hsc maths question paper 2018 commerce with solutions

CBSE Class 12 Mathematics Question Paper with Solution: 2018 Solving previous years’ papers of CBSE is the best way to check your preparedness for the upcoming board exams 2019. Need help acing your HSC for Maths Advanced? Oops! Maths Question Paper 2018 Class 12 is attached here for reference. From the two cases above, it can be concluded that ax2 + 2hxy + by2 = 0 represents a pair of lines passing through the origin. Understanding the pattern of the question paper is of much importance. \end{align*}, \begin{align*} &=\frac{6\sqrt{3}}{\sqrt{5}}\\ Maths Question Paper 2018 Class 12 is attached here for reference. &\approx 0.0319 \quad \text{(4 d.p.)} \end{gather*}, 12. Practising last 10 years Papers 12th of Gujarat Board is very important. $$ a = 1, d = 1, n = 20 $$ The only point satisfies both conditions is point \(x=b\). \end{align*}, Rearrange the equation to make \(x\) the subject. View the 2018 HSC Mathematics Extension 1 Exam Paper solutions with detailed explanations for multiple choices and extended response questions. The symmetry of this result shows that the point which divides the other two medians in the ratio 2:1 will also have the same position vector. \ = \frac{1}{5}(e^{15} – 1) \frac{1}{2}(3x)\sin30° + \frac{1}{2}(6x)\sin30° &= \frac{9\sqrt{3}}{2} \\ Question 3[A]: Attempt any two of the following. Download Maharashtra State Board previous year question papers 12th Board Exam PDFs with solutions for HSC Science (General) . [i] Find the joint equation of the pair of lines passing through the origin, which are perpendicular to the lines represented by 5x2 + 2xy – 3y2 = 0. \frac{dy}{dx} = -2\sin(2x) \\ &=3\sqrt{5}\,\,\text{unit}\\ \begin{gather*} Therefore 2018 HSC Mathematics Advanced Exam Paper Solutions … [iv] Find the vector equation of the line which passes through the point with position vector 4i – j + 2k and is in the direction of -2i + j + k. The equation of the line which passes through the point is. \end{align*}, \begin{align*} Case (i): If f (x) is an even function, then f (-x) = f (x). The previous year GSEB question papers will help the students to get familiarised with the pattern, and the types of questions asked in the exams. 9x &= 18\sqrt{3} \\ HSC Archived Threads. x = \frac{t^3}{3} – 2t^2 + 3t \\ \end{gather*}, Using cosine rule, = 2 cos2 ɑ – 1 + 2 cos2 ꞵ – 1 + 2 cos2 – 1 + 1. \text{therefore} \ AD+ BD &= AB \\ \end{align*} (d) iii. In this post, we will work our way through the 2018 HSC Maths Advanced paper and give you the solutions, written by our leading teacher Oak Ukrit and his team. Hence, the medians of a triangle are concurrent at G. [iii] If the origin is the centroid of the triangle whose vertices are A (2, p, -3), B (q, -2, 5), R (-5, 1, r), then find the value of p, q and r. Let a, b and c be the position vectors of the triangle ABC whose vertices are A (2, p, -3), B (q, -2, 5), R (-5, 1, r). k+3 &= 12 \quad (\text{because} \ k > 0) \\ [i] Using the vector method prove that the medians of a triangle are concurrent. &= 0.145 MHT-CET Question Paper 2018 solution. ∫-aa f (x) dx = ∫0a [- f (x) + f (x)] dx = 0, Question 6[A]: Attempt any two of the following. Physics, Chemistry, Maths, Biology, English, Hindi and Marathi Subjects This is the joint equation of lines x = 0 and (ax + 2hy) = 0. $$-3 < k < 3$$, DAY 1: \(n = 1 \Rightarrow 2^{1} + 1 = 3\) downloads Then you have reached to the right place. Download Maharashtra Board HSC Question Papers with solution PDF