SAMPLE QUESTION PAPER Class- XI Sub- MATHEMATICS

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SAMPLE QESTION PAPER Class- XI Sub- MATHEMATICS

SAMPLE QESTION PAPER Class- XI Sub- MATHEMATICS Time : Hrs. Maximum Marks : 00 General Instructions :. All the questions are compulsory.. The question paper consists of 0 questions divided into four sections A, B, C, D. Section A comprises of 6 questions of one mark each. Section B comprises of 6 questions of two marks each. Section C comprises of questions of four marks each and section D comprises of 5 questions of six marks each.. This set of model questions is not unique in character. Several such set of model questions can be framed. Teachers are requested to frame model questions of this kind for their Students. Section- A Question numbers to 6 carry mark each. For each question four options are provided out of which only one is correct. Write the correct option.. Î!ò A = {a, b, c} ~ÓÇ B = {b, c} Î ï ˆÏÓ n (A x B) ~Ó üyö ˆÏÓ (i) (ii) 6 (iii) 9 (iv) 8 x 6 = 6 If A = {a, b, c} and B = {b, c} Then value of n (A x B) will be (i) (ii) 6 (iii) 9 (iv) 8. n ~Ó ˆÎ ˆÜ yö ôöydü õ)î üyˆïö (- - ) n+ ~Ó üyö ˆÏÓ (i) (ii) - (iii) i (iv) -i For any positive integral value of n the value of (- - ) n+ is (i) (ii) - (iii) i (iv) -i. x - 5 <, x C R ˆÏ x ~Ó üyö ˆÏÓ (i) < x < (ii) < x < (iii) (iv) < x < < x < if x - 5 <, x R then the value of x will be C < x < < x < < (i) (ii) (iii) x < (iv) < x <. ˆÎ!Ó %ˆÏï S5, - ) ~ÓÇ SÈ-, )!Ó %mˆïî Ó ÇˆÏÎyçÜ ˆÓ áyç : xö% õyˆïï xhsˇ!ó û = Î ï yó fiìyöyçü ˆÏÓ (i) (, ) (ii) (, ) (iii) (-, 0) (iv) (, ) The line segment joining the points (5, -) and (-, ) is divided internally in the ratio : at the point whose coordinates are (i) (, ) (ii) (, ) (iii) (-, 0) (iv) (, ) 5. ü)!ó %àyü# ˆÎ Ó,ˆÏ_Ó ˆÜ w S0, )!Ó %ˆÏï xó!fiìï ï yó ü#ü Ó î ˆÏÓ (i) x + y - x = 0 (ii) x + y - y + = 0 (iii) x + y - y = 0 (iv) x + y - x + = 0 Page :

Equation of the circle with centre at (0, ) which passes through the origin is (i) x + y - x = 0 (ii) x + y - y + = 0 (iii) x + y - y = 0 (iv) x + y - x + = 0 6. ~Ü!ê ï yˆï Ó õƒyˆïü ˆÏê x!óöƒhflï û yˆïó 5!ê ï y xyˆïåè ï yˆï Ó õƒyˆïü ê ˆÌˆÏÜ ÎˆÏÌFåÈ û yˆïó ~Ü!ê ï y ê yöy ˆÏ y ï y!ê ~Ü!ê Ü yˆï y Ó ˆÏäÓ Ó yçy ÄÎ yó Ω yóöy ˆÏÓ (i) (ii), (iii) (iv) ˆÜ yö!ê z öˆï 6 From a well-shuffled pack of 5 cards, a card is drawn at random. The probability of it being a king of black colour is 6 (i) (ii), (iii) (iv) none of these Section- B Question numbers to carry two marks each.. f (x) = xˆï õ«ü!ê Ó ÇK yó ˆ«e ~ÓÇ Ã yó!öî Î Ü ˆÏÓ y - x Find the domain and range of the function f (x) = - x 8. x -, x C R xˆï õ«ü!ê Ó ˆ á!ã e xaü ö Ü ˆÏÓ y Draw a graph of the function x -, x C R 9. Cos 0 0 Sin (- 0 0 ) + Sin (- 0 0 ) Cos (- 0 0 ) ~Ó üyö!öî Î Ü Ó Find the value of Cos 0 0 Sin (- 0 0 ) + Sin (- 0 0 ) Cos (- 0 0 ) 0. (- - i) ˆÜ ˆüÓ % xyü yˆïó ÃÜ y Ü Ó Represent (- - i) in polar form.. Ó Ü Ó É lim - Cosx x _ 0 x Simplify : Ó Ü Ó É lim x _ 0 lim x _ 0 - Cosx x Sin x - Sin 5x x Simplify : lim Sin x - Sin 5x x _ 0 x.!ö!!áï ï ̃à%! Ó üü!óã% ƒ!ï!öî Î Ü Ó É, 6,, 9,, 5, Find the standard deviation for the following data :, 6,, 9,, 5, Section- C Question numbers to 5 carry marks each..!ï ö!ê ˆ ê A, B ~ÓÇ C ~Ó ) õ ˆÎ AB = AC ~ÓÇ A B = A C, ˆòáyÄ ˆÎñ B = C Let A, B and C be three sets such that AB = AC and A B = A C, Show that B = C. ABC!eû% ˆÏç A = ˆÏ ˆòáyÄ ˆÎñ x 6 = x = 5 Page :

