{"id":21498,"date":"2020-01-27T16:15:47","date_gmt":"2020-01-27T10:45:47","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21498"},"modified":"2021-07-02T15:26:30","modified_gmt":"2021-07-02T09:56:30","slug":"2nd-puc-basic-maths-previous-year-question-paper-march-2018","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-previous-year-question-paper-march-2018\/","title":{"rendered":"2nd PUC Basic Maths Previous Year Question Paper March 2018"},"content":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper March 2018, Karnataka <a href=\"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-model-question-papers-with-answers\/\">2nd PUC Maths Model Question Papers with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n<h2>Karnataka 2nd PUC Basic Maths Previous Year Question Paper March 2018<\/h2>\n<p>Time: 3 Hours 15 Min.<br \/>\nMax.Marks: 100<\/p>\n<p>Instructions:<\/p>\n<ul>\n<li>The question paper has 5 parts A, B, C, D and E. Answer all the pats.<\/li>\n<li>Part-A carries 10 marks\\, Parts &#8211; B carries 20 marks, Part &#8211; C carries 3 marks, Part &#8211; D carries 30 marks and Pat- E carries 1 marks.<\/li>\n<li>Write the question number properly as indicated in the question paper.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; A<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer all the ten questions: (10 \u00d7 1 = 10)\u00a0<\/span><\/p>\n<p>Question 1.<br \/>\nIf A = \\(\\left[ \\begin{matrix} 2 &amp; 4 \\\\ 3 &amp; -1 \\\\ 4 &amp; 0 \\end{matrix} \\right]\\) Show that (A&#8217;) = A<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65984\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-1.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 1\" width=\"376\" height=\"83\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-1.png 376w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-1-300x66.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 2.<br \/>\nHow many different 4 digit number can be formed using the digits 1,2,4,5, 7, 8, 9. No digit being repeated.<br \/>\nAnswer:<br \/>\nRequired arrangement = <sup>7<\/sup>P<sub>4<\/sub> =840<\/p>\n<p>Question 3.<br \/>\nSymbolise the proposition.<br \/>\n2 + 5 = 6 or all integers are rationals.<br \/>\nAnswer:<br \/>\nP : 2 + 5 = 69: All integers are rationals Symbol: p \u2228 q.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 4.<br \/>\nFind the duplicate ratio of 5 : 3.<br \/>\nAnswer:<br \/>\nDuplicate ratio of 5 : 3 = 5<sup>2<\/sup> : 3<sup>2<\/sup> = 25 : 9<\/p>\n<p>Question 5.<br \/>\nWhat rate of interest is obtained by investing in 9% stock at 180?<br \/>\nAnswer:<br \/>\nYield = \\(\\frac{9}{180} \\times 100\\) = 5%<\/p>\n<p>Question 6.<br \/>\nIf sin A = \\(\\frac { 3 }{ 5 }\\), find the 2A.<br \/>\nAnswer:<br \/>\nSin 2A = 2 sin ACos A = \\(2 \\cdot \\frac{3}{5} \\cdot \\frac{4}{5}=\\frac{24}{25}\\)<\/p>\n<p>Question 7.<br \/>\nFind the equation of directrix for a given parabola x<sup>2<\/sup> = 6y<br \/>\nAnswer:<br \/>\n4a = 6 a = \\(\\frac{3}{2}\\) Equation of directrix y = \\(\\frac{-3}{2}\\)<\/p>\n<p>Question 8.<br \/>\nEvaluate: \\(\\lim _{x \\rightarrow 0} \\frac{\\sin a x}{b x}\\)<br \/>\nAnswer:<br \/>\n\\(\\lim _{x \\rightarrow 0}=\\frac{\\sin a x}{a x} \\cdot \\frac{a}{b}=\\frac{a}{b}\\)<\/p>\n<p>Question 9.<br \/>\nIf y = 5a<sup>x<\/sup> \u2013 log x= 3\u221ax find any \\(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{d y}{d x}=5 a^{x} \\cdot \\log a-\\frac{1}{x}=\\frac{3}{2 \\sqrt{x}}\\)<\/p>\n<p>Question 10.<br \/>\nEvaluate: \\(\\int \\frac{1}{5 e^{-x}} d x\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{5} \\int e^{x} d x=\\frac{1}{5} e^{x}+c\\)<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; B<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any ten questions: (10 \u00d7 2 = 20 )<\/span><\/p>\n<p>Question 11.<br \/>\nSolve by Cramer&#8217;s rule 3x + 4y = 7 and 7x &#8211; y = 6.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65983\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-2.