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2 Model Question Papers Based on Scheme of Eamination as per G.O. (D). No. 50 dated : Type of Questions Mathematics Time : ½ hours Written Eam Marks : 90 Marks Higher Secondary - First year Question Paper Pattern (For Subjects without Practical Eam) Marks No. of Questions to be answered Total Marks Mark questions 0 0 Questions for Very Short Answers : (Total 0 questions. Out of which question is compulsory). Questions for Short Answers : (Total 0 questions. Out of which question is compulsory). Questions for Long Answers : (With sub-sections) Total 90 For Order : orders@surabooks.com Ph: /

3 th STD. Model Question Paper Time : ½ Hours Mathematics Marks : 90 Part - I All questions are compulsory. (0 = 0) Choose the correct answer.. Number of elements in a matri of order is (a) 5 (b) (c) (d) 6. If A is a square matri of order 4 then KA is (a) K A (b) K A (c) K A (d) K 4 A. If G is centroid of the triangle ABC and O is any other point then OA + OB + OC is equal to (a) O (b) OG (c) OG (d) 4 OG 4. If a = i j and b = j k then the magnitude of a b is (a) (b) 9 (c) (d) 5. A polygon has 44 diagonals, then the number of its sides is (a) (b) 7 (c) 8 (d) If ( ) ( ) = A then A is (a) (b) (c) 0 (d) 0 7. The A.M., G.M., H.M., between two positive numbers a and b are equal then (a) a = b (b) ab = (c) a > b (d) a < b 8. If a n = n n then the third term is (a) 9 (b) (c) (d) 9. If the pair of straight lines given by a + hy + by = 0 are perpendicular, then (a) ab = 0 (b) a + b = 0 (c) a b = 0 (d) a = 0 0. The radius of the circle + y + 4y 4 = 0 is (a) (b) (c) (d) 4 For Order : orders@surabooks.com Ph: / []

4 + Std - Mathematics Sura s Model Question Papers. If cos θ = 0 then θ is (a) nπ (b) (n+) π (c) π (d) nπ. If the terminal side is collinear with the initial side in the opposite direction, then the angle included is (a) 0 (b) 90 (c) 80 (d) 70. The range of the function log e is (a) (0, ) (b) (, ) (c) (, 0) (d) [0, ) 4. The value of [.5] is 5. (a) (b) (c) 4 (d) 5 d ( log )is d (a) (b) 6. lim + is (a) e (b) e (c) e (d) 7. log d = (a) + c (b) 8. e sin d( ) is (a) e ( log ) + c (c) (c) log + + c (d) (d) log + c (sin cos ) + c (b) e ((sin cos ) + c (c) e e ((sin + cos )+c (d) ((cos + sin ) + c 9. If two events A and B are independent then P(A/B)= (a) P(A) (b) P(A B) (c) P(A) = P(B) (d) P( A) P( B) 0. X speaks truth in 95 percent of cases and Y in 80 percent of cases. The percentage of cases they likely to contradict each other in stating same fact is (a) 4% (b) 86% (c) % (d) 85.5% For Order : orders@surabooks.com Ph: /

5 4 + Std - Mathematics Sura s Model Question Papers Part - II Answer any Seven questions. (7 = 4) Question No.0 is compulsory.. Prove that a b a a = a ab + + a ab ab b ab. If ABC and A B C are two triangles and G, G be their corresponding centroids, prove that AA + BB + CC = GG. If 0P r = 5040, find the value of r. 4. A point moves so that it is always at a distance of 6 units from the point (, 4). Find its locus. 5. Simplify : Cos ( 870 ) 6. If f, g : R R, defined by f()= + and g() = then find (fog) () 7. Find d y if y = d Evaluate : cos d 9. Three coins are tossed once. Find the probability of getting atleast two heads. 0. Show that e e b Part - III Answer any Seven questions. (7 = ) Question No.40 is compulsory.. Prove that the sum of the vectors directed from the vertices to the mid-point opposite sides of a triangle is zero.. Find the co- efficient of 5 in the epansion of + For Order : orders@surabooks.com Ph: /