b+c = a Cos B - C In triangle ABC, if A= B - C b+c = a Cos then show that, Ãüyî Ü Ó Cos Cos Cos 8 Cos = 5 5 5 5 6 Prove that Cos Cos Cos 8 Cos = 5 5 5 5 6 5. x = a + b, y = aw + bw ~ÓÇ z = aw + bw ˆÏ ˆòáyÄ ˆÎñ xyz = a +b, ˆÎáyˆÏö w ˆÏ ~Ó âöü) If w is the cube root of unity and x = a + b, y = aw + bw, z = aw + bw, then show that xyz = a + b z Î!ò z = i ~ÓÇ z = -i, Î ï ˆÏÓ arg ( ) ~Ó üyö!öî Î Ü Ó z z If z = i and z = -i then find the value of arg ( ) z 6. ày!î!ï Ü xyˆïó y Ó ï ˆÏ_ Ó y yˆïîƒ Ãüyî Ü ˆÏÓ y ˆÎ n + 5n -, n C N. Ó òy 9 myó y!óû yçƒ sing the principle of mathematical induction prove that n + 5n - is divisible by 9 for all n C N.. n ÇáƒÜ õò õî hsˇ!öˆï Ó ˆ î#!ê Ó ˆÎyàú!öî Î Ü Ó.5 + 5.8 + 8. +... Find the sum of n terms of the series.5 + 5.8 + 8. +... 8. (9x - ) ~Ó!Óhfl,Ï!ï ˆÏï x Ó!ç ï õò!ê!öî Î Ü ˆÏÓ y x Find the term independent of x in the expanssion of (9x - ) x ( + x) 5 ~Ó!Óhfl,Ï!ï Ó (r + ) ï ü õò ~ÓÇ (r + ) ï ü õˆïòó àmˆïî Ó xö% õyï : 5 ˆÏ r ~Ó üyö!öî Î Ü Ó If the ratio of the co-efficients of (r + )th and (r + )th term of the expanssion ( + x) 5 are in the ratio : 5, find r. 9.!ö!!áï x ü#ü Ó îà%! Ó üyôyö xm!öö Î Ü ˆÏÓ y É x - y <, x + y >, x > 0, y >. Find the solution region of the following in equations x - y <, x + y >, x > 0, y >. 0. y = ax x!ôó,ˆï_ó öy!û àyü# çƒy ~Ó xˆï«ó ˆÏAà Ø ˆÜ yî í zí õß Ü Ó ˆÏ ñ ˆòáyÄ ˆÎñ çƒy!ê Ó òâ ƒ ˆÏÓ a cosec Ø Focal chord of a parabola y = ax makes an angle Ø with its axis. Show that the length of the focal chord is a Cosec Ø.. ~Ü!ê xô ÈÙÈí z õó,_yü yó!á yˆïöó!óhfl,ï!ï 8!üê yó ~ÓÇ ˆÜ w ˆÌˆÏÜ í zfã ï y!üê yó!óhfl,ï!ï Ó ˆÜ w!ó % ˆÌˆÏÜ.5!üê yó ò)ˆïó!á yö!ê Ó í zfã ï y!öî Î Ü ˆÏÓ y An arch is of the form of a semi-ellipse. It is 8m wide and m high from the centre. Find the height of the arch Page :