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 2\" width=\"381\" height=\"101\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-2.png 381w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-2-300x80.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 12.<br \/>\nFind n, if <sup>n<\/sup>P<sub>3<\/sub> = 210.<br \/>\nAnswer:<br \/>\n<sup>n<\/sup>P<sub>3<\/sub> = 210 n(n &#8211; 1) (n &#8211; 2) = 7 (7 &#8211; 1) (7 &#8211; 2)<br \/>\n\u2234 n = 7<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 13.<br \/>\nTwo dice are thrown at once. What is the probability of getting face upwards with &#8220;sum equal to 4 or 5&#8221;.<br \/>\nAnswer:<br \/>\nA: sum equal to 4 = {(1, 3)(2, 2)(3, 1)}<br \/>\nB: sum equal to 5 = {(1,4)(2,3)(3,2)(4,1)}<br \/>\nP(A \u222a B) = P(A) + P(B) = \\(\\frac{3+4}{36}=\\frac{7}{36}\\)<\/p>\n<p>Question 14.<br \/>\nIf the truth valued of propositions p,q,r ar T,T,F respectively. Then find the truth values of the compound propositions (p \u2228 r) \u2227 q.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65982\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-3.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 3\" width=\"247\" height=\"62\" \/><\/p>\n<p>Question 15.<br \/>\nMonthly income of A and B are in the ratio 2:3 and their monthly expenditure are in the ratio 3:5. If each saves \u20b9 100 per month. Find the monthly incomes of A and B.<br \/>\nAnswer:<br \/>\nLet the monthly incomes be 2x and 3x respectively since their savings are \u20b9 100 their expenditure would be<br \/>\n(2x &#8211; 100) and (3x &#8211; 100) Given \\(\\frac{2 x-100}{3 x-100}=\\frac{3}{5}\\) \u21d2 x = \u20b9100<br \/>\n\u2234 Monthly incomes of A = \u20b9 400<br \/>\nMonthly income of B = \u20b9 600<\/p>\n<p>Question 16.<br \/>\nA bill drawn for 3 month was legally due on 06.07.2018. Find the date of drawing of the bill.<br \/>\nAnswer:<br \/>\nDate of drawing = 06 &#8211; 07 &#8211; 2018<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65981\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-4.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 4\" width=\"248\" height=\"79\" \/><\/p>\n<p>Question 17.<br \/>\nFind the value of sin 15\u00b0.<br \/>\nAnswer:<br \/>\n\u015fin 15 = sin(45\u00b0 &#8211; 30%) = sin 45\u00b0 cos 30\u00b0 &#8211; cos 45 sin 30<br \/>\n\\(=\\frac{1}{\\sqrt{2}} \\cdot \\frac{\\sqrt{3}}{2}-\\frac{1}{\\sqrt{2}} \\cdot \\frac{1}{2}=\\frac{\\sqrt{3}-1}{2 \\sqrt{2}}\\)<\/p>\n<p>Question 18.<br \/>\nShow that tan (45\u00b0 + A) tan(45\u00b0- A) = 1.<br \/>\nAnswer:<br \/>\nL.H.S = tan(45\u00b0 + A).tan(45\u00b0 + A) = \\(\\frac{1+\\tan A}{1-\\tan A} \\cdot \\frac{1-\\tan A}{1+\\tan A}\\)<br \/>\n= 1 = R.H.S<\/p>\n<p>Question 19.<br \/>\nFind the equation of parabola given that vertex is origin (0,0) and passing through the point P(5,2) and symmetric with respect to the y-axis.<br \/>\nAnswer:<br \/>\nEquation of parabola is x<sup>2<\/sup> = 4ay<br \/>\nHere parabola passing through(5,2) \u2234 5<sup>2<\/sup> = 4a(2) 4a = \\(\\frac{25}{2}\\)<br \/>\n\u2234 Equation is x<sup>2<\/sup> = \\(\\frac{25}{2} y\\)<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65980\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-5.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 5\" width=\"451\" height=\"56\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-5.png 451w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-5-300x37.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><br \/>\nAnswer:<br \/>\n\\(\\lim _{x \\rightarrow 1} f(x)=f(1) \\Rightarrow \\lim _{x \\rightarrow 1} 4 x+3=k+1\\)<br \/>\n\u21d2 4 + 3 = k + 1 \u21d2 k = 6<\/p>\n<p>Question 21.<br \/>\nFind \\(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\) if y = \\(\\sqrt{x+\\sqrt{x+\\sqrt{x+\\dots \\infty}}}\\)<br \/>\nAnswer:<br \/>\ny = \\(\\sqrt{x+y}\\) y<sup>2<\/sup> &#8211; 2y = x<br \/>\n\\(\\frac{d y}{d x}=\\frac{1}{2 y-1}\\)<\/p>\n<p>Question 22.<br \/>\nIf S = 5t<sup>2<\/sup> +4t &#8211; 8.Find the initial velocity and acceleration.