in Marathi and English for all subjects. &=300000(1.04)^{3}-P((1.04)^{2}+1.05(1.04)+(1.05)^{2})\,\,\,\text{As Required}\\ Maharashtra HSC 12th Question Paper 2020-2021 with answers for Science, Physics, Arts now available. (D) Since \(x^{2}=4ay\), at \(y=4, x=12\) (via symmetry) Substituting values of \(x\) and \(y\) gives \(a=9\), 9. Thus all the conditions on Rolle’s theorem are satisfied. In this equation at least one of the coefficients a, b or h is non 0. \end{align*}, \begin{align*} These samplers help a lot in knowing the pattern of the question paper. \text{therefore} \ P(\sqrt{3},-4\sqrt{3})\\ \frac{3x}{4} + \frac{6x}{4} &= \frac{9\sqrt{3}}{2} \\ [8]. &= 4x^2 + 6xy + 9y^2 \\ These guess papers are for commerce students and will help you in getting a better understanding of examination patterns. x &= 2\sqrt{3} \text{ units} Maharashtra State Board Class 12 maths 2018 question paper with solutions are available on this page, by BYJU’S, in downloadable pdf format and also in the text for the students to prepare well for the MSBSHSE exams. \text{Since } \angle ABC \text{ is common, } \triangle CBD \, ||| \, \triangle ABC \,\,\text{(Equiangular)} Question Bank of DBATU Architecture Examinations. Unauthorised use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. \end{gather*} CBSE Question Paper Class 12 are provided below for Maths. \begin{align*} \begin{gather*} To obtain the value of c, the following steps are followed. BD &= \frac{4}{3} \\ \frac{2\pi t}{366} &= \frac{2\pi}{3},\frac{4\pi}{3} \\ [iii] Find the distance of the point (1, 2, -1) from the plane x – 2y + 4z – 10 = 0. \end{align*}, \begin{align*} If \(f(x)\) has no stationary points, \(f'(x)\) has no roots. k &= \frac{1}{50}\ln\left(\frac{184}{92}\right) \\ Question 1[A]: Select and write the most appropriate answer from the given alternatives in each of the following sub-questions. Your email address will not be published. &=\frac{2\pi x(100-x^{2})-\pi x^{3}}{3\sqrt{100-x^{2}}}\\ Share your notes and trial papers on our Notes & Resources page . V&= \frac{1}{3}\pi^{2}h,\\ \text{Hence OA}\,&=\sqrt{3^{2}+6^{2}}\\ Here we have your CBSE class 12th guess papers for session 2018-19. march 2018 hsc commerce maths paper solution. 300000(1.04)^{n}-P(1.05^{n}-1.04^{n})&>0\\ Previous Year Maharashtra HSC … Free PDF download of Maharashtra HSC Board Class 12 Maths question paper 2018 with solutions solved by expert teachers on Vedantu.com. The subjects are – English, Assamese, General science, General mathematics, advanced mathematics, Social science, Hindi, Computer Science, IT (a) ii. 2\ln(k+3) &= \ln 144 \\ Previous year question papers serve as an important source to know important topics and type … No roots if \(\Delta < 0, B^2 – 4AC < 0\). = (1 / 2)*ʃ {sec (x / 2)2}*dx / [1 + [1 + {tan (x / 2)}2]] [Multiplying both numerator and denominator by {sec (x / 2)2}. AP for \(n\): &= \frac{20}{2}(1 + 20) \\ \ = 196 – 140 \\ \begin{align*} GP for \(2^n\): (iii) f (0) = 10, f (4) = 16 – 16 + 10 = 10. \end{align*}, \begin{gather*} \text{therefore} \ h&=\sqrt{100-x^{2}}\\ \begin{align*} \text{Since} A_n>0,\\ Mah. \text{therefore} \ \theta=\frac{2\sqrt{2}\pi}{\sqrt{3}} 92e^{50k} & = 184 \\ Question 4[A]: Select and write the appropriate answer from the given alternatives from each of the following sub-questions. \text{therefore} \ \,\text{Area}\Delta\,OAP\,&=\frac{1}{2}\times\frac{6\sqrt{3}}{\sqrt{5}}\times3\sqrt{5}\\ See the exam paper, plus marking guidelines and feedback from markers, for the 2018 NSW Mathematics Higher School Certificate (HSC) exam. Let the points be A (1, 0, 1), B (1, -1, 1), C (4, -3, 2). 