at a point.5 m from the centre.. ~Ó ) õ ~Ü!ê õó yó,ˆï_ó ü#ü Ó Ïî!öî Î Ü ˆÏÓ y ÎyÓ öy!û S0, ± 0 ) ~ÓÇ Îy S, )!Ó %àyü# Find the equation of a hyperbola which passes through the point (, ) and has foci at (0 ± 0 ). ÃÌü )ˆÏeÓ y yˆïîƒ x ~Ó yˆï õˆï«cosec (x + ) ~Ó xóü à!öî Î Ü Ó Differentiate Cosec (x + ) from the first principle.. ï ƒ yó î# ÓƒÓ yó Ü ˆÏÓ Ãüyî Ü ˆÏÓ y ˆÎ ~ q V ~ p = ~ (p q) se truth table to verify that, ~ q V ~ p = ~ (p q) 5. ò% z!ê ˆéÑ yü )öƒ åèe yˆïü ΈÏÌFåÈ û yˆïó ~Ü ÓyÓ ã y yöy Ü Ó ˆÏ ñ ò% z!ê åèe yˆïï z ~Ü z Çáƒy xìóy ˆÎyàú 6 öy ÄÎ yó Ω yóöy!öî Î Ü ˆÏÓ y In a single throw of a pair of dice, find the probability that neilher a doublet nor a total of 6 will appear. Section - D Question numbers 6 to 0 carry 6 marks each. 6 x 5 = 0 6. yôyó î üyôyö!öî Î Ü ˆÏÓ y tanx + tanx + tanx = 0 Find the general solution of tanx + tanx + tanx = 0. ~Ü!ê à%ˆïîy_ó Ãà!ï Ó ÃÌü n, n ~ÓÇ n ÇáƒÜ õˆïòó ü!t ÎÌyÜ ˆÏü S, S ~ÓÇ S ˆÏ Ãüyî Ü ˆÏÓ y ˆÎ S (S - S ) = (S - S ) If the sum of first n, n and n terms of a geometric progression are respectively S, S and S then prove that S (S - S ) = (S - S ) 8. õ%öó yó,!_ öy Ü ˆÏÓ,,,, 5 xaü à%! myó y à!ë ï ÇáƒyÓ Çáƒy!öî Î Ü ˆÏÓ y à!ë ï ~ z çyï #Î Çáƒyà%! Ó ˆÎyàú Ä!öî Î Ü ˆÏÓ y Find the number of numbers that can be formed with the digits,,,, 5 without repetition. Find also the sum of the numbers thus formed. xìóy ˆÜ yö üï ˆÏ xó!fiìï 0!ê!Ó %Ó üˆïôƒ!ê üˆïó áñ x õó!ó %à%! Ó ˆÎ ˆÜ yö!ï ö!ê üˆïó á öî ~ z!ó %à%! Ó myó y à!ë ï (i) Ó ˆÓ áyó Çáƒy ~ÓÇ (ii)!eû% ˆÏçÓ Çáƒy!öî Î Ü ˆÏÓ y There are 0 points in a plane no three of which are on the same straight line, except points which are collinear. Find (i) The number of lines obtained from these points. (ii) The number of triangles that can be formed with these points. 9. (, )!Ó %àyü# ò% z!ê Ó ˆÓ áy õó flõˆïó Ó! ï 60 0 ˆÜ yî í zí õß Ü ˆÏÓ Î!ò ~Ü!ê Ó ˆÓ áyó ÃÓîï y Î ï ˆÏÓ x õó Ó ˆÓ áy!ê Ó ü#ü Ó î!öî Î Ü ˆÏÓ y Two straight lines passing through the point (, ) make an angle 60 0 with each other. It the slope of one straight line is find the equation of the other straight line. 0.!ö!!áï õ!ó Çáƒy!Óû yçö ˆÌˆÏÜ ˆû òyaü!öî Î Ü ˆÏÓ y ˆ î# 0-9 0-9 50-69 0-89 90-09 0-9 õ!ó Çáƒy 5 8 6 Calculate the coefficient of variation from the following frequency distribution table. Class 0-9 0-9 50-69 0-89 90-09 0-9 frequency 5 8 6 Page :

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