6 + Std - Mathematics Sura s Model Question Papers 5. Find 5 geometric means between 576 and The slope of one of the straight lines a +hy + by = 0 is twice that of the other, show that 8h = 9ab. 5. Show that : Sin0 Sin40 Sin 80 = 8 6. Let f : R R be defined by f () = + find f and show that fof = f of = Evaluate : Lim 0 sin 8. Integrate : ( + 4 ) + 7d 9. Two cards are drawn from a pack of 5 cards in succession. Find the probability that both are kings when, (i) The first drawn card is replaced (ii) The card is not replaced. 40. Find K so that A = KA I where A = 4 Part - IV Answer all the question. (7 5 = 5) 4. Using factor theorem prove that (b + c) a a b (c + a) b = abc (a + b + c) c c (a + b) Eamine whether the vectors i + j+ k, i j k and 7 i + 5 k are coplanar. 4. If A + B = 45, show that ( + tana) ( + tanb) = and hence deduce the value of tan State and prove Napier s formulae. For Order : orders@surabooks.com Ph: /

7 6 + Std - Mathematics Sura s Model Question Papers 4. Prove by Mathematical Induction n = n ( n+ ) ( n+ ),for all n N 6 If a, b, c are in H.P. Prove that b + a b c b a + + b c = 44. Find the equation of the circle passing through the points (,), (, ) and (,). Find the co-ordinates of orthocentre of the triangle formed by the straight lines y 5 = 0, y 8 = 0 and y 9 = If y = cos (sin), Prove that d y dy + tan + ycos = 0 d d For a < and for any rational inde n, prove that a n lim = na ( a 0) a a 46. Evaluate the definite integral as limit of sum ( + 5 ) d + Evaluate d If is real, prove that the range of f ( )= + 4 is between + + 4, In a bolt factory machines A, A, A manufacture respectively 5%, 5% and 40% of the total output of these 5, 4, percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine A? n n For Order : orders@surabooks.com Ph: /

8 th STD. Sura s Model Question Paper - Based on Scheme of Eamination as per G.O. (D). No. 50 dated : Time :.0 Hours Mathematics Marks : 90 Part - I All questions are compulsory. (0 = 0) Choose the correct answer. a b c q b y. If A = y z, B = p a then p q r r c z (a) A = B (c) A = B (b) A = B (d) A is invertible a + ab ac. The determinant = ab b + bc is divisible by ac bc c + (a) (b) (c) 0 (d) none of these. The position vector of the mid-point of the vector joining the points (,, 4) and (4,, ) is (a) i j + k (b) i + j + 4 k (c) 6 i + 4 j + k (d) i + j + k 4. The following diagram represents vectors (a) co-terminus (b) co-initial (c) collinear (d) none of these 5. If the co-efficients of r th and (r + ) th terms is the epansion of ( + 7) 9 are equal, their r = (a) 9 (b) (c) (d) The number of five-digit telephone numbers having atleast one of their digits repeated is (a) 90,000 (b),00,000 (c) 0,40 (d) 69,760 For Order : orders@surabooks.com Ph: / [7]

9 8 + Std - Mathematics Sura s Model Question Papers 7. a b c If b + c, c + a, a + b are in H.P., then b+ c c+ a c+ a (a) A.P (b) G.P (c) H.P (d) None 8. If ( + ) ( + ) n = a 0 + a + a +... and if a 0, a, a are in A.P. then n = (a) (b) (c) (d) 4 9. The lines y 6 = 0, + y 4 = 0 and λ + 4y + λ = 0 are concurrent of (a) λ =, 4 (b) λ =, (c) λ = 4, (d) λ = 4, 0. The centres of the circles + y =, + y y = 0 and + y 6 y + = 0 are (a) equal (b) lies on X-ais (c) Collinear (d) lies on Y-ais. If tan α = 5 6 and tanβ = then (a) α + β = π (b) α + β = π (c) α + β = π d) None of these 6 4. Which is greater? sin 980 or cos 980 (a) sin 980 (b) cos 980 (c) equal d) 0. Which of the following function is an odd function? (a) f() = cos (b) 4. The solution of 5 < 5 is y = 4 (c) y = (d) sin (a) <. (b) =. (c) >. (d) none of these 5. If + y = and y = A y then A = (a) 0 (b) (c) (d) None of these 6. The function y = sin (log ) + cos (log ) satisfies the equation. a) y + y + y = 0 b) y + y = 0 c) y + = 0 d) y = 0. For Order : orders@surabooks.com Ph: /