4. [B] Attempt any two of the following: [8], [i] Prove that: sin-1 (3 / 5) + cos-1 (12 / 13) = sin-1 (56 / 65). So we had mentioned some HSC Study Tips to help students in Cracking HSC Exams.. After the tremendous success of our last year Important Questions Bank for Tamil Nadu HSC (12th Std) Board Exam 2017, we have also created a list of 51 Most Important Question … Hence \(\int_0^3 f(x)\,dx = 10+3 = 13\) = 2 cos [(C + A) / 2] sin [(C – A) / 2] / 2 sin [(C + A) / 2] cos [(C – A) / 2], tan [(C – A) / 2] = [c – a] / [c + a] cot (b / 2). By practising Class 12 Maths Maharashtra board question paper to score more marks in your examination. NESA 2018 HSC Mathematics General 2 Marking Guidelines Page 5 of 21 . DAY 3: \(n = 3 \Rightarrow 2^{3} + 3 = 11\) downloads. Show that \(\dfrac{d^2y}{dx^2}\) at \(x = 2\) is zero, and \(\dfrac{d^2y}{dx^2}\) changes sign at \(x= 1\) and \(x = 3\). P(50) & = 184 \quad \quad \text{* units in millions} \\ 6. Let θ be the acute angle between the 2 given lines. (C) P(Matching Pairs) = P(Any Shoes) \(\times P(Matching Shoe) = 1\times\frac{1}{7}  =  \frac{1}{7}\), 7. These sample papers also let you know your ability and the level of preparation. T_{50} &= (a + 2d) + 47d \\ A_4&=300000(1.04)^{4}-P(1.04^{3}+1.04^{2}(1.05)+1.04(1.05)^{2}+(1.05)^{3})\\ \text{Simiarly, In } \triangle ABC, AB = CD \quad \text{(isosceles triangle)} \\ \end{align*}, \begin{gather*} The Question papers and Answer key of March 2017 & 2018 Higher secondary examinations are published here, after the conduct of examination of each subject. [ii] Find the angle between the lines (x – 1) / 4 = (y – 3) / 1 = z / 8 and (x – 2) / 2 = (y + 1) / 2 = (z – 4) / 1. Jun 29, 2018; Maharashtra Board HSC Examination 2016 Question Papers. a = 2, r = 2, n = 20 \\ Here we are providing the Maharashtra Board HSC Question Papers of Mathematics subject.With the help of these MBSE question papers for Mathematics, candidates can estimate the level and pattern of questions asked by the Maharashtra board in the upcoming Senior Secondary examination.As these papers … y&=x^{3}-7x\\ Consider AP & GP separately. CBSE Question Paper Class 12 2018 Maths with Answers … AC^2 &= AB^2 + BC^2 – 2AB\cdot BC\cdot \cos 110° \\ Given \(y = 6x^2 – x^3\), \(\frac{dy}{dx} = 12x – 3x^2\) Let \(\frac{dy}{dx} = 0\), and solve for \(x\). \text{Test the nature of the stationary point using either table method or Second derivative} \\ [i] Evaluate ∫1 / [3 + 2 sinx + cos x] dx. HSC Board Exams are fast approaching and students are getting anxious about how to prepare for their HSC Board Exams. While it may take a few months for the official marking guidelines to come out, I have worked through the 2018 HSC Mathematics General 2 exam for you to provide you with the solutions early! Get Last Year Question Paper for 12th Board Exam and solved answers for practice … \end{align*} [ii] In △ABC prove that tan [c – a] / 2 = [c – a] / [c + a] cot (b / 2). 