<br \/>\nAnswer:<br \/>\nv = 10t + 4 Initial velocity = 0 + 4 = 4<br \/>\na = 10<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 23.<br \/>\nEvaluate: \u222b(4x<sup>2<\/sup> &#8211; 2x + 7)<sup>3\/2<\/sup> (4x &#8211; 1)dx.<br \/>\nAnswer:<br \/>\nPut 4x<sup>2<\/sup> &#8211; 2x + 7 = t (8x &#8211; 2)dx = dt (4x-1)dx = \\(\\frac{\\mathrm{dt}}{2}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65979\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-6.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 6\" width=\"351\" height=\"79\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-6.png 351w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-6-300x68.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\n= \\(\\frac{1}{5}\\)(4x<sup>2<\/sup> &#8211; 2x + 7)<sup>5\/2<\/sup> + c<\/p>\n<p>Question 24.<br \/>\nEvaluate: \\(\\int_{1}^{2} \\frac{1}{x} d x\\)<br \/>\nAnswer:<br \/>\n(log x)<sup>2<\/sup><sub>1<\/sub> = log 2<br \/>\nAppendix B: Examination Question Papers L<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; C<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any ten questions: (10 \u00d7 3 = 30 )<\/span><\/p>\n<p>Question 25.<br \/>\nIf A = \\(\\left[ \\begin{matrix} -1 &amp; 2 \\\\ 3 &amp; 4 \\end{matrix} \\right] \\) show that A(adj A) = (adj A)A = |A|I.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65978\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-7.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 7\" width=\"469\" height=\"191\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-7.png 469w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-7-300x122.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 26.<br \/>\nShow that \\(\\left| \\begin{matrix} -{ a }^{ 2 } &amp; ab &amp; bc \\\\ ab &amp; -{ b }^{ 2 } &amp; bc \\\\ ac &amp; bc &amp; -{ c }^{ 2 } \\end{matrix} \\right| \\) = 4a<sup>2<\/sup>b<sup>2<\/sup>c<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65977\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-8.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 8\" width=\"356\" height=\"163\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-8.png 356w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-8-300x137.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p>Question 27.<br \/>\nA team of 11 is to be chosen from 18 cricketers of whom 6 are bowlers and 3 are wicket keepers. In how many ways can a team be chosen so that.<br \/>\ni. There are exactly 4 bowlers and one wicket keeper<br \/>\nii. There are atleast 4 bowlers and atleast 2 wicket keepers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65976\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-9.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 9\" width=\"668\" height=\"363\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-9.png 668w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-9-300x163.png 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p>Question 28.<br \/>\nIf A and B are event with P(A) = \\(\\frac { 5 }{ 8 }\\) P(B) = \\(\\frac { 3 }{ 8 }\\) and P(A \u222a B) = \\(\\frac { 3 }{ 4 }\\) Find<br \/>\n(1) P(B\/A)<br \/>\n(ii) P(A\/B)<br \/>\nAnswer:<br \/>\nP(A \u2229 B) = P(A) + P(B) &#8211; P(A \u222a B)<br \/>\n\\(=\\frac{5}{8}+\\frac{3}{8}-\\frac{3}{4}=\\frac{5+3-6}{8}=\\frac{2}{8}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65975\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-10.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 10\" width=\"346\" height=\"169\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-10.png 346w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-10-300x147.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 29.<br \/>\nTwo taps can separately fill a tank in 12 min and 15 minutes respectively. The tank when full can be emptied by a drain pipe is 20 minutes. When the tank was empty, all the three were opened simultaneously. In what time will the tank be filled up?