^{ 2 } } \\)<\/p>\n
Question 43.
\n(a) If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then and the ranks of the words<\/p>\n
\n- GARDEN<\/li>\n
- DANGER<\/li>\n<\/ol>\n
[OR]<\/p>\n
(b) \\(\\underset { x\\rightarrow a }{ lim } \\) \\(\\frac{\\sqrt{x-b}-\\sqrt{a-b}}{x^{2}-a^{2}}\\) (a>b)<\/p>\n
<\/p>\n
Question 44.
\n(a) If the binomial coefficients of three consecutive terms in the expansion of (a + x)n<\/sup> are in the ratio 1 : 7 : 42 then find n?<\/p>\n[OR]<\/p>\n
(b) Evalute \\(\\sqrt { x^{ 2 }+y^{ 2 } } \\) = tan-1<\/sup>(\\(\\frac{y}{x}\\))<\/p>\nQuestion 45.
\nLet \\(\\vec { a } \\), \\(\\vec { b } \\), \\(\\vec { c } \\) be three vectors such that |\\(\\vec { a } \\)| = 3, |\\(\\vec { b } \\)| = 4, |\\(\\vec { c } \\)| = 5 and each one of them being perpendicular to the sum of the other two, find |\\(\\vec { a } \\) + \\(\\vec { b } \\) + \\(\\vec { c } \\)|.<\/p>\n
[OR]<\/p>\n
(b) Evaluate \u222bsec3<\/sup> 2xdx<\/p>\n
<\/p>\n
Question 46.
\n(a) Find all the equations of the straight lines in the family of the lines y = mx – 3, for which m and the x-coordinate of the point of intersection of the lines with x – y = 6 are integers?<\/p>\n
[OR]<\/p>\n
(b) There are two identical boxes containing respectively 5 white and 3 red balls, 4 white and 6 red balls. A box is chosen at random and a ball is drawn from it<\/p>\n
\n- Find the probability that the ball is white<\/li>\n
- If the ball is white, what is the probability that it from the first box?<\/li>\n<\/ol>\n
<\/p>\n
Question 47 (a).
\nIf Ai<\/sub> Bi<\/sub>, Ci<\/sub> are the cofactors of ai<\/sub>, bi<\/sub>, ci<\/sub>, respectively, i = 1 to 3 in<\/p>\n[OR]<\/p>\n
(b) Express the matrix \\(\\left(\\begin{array}{ccc}
\n3 & 3 & -1 \\\\
\n-2 & -2 & 1 \\\\
\n-4 & -5 & 2
\n\\end{array}\\right)\\) as the sum of symmetric martix and a skew-symmetric martix?<\/p>\n","protected":false},"excerpt":{"rendered":"
Students can Download Tamil Nadu 11th Maths Model Question Paper 2 English Medium Pdf, Tamil Nadu 11th 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 11th Maths Model Question Paper 2 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":[6],"tags":[],"class_list":["post-2793","post","type-post","status-publish","format-standard","hentry","category-class-11"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2793"}],"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=2793"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2793\/revisions"}],"predecessor-version":[{"id":40127,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2793\/revisions\/40127"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=2793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=2793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=2793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}