10th std. So, without wasting … BK Economics Mathematics (Paper 1) Mathematics (Paper 2) OC SP. [i] Show that a homogeneous equation of degree 2 in x and y that is ax2 + 2hxy + by2 = 0 represents a pair of lines passing through the origin if h2 – ab ≥ 0. Download Free Previous Years HSC Science Question Papers from 2013-2020. A_1&=300000\times1.04-P \\ &=\sqrt{45}\\ \begin{align*} (b x c). \end{align*}, \begin{align*} maharashtra: 9th std. If you continue to use this site, you consent to our use of cookies. A_3&=A_2(1.04)-P(1.05)^{2}\\ (1.04^{n-1}+…+1.05^{n-1})&=(1.05^{n}-1.04^{n})(100)\\ Marking scheme of each set of Class 12 Question Paper is also provided to help you calculate marks you can score step wise. \frac{dV}{dx}&=\frac{2}{3}\pi x\sqrt{100-x^{2}} – \frac{2}{3}\pi x^{3} \frac{1}{\sqrt{100-x^{2}}}\times\frac{1}{2}\\ [ii] Prove that ∫(1 / a2 – x2) dx = (1 / 2a) log [(a + x) / (a – x)] + c. = (1 / 2a) ∫[(a + x) / (a – x) / (a + x) / (a – x)] dx, = (1 / 2a) ∫(1 / (a + x)) + (1 / (a – x)) dx, = (1 / 2a) [∫(1 / (a + x)) dx + ∫(1 / (a – x)) dx], = (1 / 2a) [log |a + x| – log |a – x|] + c. [iii] Show that ∫-aa f (x) dx = 2 ∫0a f (x) dx, if f (x) is an even function. Make your board exam preparations easy and effective by solving the previous year question papers. Question 5[A]: Attempt any two of the following. (C) Given that \(\int_0^4f(x)\,dx = 10\) which takes into account negative area between \(x=3\) and \(x=4\) 10. \ = \frac{1}{5}e^{15} – \frac{1}{5}e^0 \\ \text{therefore} \ \text{at } t= 1,3\,\,s \text{ particle is stationary} [i] Find the maximum and minimum value of the function f (x) = 2x3 – 21x2 + 36x – 20. \end{align*} \end{align*}, \begin{align*} (B) Point of inflexion occurs when gradient of \(f'(x)=0\) and gradient of \(f'(x)\) changes sign. Accountancy CBSE Class 12th Commerce Papers. Go ahead and download these question papers free of charge and practice them at your convenience: Previous Year Maharashtra HSC Class 12 Mathematics Board Question Papers. Maharashtra State Board Class 12 maths 2018 question paper with solutions are available on this page, by BYJU’S, in downloadable pdf format and also in the text for the students to prepare well for the MSBSHSE exams. SEBA HSLC Question Papers 2018:- Here you can Download SEBA HSLC exam question papers pdf of the 2018 year. &= 210 [ii] Find the vector equation of the plane passing through the points A (1, 0, 1), B (1, -1, 1), C (4, -3, 2). \text{at } x = \frac{\pi}{6}, \quad \frac{dy}{dx} = -\sqrt{3} \\ HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019. Excerpts and links may be used, provided that full and clear credit is given to Matrix Education and www.matrix.edu.au with appropriate and specific direction to the original content. Thus \(\min [L(t)] = 12 – 2 = 10 \text{hrs}\). Given the homogeneous equation is 5x2 + 2xy – 3y2 = 0 which is factorisable, (x + y) = 0 and (5x – 3y) = 0are the two lines represented by the equation. The distance of the point (x1, y1, z1) to the plane ax + by + cz + d = 0 is, D = |ax1 + by1 + cz1 + d / √a2 + b2 + c2 + d2|, D = |1 – 2 * 2 + 4 * (-1) – 10 / √1 + 4 + 16|. Thus we have, minimum stationary point at \((0,0)\) Students must also practice Mathematics by solving numerically rather than orally understanding question answers. DF = DC – FC = BE \\ |. CHEMISTRY XII HSC SOLUTION 27th, February, 2019. Therefore \(\int_{-1}^3 f(x)\,dx = 13-2 = 11\), 8. \int_{0}^k\frac{1}{x+3}\,dx &= \int_{k}^{45} \frac{1}{x+3}\,dx \\ A_0&=300000 \\ \frac{8x^3 – 27y^3}{2x – 3y} &= \frac{(2x – 3y)(4x^2 + 6xy + 9y^2)}{2x – 3y} \\ Negation: Some students of this college do not live in the hostel. Let O be the fixed point. 