<br \/>\nAnswer:<br \/>\n1<sup>st<\/sup> tap can fill \\(\\frac{1}{12}\\)th tank in 1 min<br \/>\n2<sup>nd<\/sup> tap can fill \\(\\frac{1}{15}\\)th tank in 1 min<br \/>\nDrain pipe drain out \\(\\frac{1}{20}\\)th tank in 1 min<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65962\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-23.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 23\" width=\"423\" height=\"54\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-23.png 423w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-23-300x38.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><br \/>\n\u2234 the tank will get filled in 10 minutes.<\/p>\n<p>Question 30.<br \/>\nThe banker&#8217;s gain on a bill is \\(\\frac{1}{5}\\) of the banker&#8217;s discount and the rate of interest is 20% p.a. Find the unexpired period of the bill.<br \/>\nAnswer:<br \/>\nBG = \\(\\frac{1}{5}\\) BD r = 20% = 0.2<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65974\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-11.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 11\" width=\"299\" height=\"176\" \/><\/p>\n<p>Question 31.<br \/>\nRakshith decides to invest in TCS shares which are selling at 2020 per share. How much money is required to purchase 10 shares, if the brokerage in 0.5%<br \/>\nAnswer:<br \/>\nAmount required to purchase 10 TCS shares = 2,020 \u00d7 10<br \/>\n= 20,200<br \/>\nBrokerage = 0.005 \u00d7 20,200 = 101<br \/>\nNet amount = 20,200 + 101 = 20,301<\/p>\n<p>Question 32.<br \/>\nThe price of a washing machine inclusive of sales tax is 13,530. If the sales tax is 10% . Find the basic price.<br \/>\nAnswer:<br \/>\nSuppose the basic price (MP) of the washing machine = Rs. x<br \/>\n\u2234 total amount paid = MP + ST % of MP<br \/>\n13,530 = x + 0.1x<br \/>\nx = 12,300<\/p>\n<p>Question 33.<br \/>\nFind the length of the chord of the circle x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 6x &#8211; 4y &#8211; 12 = 0 on the coordinate axes.<br \/>\nAnswer:<br \/>\nFormulas<br \/>\nx = intercept = \\(2 \\sqrt{g^{2}-c}=2 \\sqrt{9+12}=2 \\sqrt{21}\\)<br \/>\ny &#8211; intercept \\(2 \\sqrt{f^{2}-c}=2 \\sqrt{4+12}=2 \\sqrt{4+12}\\) = 8<\/p>\n<p>Question 34.<br \/>\nIf x = a sec \u03b8, y = b tan \u03b8 find \\(\\frac{d y}{d x}\\) at \u03b8 = \\(\\frac{\\pi}{4}\\)<br \/>\n\\(\\frac{d y}{d x}=\\frac{b \\sec \\theta}{a \\tan \\theta}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65972\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-13.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 13\" width=\"138\" height=\"61\" \/><\/p>\n<p>Question 35.<br \/>\nThe volume of a sphere is increasing at the rate 4\u03c0 cc\/sec, Find the rate at which the area of its surface increases when its radius is 10cm.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65973\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-12.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 12\" width=\"444\" height=\"140\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-12.png 444w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-12-300x95.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 36.<br \/>\nShow that x<sup>x<\/sup> is minimum at x = \\(\\frac{1}{e}\\)<br \/>\nAnswer:<br \/>\ny = x<sup>x<\/sup> \\(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\) = x<sup>x<\/sup>(1 +log x)<br \/>\n\\(\\frac{d^{2} y}{d x^{2}}=x^{x}\\left(\\frac{1}{x}\\right)+x^{x}(1+\\log x)^{2}=x^{x}\\left\\{\\frac{1}{x}+(1+\\log x)^{2}\\right\\}\\)<br \/>\nFor minima \\(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\) = 0 x<sup>x<\/sup> (1 + log x) = 0 \u21d2 x = \\(\\frac{1}{e}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65971\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-14.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 14\" width=\"176\" height=\"66\" \/><br \/>\n\u2234 y is minimum at x = \\(\\frac{1}{e}\\)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 37.<br \/>\nEvaluate: \u222bx<sup>2<\/sup> log x dx.<br \/>\nAnswer:<br \/>\n\u222bx<sup>2 <\/sup>log xdx<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65970\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-15.