10 + Std - Mathematics Sura s Model Question Papers 9 d 7. If = Atan e then A is e + e (a) (b) (c) (d) 8. The anti - derivative of every odd function is a function (a) odd (b) even (c) neither odd nor even (d) none 9. For two events A and B if P(A) = P(A/B) = 4 and P(B/A) = then A and B are (a) mutually eclusive (b) dependent (c) independent (d) ehaustive 0. If P(A B) = P(A B) then the relation between P(A) and P(B) is (a) P(A) = P(B) (b) P(A) < P(B) (c) P(A) = 0 (d) P(A) = Part - II Answer any Seven questions. (7 = 4) Question No.0 is compulsory.. What is Triangular matri?. y If z w 4 5, then find the values of, y.. What is negative vector? 4. A coin is tossed five times and outcomes are recorded. How many possible outcomes are there? 5. Evaluate 8 P. 6. If the point P(5t 4, t + ) lies on the line 7 4y + = 0, find the co-ordinates of P. 7. What is locus? 8. π into degrees. 4 For Order : orders@surabooks.com Ph: /

11 0 + Std - Mathematics Sura s Model Question Papers 9. Find A B and B A if A = {, }, B = {a, b}. 0. An eperiment has the four possible mutually eclusive outcomes A, B, C and D. Check whether the following assignments of probability are permissible. P(A) = 0.7. Part - III Answer any Seven questions. (7 = ) Question No.40 is compulsory.. If A = 4, B =. Solve for if 7 4 4, C = find each of the following A + (B + C) 5 + = 0.. Find the magnitude and direction cosines of i j + 7 k. 4. A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 0 fountain pen varieties, ball pen varieties and 5 pencil varieties, in how many ways can he select these articles? 5. In how many ways can an eamine answer a set of 5 true / false type questions? 6. Write the first five terms of the sequence given by : a = a =, a n = a n, n >. 7. Determine the equation of the straight line passing through (, ) and having slope Identify the name of the function, the domain, Co-domain, independent variable, dependent variable and range if f : R R defined by y = f () =. For Order : orders@surabooks.com Ph: /

12 + Std - Mathematics Sura s Model Question Papers 9. If A and B are two independent events such that P(A) = 0.5 and P(A B) = 0.8. Find P(B). 40. The difference between two positive numbers is 8 and 4 times their G.M is equal to 5 times their H.M. Find the numbers. Part - IV Answer all the question. (7 5 = 5) 8 4. If A = 4, B = 7 4, C = Prove that (i) AB BA (ii) A(B + C) = AB + AC 4 6 Solve : X + Y = 8 0, X Y = 0 4. Show that the points with position vectors a b + c, a + b + c and 8 a + b are collinear. How many three digit odd numbers can be formed by using the digits 4, 5, 6, 7, 8, 9 if (i) the repetition of digits is not allowed? (ii) the repetition of digits is allowed? 4. Find the sum 0 th terms to 00 th terms of the series n= n Resolve into partial fractions For Order : orders@surabooks.com Ph: /

13 + Std - Mathematics Sura s Model Question Papers 44. Find the locus of the point which is equidistant from (, ) and (4, ). Write the first 5 terms of each of the following sequences. (i) a n = ( ) n 5 n+ (ii) a n = ( ) nn Find the values of (i) cos (5 ) (ii) sin (40 ) (iii) sec (5 ) (iv) cos( 50 ) (v) cot (5 ) If is real, prove that lies between 5+ 9 and. 46. Evaluate the left and right limits of f () = 7 at =. Does the limit of f () as eist? Justify your answer n = n n ( +). 4 seca coseca 47. Prove that ( + cot A + tan A ) (sin A cos A) = cosec A sec A A die is thrown twice. Let A be the event. First die shows 4 and B be the event, second die shows 4. Find P(A B). For Order : orders@surabooks.com Ph: /