11 &= 12 + 2\cos\left(\frac{2\pi t}{366}\right) \\ Forums. Our website uses cookies to provide you with a better browsing experience. For finding the critical points, f‘ (x) = 0, Maximum values of f (x) at x = 1, f (1) = -3, Minimum values of f (x) at x = 6, f (6) = -128. -\frac{1}{2} &= \cos\left(\frac{2\pi t}{2}\right) \\ Are you searching for WBCHSE mathematics question paper solution 2018 ? \frac{d}{dx}\left(\frac{e^x}{x+1}\right) &= \frac{(x+1)e^x – e^x}{(x+1)^2} \quad \text{(quotient rule)} \\ Have you seen the 2018 HSC Mathematics Advanced Paper, yet? \text{In } \triangle ADF, \triangle ABE \\ HSC XII ACCOUNTS 2019 6th March, 2019. These are fully worked solutions for the multiple choice and extended response questions. These lines pass through the origin when h2 – ab > 0. &= 424 \text{ million} \quad \text{(nearest million)} Use perpendicular distance formula to obtain radius of the circle, which is \(4\).From these information, we can write out the equation of the circle – which is option D. 5. f(0) = 0, f(1.5) = 10.125 = \frac{81}{8}, \ f(3) = 0 \\ NESA is regularly updating its advice as the coronavirus outbreak unfolds. \Rightarrow \text{Max point at}\, x=\sqrt{\frac{200}{3}}\\ Let \frac{dV}{dx}=0\\ (C) Use mid-point formula, results \(Q(13, 7)\). It will also help you to increase your paper solving speed and get to know about how to solve the paper in time or before time. y’&=3x^{2}-7\\ \end{align*}, \begin{align*} 2018 HSC Mathematics Extension 1 Exam Paper Solutions. \begin{align*} \text{Now}\, 2\pi x=10\,\theta \,\,\, \text{By equating circumference}\\ [iii] Find the inverse of the matrix using elementary row transformations. \ = \frac{xe^x}{(x+1)^2} \text{therefore} \ (\frac{105}{104})^{n}&<1+\frac{3000}{P}\,\,\,\text{As Required} [b] 6 is an even number or 36 is a perfect square. This GSEB HSC Question Paper is according to latest Gujarat Board 12th Syllabus released by Gujarat Secondary and Higher Secondary Education. In this post, we will work our way through the 2018 HSC Maths Advanced paper and give you the solutions, written by our leading teacher Oak Ukrit and his team. 11th std 12th std.. jee main 2020 best tips for attempting paper home 2019 board paper solution tips to study smart grammar & writing skills cbse sample papers 2020 icse board isc board cbse class 12 all subjects 2019-2020 cbse sample papers … [iii] Examine the continuity of the function f (x) = log 100 + log (0.01 + x) / 3x for x ≠ 0, 100 / 3 for x = 0, at x = 0. \end{gather*}, \begin{gather*} \text{stationary when } v= 0 \\ [ii] If a line makes angles ɑ, ꞵ, with the coordinate axes, prove that cos 2ɑ + cos 2ꞵ + cos 2 + 1 = 0. $$y = -\sqrt{3}x + \frac{\pi\sqrt{3} + 3}{6}$$, \begin{gather*} of our 2019 students achieved an ATAR above 90, of our 2019 students achieved an ATAR above 99, was the highest ATAR achieved by 3 of our 2019 students, of our 2019 students achieved a state ranking. \text{P(A, NF, NF)} + \text{P(B, NF, NF)} &= \frac{1}{2}\left(\frac{9}{10}\right)\left(\frac{9}{10}\right) + \frac{1}{2}\left(\frac{19}{10}\right)\left(\frac{19}{10}\right) \\ HSC Commerce Papers. \end{align*}, \begin{align*} Reference to the previous years HSC Question Papers would give a clear idea about the exam pattern, topics covered, marking scheme, time management, etc. A_2&=A_1(1.04)-P(1.05)\\ [B] Attempt any two of the following. t &= -\frac{b}{2a} \text{ from quadratic } t^2 – 4t + 3 \\ \frac{d}{dx}(x^2\tan x) &= 2x\tan x + x^2\sec^2x \quad (\text{product rule}) There are 2 cases. [iii]: The measure of the acute angle between the Lines whose direction ratios are 3, 2, 6 and –2, 1, 2 is ______. \end{align*}, \begin{align*} Shaalaa.com gives you the well arranged sets of previous years question papers along with solutions, to study for your Maharashtra State Board 12th Board Exam Book Keeping and Accountancy, Co-operation, Economics, English, Hindi, Marathi, Mathematics and Statistics, Organisation of Commerce and Management, … &=2\,\,s -3x &> 9 \\ All Rights Reserved. 