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 15\" width=\"160\" height=\"123\" \/><br \/>\n\\(=\\frac{x^{2}}{3} \\log x-\\int \\frac{x^{3}}{x} d x\\)<br \/>\n\\(=\\frac{x^{3}}{3} \\log x-\\frac{x^{3}}{9}+c\\)<\/p>\n<p>Question 38.<br \/>\nEvaluate \u222bcosec x[cosec x + cot x]dx.<br \/>\nAnswer:<br \/>\n\u222b(Cosec<sup>2<\/sup>x + Cosec xCotx)dx<br \/>\n= cot x &#8211; Cosec x + c<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; D<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any six questions: (6 \u00d7 5 = 30 )<\/span><\/p>\n<p>Question 39.<br \/>\nEvaluate (2 + \u221a3)<sup>5<\/sup> + (2 &#8211; 13)<sup>5<\/sup><br \/>\nAnswer:<br \/>\n(2 + \u221a3)<sup>5<\/sup> + (2 &#8211; \u221a3)<sup>5<\/sup> = 2 [<sup>5<\/sup>C<sub>0<\/sub> 2<sup>5<\/sup> + <sup>5<\/sup>C<sub>2<\/sub>2<sup>3<\/sup> (\u221a3)<sup>2<\/sup> + <sup>5<\/sup>C<sub>4<\/sub>2<sup>1<\/sup> (\u221a3)<sup>4<\/sup> ]<br \/>\n= 2[32 + 240 + 90]<br \/>\n= 724<\/p>\n<p>Question 40.<br \/>\nResolve into partial fractions: \\(\\frac{3 x+5}{(x+2)(x-1)^{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65969\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-16.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 16\" width=\"264\" height=\"57\" \/><br \/>\n3x + 5 = A(x &#8211; 1)<sup>2<\/sup> + (x + 2)(x &#8211; 1) + C(x + 2)<br \/>\nA = \\(\\frac{-1}{9}\\) C = \\(\\frac{8}{3}\\) 0 = A + B B = \\(\\frac{1}{9}\\)<br \/>\nSubstitution of A,B,C<\/p>\n<p>Question 41.<br \/>\nVerify whether the compound proposition p \u2192 p(~p \u2228 q) is a tautology or a contradiction or neither.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65968\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-17.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 17\" width=\"431\" height=\"224\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-17.png 431w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-17-300x156.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Question 42.<br \/>\nIf two men or four women can do a work in 33 days and 3 men and 5 women can do the same work in 24 days? How long shall 5 men and 2 women take to do the same work?<br \/>\nAnswer:<br \/>\n2 men and 4 women can do a work in 33 days.<br \/>\n66 men and 132 women can do a work in 1 day<br \/>\nSimilarly 3 men and 5 women can do a work in 24 days<br \/>\n72 men and 120 women can do a work in 1 day<br \/>\n\u2234 66 men + 132 women = 72 men + 120 women<br \/>\n\u2234 1 man = 2 women<br \/>\n5 men + 2 women = 10 women + 2 women =12 women<br \/>\nLet the required number of days be x<br \/>\n2 men + 4 women = 4 women + 4 women = 8 women<br \/>\n8W : 12W = x : 33<br \/>\n12x = 33 \u00d7 8 \u2234 x = 22 days<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 43.<br \/>\nSumsung company which manufacture LCD TV. The 1<sup>st<\/sup> lot of 10 units was completed in 1400 labour hours. Find each subsequent lot, the commutative production was doubled. And it has observed that 90% learning effect applies to all labour related cost. The anticipated production is 320 units of LCD TV find total labour cost required to manufacture 320 unit and also find the total labour cost at \u20b9 20\/hrs.<br \/>\nAnswer:<br \/>\nLet 10 units = 1 lot<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65967\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-18.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 18\" width=\"616\" height=\"233\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-18.png 616w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-18-300x113.png 300w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><br \/>\nTotal labour hrs = 26453.952<br \/>\nLabour cost at Rs. 20\/hr = 529079.04<\/p>\n<p>Question 44.<br \/>\nSolve the LPP graphically:<br \/>\nZ = 3x + 5y<br \/>\nSubject to : x + 3y \u2264 3<br \/>\nx + y \u2264 2<br \/>\nx,y \u2265 0.<br \/>\nAnswer:<br \/>\nx + 3y = 3. A(3,0) B(0,1)<br \/>\nx + y =2 C(2,0) D(0,2)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65966\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-19.