14 th STD. Sura s Model Question Paper - Based on Scheme of Eamination as per G.O. (D). No. 50 dated : Time :.0 Hours Mathematics Marks : 90 Part - I All questions are compulsory. (0 = 0) Choose the correct answer.. Let A and B the matrices. Then AB = 0 implies (a) A = 0 or B = 0 (b) A = 0 and B = 0 (c) either A = 0 or B = 0 (d) A = 0 and B = 0 + a. If a, b, c are all different from zero, and = + b = 0, then + + is a b c + c (a) abc (b) (c) a b c (d) a b c. The scalars in the following is (a) work done (b) force (c) velocity (d) work done and distance 4. The vector in the direction of i + j + k is (a) i j + k (b) i + j k (c) i + 4 j + 4 k (d) + i + 4 j 4 k 5. The number of squares which we can form on a chessboard is (a) 64 (b) 60 (c) 4 (d) 04 [] For Order : orders@surabooks.com Ph: /

15 4 + Std - Mathematics Sura s Model Question Papers 6. If m + n P = 90 and m n P = 0 then (m, n) is (a) (7, ) (b) (6, 8) (c) (9, ) (d) (8, ) 7. The sum to n term of the series is (a) n n (b) n (c) n + n (d) n n 8. The 0 th term of the series given as tr = n( n+ )( n+ )for all n is 6 r= (a) 0 (b) (c) 0 (d) 0 9. The points A(a, 4a), B(a, 6a) and C(a + a, 5a) are the vertices of a triangle. (a) isosceles acute angle (c) isosceles obtuse angle (b) equilateral (d) right angle 0. The equation a + by + c + ay = 0 represents a pair of straight lines if (a) a + b = 0 (b) b + c = 0 (c) a + c = 0 (d) ab = 0.. The general solution of the equation tan = cos is (a) nπ (b) nπ (c) nπ + π 4. The smallest value of θ which satisfies the equation tan θ = cot 500 is (a) 0 (b) 40 (c) 50 (d) 00 (d) nπ π 4, n Z. If f:r R is defined by f() = +, the value of f (7) is (a) {, } (b) {, } (c) {4, 4} (d) {, } 4. Which of the following function is an even function? (a) f() = + 7 (b) f() = + (c) f() = (d) f() = The function y = ( + ) 50 should be differentiated times to result in a polynomial of the 0th degree. (a) 50 (b) 00 (c) 70 (d) 0 For Order : orders@surabooks.com Ph: /

16 + Std - Mathematics Sura s Model Question Papers 5 6. If = log t and y = t then y () at t = is. (a) (b) 4 (c) (d) None of these 7. e d is (a) e 8. e d + e is (a) log ( ) (b) e (c) e d (d) + e (b) tan ( e ) (c) tan ( e ) (d) tan ( e ) + 9. If A and B are two mutually eclusive even then (a) P(A) = P(B) (b) P(A) P(B) (c) P(A) < P(B) (d) P(A B) = 0 c e 0. A and B play a game where each is asked to select a number from to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is (a) 5 (b) Answer any Seven questions. 5 (c) Part - II Question No.0 is Compulsory. (7 = 4) 5 (d) 4 5. What is Negative of matrices.. Find the value of the determinant without usual epansion.. Write any two types of vectors name. 4. Find the magnitude and direction cosines of i j + 7 k. 5. In a class there are 7 boys and 4 girls. The teacher wants to select boy and girl to For Order : orders@surabooks.com Ph: / represent a competition. In how many ways can the teacher make this selection?