1 – 3x &> 10 \\ but\,\, h^{2}+x^{2} &= 100\\ In order for you to see this page as it is meant to appear, we ask that you please re-enable your Javascript! \end{align*}, \begin{align*} Case (ii): If f (x) is an odd function, then f (-x) = – f (x). [v] If a = 3i – 2j + 7k, b = 5i + j – 2k, c = i + j – k, then find a . Some other guys are searching this by hs maths question paper 2017 solutions, wb council of higher secondary 12 maths solutions etc as I have noticed this in Mathbackup youtube channel.. \frac{BD}{2} &= \frac{2}{3} \\ Students are able to access all the Maharashtra HSC Board previous year maths question papers. 10th std. \end{align*}, let \(t = 0\), \(L(0) = 12 + 2\cos(0) = 14 \text{hrs}\). Testpaperz.com is home to the largest collection of Board test papers/ School Prelim Test Papers/ Sample Question papers of ICSE, ISC, SSC, HSC and CBSE of Maths, Science, Physics, Chemistry, English, Accountancy, Computer Science, Physical Education, Biology and many other subjects for class 9,10,11 & 12 . 1. Converse – If the measure of an angle is 90° then it is a right angle. Board Papers 2018 (12th Commerce English Medium) March 2018 July 2018; BK Economics Mathematics (Paper 1) Mathematics (Paper 2) OC SP. = ʃ dx / [2{cos (x / 2) + sin (x / 2)}2 + 2 {cos (x / 2)}2], = (1 / 2)*ʃ dx / [{cos (x / 2) + sin (x / 2)}2 + {cos (x / 2)}2]. \text{Area} &= \frac{h}{3}\left(1\times 0 + \frac{81}{8}\times 4 + 1 \times 0\right) \\ Download all HSC Comm 2018 Quest. BATU Question Papers of Winter 2018. (dy) / (dx) = – (y(1/3) / a (1/3)) / (x(1/3) / a(1/3)). Therefore, the Total number of downloads is \(2097150 + 210 = 2097360\). [ii] Find the particular solution of the differential equation y (1 + log x) dy / dx – x log x = 0 when y = e2 and x = e. [iii] Find the variance and standard deviation of the random variable X whose probability distribution is given below, Standard deviation = √Var (X) = √3 / 4 = √3 / 2, Your email address will not be published. &= \frac{9\sqrt{3}}{2} \text{ unit}^2 HSC … \end{gather*}, \begin{align*} \text{P(at least one fault)} &= 1 – \text{P(no fault)} \\ a + 2d &= 8 \quad (1) \\ (b x c) = 3 (- 1 + 2) + 2 (- 5 + 2) + 7 (5 – 1), Question 2[A]: Attempt any two of the following. \text{Area} &= -\int_0^3(x^3 – 7x)\,dx + \int_0^32x\,dx \\ \text{note: } EC = FC, DC = BC \\ Equation of the plane through A, B and C in vector form is. \text{therefore} \  \angle ABC = 110° [i] Write the negations of the following statements: [a] All students of this college live in the hostel. \end{gather*} &= \int_0^3(2x + 7x – x^3)\,dx = \int_0^3(9x- x^3)\,dx \\ a + 19d &= 59 \quad (2) \text{therefore} \ AC &\approx 420\text{km} \quad \text{(nearest 10km)} \text{Let}\,\,y’&=2\,\Rightarrow x=\sqrt{3}\,\,,y=-4\sqrt{3}\\ \end{align*}, Finding co-ordinate of \(P\) After solving simultaneously, \(d = 3\), \begin{align*} \begin{gather*} \text{at } t = 0, v = 3 \text{ms}^{-1} Given that the origin O is the centroid of the triangle ABC, 2i + pj – 3k + qi – 2j + 5k + [-5i] + j + rk = 0, [B] Attempt any two of the following. S_{20} = \frac{a(r^n-1)}{r-1} = 2097150 \\ &= 320^2 + 190^2 – 2(320)(190)\cos 110° \\ Inverse – If an angle is a not right angle then its measure is not 90°. [6], [i] Let the pmf of a random variable X be –, (a) 1 / 2 (b) 1 / 3 (c) (1 / 4) (d) 1 / 5, (1 / 2) * (1 / 2) * [tan-1 (2x)]k0 = / 16, [iii] Integrating factor of linear differential equation x * (dy / dx) + 2y = x2 log x is. = tan-1 (5x + 1) / (1 – (3x + 2) (2x – 1)), = tan-1 ((3x + 2) (2x – 1) / (1 – (3x + 2) (2x – 1)), dy / dx = [3 / 1 + (3x + 2)2] + [1 / 1 + (2x – 1)2], = [3 / 9x2 + 12x + 5] + [1 / 2x2 – 2x + 1]. Download from here last 5 years CBSE accounts guess papers. \int_0^3 e^{5x}\,dx \ = \left[\frac{1}{5}e^{5x}\right]_0^3 \\ \text{Now,}\,\, 1.05^{n}-1.04^{n}&=(1.05-1.04)(1.04^{n-1}+…+1.05^{n-1})\\ ∫-aa f (x) dx = ∫-a0 f (x) dx + ∫0a f (x) dx —– (1), ∫-aa f (x) dx = ∫0a f (-x) dx + ∫0a f (x) dx. [ii] If x = a cos3 t, y = asin3 t, then show that dy / dx = – (y / x)⅓. A_n&=300000(1.04)^{n}-P((1.04)^{n-1}+(1.04)^{n-2}(1.05)+…+(1.05)^{n-1})\\ As \(-1 \leq \cos\left(\frac{2\pi t}{366}\right) \leq 1\), it is least when \(\cos\left(\frac{2\pi t}{366}\right) = -1\). (D) Given centre of the circle at \(Q(3,-2)\). HSC Comm. \end{align*}, Using sine rule, 11th std. [v] Given X ~ B (n, p) if n = 10, p = 0.4, find E (X) and Var (X). &= \frac{137}{160} AD &= AB – BD \\ Let a and b be the vectors in the direction of the lines (x – 1) / 4 = (y – 3) / 1 = z / 8 and (x – 2) / 2 = (y + 1) / 2 = (z – 4) / 1, respectively. \frac{3000}{P}&>(\frac{105}{104})^{n}-1\\ S_{20} &= \frac{n}{2}(a+l) \\ educational institution and also for … HSC XII BIOLOGY 2019 6TH March, 2019. This awareness will be of immense value to you when facing eventually the actual question papers. By practicing Class 12 Maths 2018 Maharashtra board question paper … \end{align*}, \begin{align*} This gives \(x = 0, 4\). ∫-aa f (x) dx = ∫0a [f (x) + f (x)] dx = 2 ∫0a f (x) dx. SSC ENGLISH STD 10 5TH MARCH, 2019. HSC BOARD QUESTION PAPER & SOLUTIONS-2020 (STD - XII) Sr.No. &= \frac{4}{2}\\ 6 is not an even number and 36 is not a perfect square. The required two lines respectively are 1 and 3 / 5 and the line passes through the origin and their individual equations are: Their joint equation is (x – y) (3x + 5y) = 0. \begin{align*} \end{gather*}, $$Pr(Win) =\frac{1}{36}\times(\frac{2\times20}{6})=\frac{5}{27}$$, \begin{align*} [\ln(x+3)]_0^k &= [\ln(x+3)]_k^{45}\\ \ = 56 \text{cm}^2 &= \left[\frac{9}{2}x^2 – \frac{1}{4}x^4\right]^3_0 \\ The state's top maths student shows us how to answer the hardest HSC question By Pallavi Singhal Updated December 20, 2018 — 12.51pm first published at 12.44pm h h ab x by 0 and h h ab x by 0 2 2 These lines passes through the origin. [i] Evaluate ∫(ex [cos x – sin x] / sin2 x) dx. [6]. \end{align*}, \begin{gather*} d&=\frac{|2\sqrt{3}-(-4\sqrt{3})|}{\sqrt{2^{2}+1^{2}}}\\ x &= (y – 1)^{\frac{1}{4}} \\ &=300000(1.04)^{2}-P(1.04+1.05)\\ Date Subject Question Papers Solutions; 1: 2020-02-18: English: HSC Board English Question Paper Set J-301/A A_{ACEF} &= 14^2 – 2\left(\frac{1}{2} \times 10\times 14\right) \\ A_{\triangle KLN} + A_{\triangle NLM} &= \frac{9\sqrt{3}}{2} \\ Required fields are marked *. [ii] Find dy / dx if y = tan-1 (5x + 1) / (3 – x – 6x2). (D) \(\frac{d}{dx}\sin(\ln{x}) = \frac{1}{x} \cos(\ln{x})\) using chain rule. [i] Verify Rolle’s theorem for the following function: f (x) = x2 – 4x + 10 on [0, 4]. v = \frac{dx}{dt} = t^2 – 4t + 3 \\ Papers (zip) &= 3 – \frac{4}{3} \\ t^2 – 4t + 3 = (t-3)(t-1) = 0 \\ $$\text{therefore} \ \text{at } t = 2, x = \frac{8}{3} – 8 + 6 = \frac{2}{3}\,\,m$$. \end{align*}, \begin{align*} Read on to see how to answer all of the 2018 questions. To make LHS a complete square, we add h2x2 on both sides. 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