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 19\" width=\"238\" height=\"192\" \/><\/p>\n<p>Question 45.<br \/>\nIn any triangle ABC, prove that<br \/>\nsin 2A + sin 2B &#8211; sin 2C = 4 cos A cos B sin C.<br \/>\nAnswer:<br \/>\nLHS = sin 2a + sin 2B &#8211; sin 2C<br \/>\n= 2sin (A + B) cos (A &#8211; B) &#8211; 2 sin C cos C<br \/>\n{A + B + C = 180\u00b0 A + B = 180 &#8211; c}<br \/>\n{Sin(A + B) = Sinc Cos(A + B) = -Cosc}<br \/>\nLHS = 2 Sin C {Cos (A &#8211; B)-2 sin CCos C<br \/>\n= 2 sin C {Cos (A &#8211; B) + Cos(A + B)}<br \/>\n= 4 Cos A Cos B Sin C<\/p>\n<p>Question 46.<br \/>\nFind the equation of the circle passing through the points (0,2) (3,0) and (3,2).<br \/>\nAnswer:<br \/>\nLet equation of circle be<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> + 2gx + 2fy + c = 0 &#8230;. (1)<br \/>\nHere circle passing through (0,2)(3,0) and (3,2)<br \/>\n6g + C = -9 &#8230;. (2)<br \/>\n4f + C = 4 &#8230;. (3)<br \/>\n6g + 4f + c = -13 &#8230;. (4)<br \/>\n6g &#8211; 4 = -13 6g = -9 g = \\(\\frac{-3}{2}\\)<br \/>\n4f &#8211; 9 = 13 4f = -4 f = -1<br \/>\n-4 + c = -4 c = 0<br \/>\n(1) \u21d2 x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 6x &#8211; 2y = 0<\/p>\n<p>Question 47.<br \/>\nIf y &#8211; a cos (log x) + b sin (log x). Prove that x<sup>2<\/sup>y<sub>2<\/sub> + xy<sub>1<\/sub> + y = 0<br \/>\nAnswer:<br \/>\ny = a cos (log x) + b sin (log x)<br \/>\ny<sub>1 = <\/sub>\\(\\frac{-a \\sin (\\log x)}{x}+\\frac{b \\cos (\\log x)}{x}\\)<br \/>\nxy<sub>1<\/sub> = &#8211; a sin (log x) +b cos(log x)<br \/>\n\\(x y_{1}+y_{1}=\\frac{-a \\cos (\\log x)}{x}+\\frac{b \\sin (\\log x)}{x}\\)<br \/>\nx<sup>2<\/sup>y<sub>2<\/sub> + xy<sub>1<\/sub> = &#8211; [a cos (log x) + b sin (log x)]<br \/>\nx<sup>2<\/sup>y<sub>2<\/sub> + xy<sub>1<\/sub> = -y<br \/>\nx<sup>2<\/sup>y<sub>2<\/sub> + xy<sub>1<\/sub> + y = 0<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>Question 48.<br \/>\nFind the area enclosed between the curves y<sup>2<\/sup> = x and x<sup>2<\/sup> = y.<br \/>\nAnswer:<br \/>\ny<sup>2<\/sup> = x &#8230; (1)<br \/>\nx<sup>2<\/sup> = y &#8230; (2)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65965\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-20.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 20\" width=\"242\" height=\"158\" \/><br \/>\nSolving (1) and (2) we get<br \/>\nx=0 x = 1<br \/>\nRequired area \\(\\int_{0}^{1}\\left\\{\\sqrt{x}-x^{2}\\right\\} d x=\\left\\{\\frac{2}{3} x^{\\frac{3}{2}}-\\frac{x^{3}}{3}\\right\\}_{0}^{1}\\)<br \/>\n= \\(\\frac{2}{3}-\\frac{1}{3}=\\frac{1}{3}\\) sq.units<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">Part &#8211; E<\/span><\/p>\n<p><span style=\"color: #0000ff;\">Answer any six questions: (6 \u00d7 5 = 30 )<\/span><\/p>\n<p>Question 49.<br \/>\n(a). A school wants to award its students for the values of punctuality, good behavior and hard work with a total cash award \u20b9 6,000. Three time the award money for hard work together with the award money for punctuality is \u20b9 11,000 the award money for punctuality and hard work together is double the one given for Good Behavior. Represent the above situation algebraically and also find the award money<br \/>\nfor each value. Using matrix method.<br \/>\nAnswer:<br \/>\nLet the values of punctuality. Good Behavior and Hard work be denote by x,y and z respectively<br \/>\nx + y + z = 6000<br \/>\nx + 32 = 11000<br \/>\nx &#8211; 2y + z = 0<br \/>\nIts matrix form is Ax = B where<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65964\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-21.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 21\" width=\"285\" height=\"241\" \/><\/p>\n<p>\u2234 x = \u20b9 500 y = \u20b9 2000 \u2234 z = \u20b93500<\/p>\n<p>b. Find the value of (1,01)<sup>5<\/sup> using Bonomial upto 4 decimal places.