17 6 + Std - Mathematics Sura s Model Question Papers 6. What is a sequence. 7. Find the indicated terms of the following sequences whose n th term is a n = + n ; a 5, a Determine the equation of the straight line passing through (, ) and having slope Find the quadrants in which the terminal sides of the following angles be Find A B and B A if A = {, }, B = {a, b}. Part - III Answer any Seven questions. (7 = ) Question No.40 is compulsory. 7. Find the matri C if A = 5, B = and 5C + B = A. 4. Find the components along the co-ordinates of the position vector of p( 4, ).. Find the unit vectors parallel to the sum of i 5 j + 8 k and j k. 4. How many 4-digit numbers are there? 5. Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them. 6. IA point moves so that it is always at a distance of 6 units from the point (, 4). Find its locus. cot( 90 θ)sin ( 80 + θ)sec( 60 θ) 7. Simplify:. tan( 80 + θ)sec ( θ)cos( 90 + θ) 8. Solve : 9 9. Integrate : sin. 40. The probability of an event A occurring is 0.5 and B occurring is 0.. If A and B are mutually eclusive events, then find the probability of neither A nor B occurring. For Order : orders@surabooks.com Ph: /

18 + Std - Mathematics Sura s Model Question Papers 7 Part - IV Answer all the questions. (7 5 = 5) 4. If A = 4 find k so that A =ka I. In a triangle ABC, if D and E are the mid-points of sides AB and AC respectively, show that BE + DC = BC If the A.M. between two numbers is, prove that their H.M is the square of their G.M. 4. Find a so that the straight lines 6y + a = 0, + y + 4 = 0 and + 4y + = 0 may be concurrent. If a cosa = b cosb then show that the triangle is either an isosceles triangle or right angled triangle? 44. Draw the graph of the function f () =.,if0 Let f be defined by f() = +,if< 45. An integer is chosen at random from the first fifty positive integers. What is the probability that the integer chosen is a prime or multiple of 4? (i) Epress the following as functions of A sec A π (ii) Integrate : For Order : orders@surabooks.com Ph: /

19 8 + Std - Mathematics Sura s Model Question Papers 46. The probability that a girl will get an admission in IIT is 0.6, the probability that she will get an admission in Government Medical College is 0.4, and the probability that she will get both is 0.. Find the probability that (i) She will get atleast one of the two seats (ii) She will get only one of the two seats. Evaluate : (i) lim (ii) lim ( + ) Given A = 4 B = C = 0 verify the following results : (i) AB π BA (ii) (AB) C = A (BC) If the 5 th and th terms of a H.P are and 5 respectively, find the 5 th term. For Order : orders@surabooks.com Ph: /

20 th STD. Sura s Model Question Paper - Based on Scheme of Eamination as per G.O. (D). No. 50 dated : Time :.0 Hours Mathematics Marks : 90 Part - I All questions are compulsory. (0 = 0) Choose the correct answer If = a + b + c + d, then (a) a = b = c = (b) a = b = c = 0 (c) a =, b =, c = (d) none of these bc bc b+ c. If a, b and c are non-zero real numbers, then = ca ca c+ a = ab ab a+ b (a) abc (b) a b c (c) ab + bc + ca (d) 0. The vectors among the following measures will be (a) 0 kg (b) 40º (c) 40 watt (d) 0 m/sec 4. Represent the diagram in vector form (a) 5 km 60 north of east (b) 60 km 5 north of east (c) 5 km 60 east of north (d) none of these N 60 W 0 S 5 km E P 5. The number of ways in which 7 distinct toys can be distributed among children is (a) 7 (b) 7 (c) 7C (d) 7P 6. If a polygon has 54 diagonals, then the number of its sides is (a) (b) (c) 0 (d) 9 [9] For Order : orders@surabooks.com Ph: /

21 0 + Std - Mathematics Sura s Model Question Papers 7. The number of divisions of 09, 547 and are in (a) A.P (b) G.P (c) H.P (d) None of these 8. tan 70, tan 50, + tan 0 and tan 0 are in (a) A.P (b) G.P (c) H.P (d) None of these 9. The circles + y + y + = 0 and + y y + = 0. (a) touch each other eternally (c) intersect on the Y-ais (b) touch each other internally (d) intersect on the X-ais 0. The equation + hy + y = 0 represents a pair of straight lines passing through the origin. The two lines are (a) real and different if h > (b) real and different if h > 9 (c) real and coincident if h = (d) imaginary if h < 9. sin α. If = y then cosα+ sin α = + cosα+ sin α + sin α (a) y (b) y (c) y (d) y.. If A lies in the II quadrant and tana+ 4 = 0, then cota 5 cosa + sina = (a) 5 0 (b) 0 (c) 7 0 (d) 7 0. The domain of the function f() + 6 is (a) [, ) (b) (, 6) (c) [,6] (d) none of these 4. Let f: R R defined by f() = 6+, then fof () is (a) 77 (b) 6 (c) 08 (d) The value of y n () if y y 5 = 0 when y () = is equal to (a) 7 (b) 7 8 (c) 8 (d) 8 7 For Order : orders@surabooks.com Ph: /