<br \/>\nAnswer;<br \/>\n(1.01)<sup>5<\/sup> = (1 + 0.01)<sup>5<\/sup><br \/>\n= 1 + <sup>5<\/sup>C<sub>1<\/sub>(0.01) + <sup>5<\/sup>C<sub>2<\/sub>(0.01)<sup>2<\/sup> + <sup>5<\/sup>C<sub>3<\/sub> (0.01)<sup>3<\/sup> + <sup>5<\/sup>C<sub>4<\/sub> (0.01)<sup>4<\/sup> + <sup>5<\/sup>C<sub>5<\/sub> (0.01)<sup>5<\/sup><br \/>\n= 1 + 5(0.01)+10(0.001)+10(0.000001) + ignoring the further terms<br \/>\n= 1.0510[correct upto 4 decimals]<\/p>\n<p>Question 50.<br \/>\nAnswer:<br \/>\n(a). If n is a rational number and &#8216;a&#8217; is non-zero real number, then prove that \\(\\lim _{x \\rightarrow a} \\frac{x^{n}-a^{n}}{x-a}=n a^{n-1}\\)<br \/>\nAnswer<\/p>\n<p>Case &#8211; 1 : Let n be a positive integer.<br \/>\nx<sup>n<\/sup> &#8211; a<sup>n<\/sup> = (x &#8211; a)(x<sup>n -1<\/sup> + x<sup>n-2<\/sup> . a + x<sup>n-3<\/sup> . a<sup>2<\/sup> + &#8230;&#8230;. + a<sup>n-1 <\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65986\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-24.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 24\" width=\"569\" height=\"240\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-24.png 569w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-24-300x127.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Case &#8211; 2: Let n be a positive integer<br \/>\nPut n = -m, m &gt; 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65987\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-25.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 25\" width=\"646\" height=\"147\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-25.png 646w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-25-300x68.png 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65988\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-26.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 26\" width=\"349\" height=\"222\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-26.png 349w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-26-300x191.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p>Case &#8211; 3: Let n = p\/q where p and q are integers and q \u2260 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65989\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-27.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 27\" width=\"500\" height=\"376\" srcset=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-27.png 500w, https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-27-300x226.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2019\/11\/KSEEB-Solutions.png\" alt=\"KSEEB Solutions\" width=\"172\" height=\"16\" \/><\/p>\n<p>(b). The angles of depression of two boats as observed from the mast head of a ship 50m high are 45o and 30\u00b0. What is the distance between the boats if they are on the same side of the mast head in line with it?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65963\" src=\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2020\/01\/2nd-PUC-Basic-Maths-Previous-Year-Question-Paper-March-2018-22.png\" alt=\"2nd PUC Basic Maths Previous Year Question Paper March 2018 - 22\" width=\"289\" height=\"191\" \/><br \/>\nLet point D be the position of observer<br \/>\nPoints A and B be the position of boats<br \/>\nCD = height of mast head = 50m<br \/>\nA = 30\u00b0 B = 45\u00b0 AB = ?<br \/>\nFrom triangle BCD, tan 45\u00b0 = \\(\\frac{50}{\\mathrm{CB}}\\) \u2234 CB = 50<br \/>\nFrom triangle ACD, tan 30\u00b0= \\(\\frac{50}{\\mathrm{AC}}\\) AC = 50\u221a3<br \/>\nAB &#8211; BC = 50\u221a3<br \/>\nAB = 50\u221a3 + 50 = 50(\u221a3 &#8211; 1)<br \/>\nDistance between boats = 50(\u221a3 &#8211; 1)m<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download 2nd PUC Basic Maths Previous Year Question Paper March 2018, Karnataka 2nd PUC Maths Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Previous Year Question Paper March 2018 Time: 3 Hours 15 Min. &hellip;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21498"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=21498"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21498\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}