22 + Std - Mathematics Sura s Model Question Papers 6. The derivative of an even derivable function is always an function. (a) odd (b) even (c) constant (d) linear ( ) 7. cos sin d is + c (a) sin cos (c) sin cos (b) sin + cos (d) sin + cos 8. If the velocity of the moving particle is constant, its path is a (a) straight line (b) parabola (c) circle (d) curve 9. If A and B are two events, the probability that eactly one of them occurs is given by (a) P(A) + P(B) P(A B) (b) P(A B ) + P( A B) (c) P( A B) (d) P(A B ) 0. One card is drawn at randon from a well shuffled pack of 5 cards. Let A denote the event the card drawn is a king or a queen and B be the event the card drawn in a queen or a jack. Then A and B are (a) independent (b) not independent (c) mutually eclusive (d) equally likely Part - II Answer any Seven questions. Question No.0 is Compulsory. (7 = 4). What is magnitude of a vector?. Find a unit vector in the direction of i + j.. In a class there are 5 boys and 0 girls. The teacher wants to select a boy and a girl to represent the class in a function. In how many ways can the teacher make this selection? 4. Find the single A.M. between 5 and. 5. Determine For Order the equation : orders@surabooks.com of this straight line whose slope Ph: is and Y - / intercept is 7.

23 + Std - Mathematics Sura s Model Question Papers 6. Find the distance between the parallel lines + y 6 = 0 and + y + 7 = Simplify - tan What is linear function? 9. For the functions f, g as defined in () define - f g () 0. Differentiate the following functions with respect to -. e cos. Part - III Answer any Seven questions. (7 = ) Question No.40 is compulsory.. Find the values of, y, z if y z y w = a.. Find the unit vectors parallel to the vector i + 4 j. 4. Twelve students compete in a race. In how many ways first three prizes be given? 5. Write the first 5 terms of each of the following sequences. - a n = n Determine the equation of the line with slope and y-intercept If A, B, C, D are angles of a cyclic quadrilateral, prove that cos A + cos B + cos C + cos D = 0 8. Prove the following: sin 4 A cos 4 A = cos A. 9. Show that the function y = is not one-to-one sind For Order : orders@surabooks.com Ph: /

24 + Std - Mathematics Sura s Model Question Papers Part - IV Answer all the questions. (7 5 = 5) 4. Find the value of y [ ] 0. 0 = a Prove that b c a b c =(a-b) (b -c)(c-a) (a +b+c). 4. Prove using vectors, the mid-points of two opposite sides of a quadrilateral and the midpoints of the diagonal are the vertices of a parallelogram. How many different numbers of si digits can be formed from the digits,, 0, 7, 9, 5 when repetition of digits is not allowed? 4. Find the n th partial sum of the series n n= Find the locus of the point which is equidistant from (, ) and (4, ). 44. Prove that tanθ+ secθ tanθ secθ+ sinθ = + cosθ A father d has three sons a,b,c. By assuming sons as a set A and father as a singleton set B, show that (i) the relation is a son of is a function from A B and (ii) the relation is a father of from B A is not a function. For Order : orders@surabooks.com Ph: /

25 4 + Std - Mathematics Sura s Model Question Papers 45. If f () = 8 + 0, find f () and hence find f () and f (0) Prove that sec A + cosec A = sec A cosce A. 46 A factory has two Machines-I and II. Machine-I produces 5% of items and Machine-II produces 75% of the items of the total output. Further % of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective? How many arrangements can be made with the letters of the word MATHEMATICS? sinβ 47 Compute lim, 0. 0 sin α α For n n < a and for any rational inde, n, lim a n = na ( a 0 ) a a For Order : orders@surabooks.com Ph: /