= 9 4 = = = 8 2 = 4. Model Question paper-i SECTION-A 1.C 2.D 3.C 4. C 5. A 6.D 7.B 8.C 9.B B 12.B 13.B 14.D 15.

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1 Page 1 of 8 Model Question paper-i SECTION-A 1.C.D 3.C. C 5. A 6.D 7.B 8.C 9.B B 1.B 13.B 1.D 15.A SECTION-B 16. P a, b, c, Q g,, x, y, R {a, e, f, s} R\ P Q {a, e, f, s} P Q { } 17. In given arrow diagram, every element has a unique image. Hence it is a function. 18. a 16; r 8 16 a 1 rn S n 1 r 3 1, r 1 S 5 16(1 ( 3)5 ) Let P(x) be the required rational expression Given that x 3 1 x + + P x x3 x + 3 x + P x x3 x + 3 x + x3 x + 3 x x + 0. Sum of the roots Product of the roots + 7 x3 1 x + x3 x + x The required equation is x Sum of roots x + Product of root 0 x x x 16x + 9 x 16x In general a 3 matrix is given by A a 11 a 1 a 13 a 1 a a 3 Now a ij i 3j. where i 1, and j1,, 3 a a a a a 3 a The required matrix A 5 9 6A 6 5 9, B B A 3B If (7,3), 6,1, (8,) and (P,) are the vertices of a parallelogram taken in order, then find the value of P We know that the diagonals of a parallelogram bisect each other. midpoint of AC midpoint of BD

2 , P, 1 + Page of 8 15, P, 5 Equating the X- co ordinates, We get 6 + P 15 P In ABC AD is the internal bisector of A. BD AB DC AC DC BD AC AB DC.5. 5 DC.1 cm (Angle bisector theorem).1 cm 5. Let GD be the girl s height GD 150 cm Let GC be the length of the shadow GC cm In CGD, tanθ DG GC tan θ 1 3 θ Ratio of radii of two cylinders r 1 : r : 3 r 1, r 3 Ratio of height of two cylinders 1 : 5: 3 1 5, 3 Ratio of their volumes V 1 : V πr 1 1 πr Ratio of the volumes of cylinders V 1 : V 0: 7 8. Smallest value S 1 Range R 59 Largest value L? We know that, R L S Largest Value 71 L R + S Total number of tickets available in bag 100 n S 100 Let A be the event of getting a ticket with a number divisible by 10. A 10,0,30,0,50,60,70,80,90,100 Angle of elevation of the top of the lamp post θ sinθ 1+sinθ 30. a) Given n A 10 P A n(a) n(s) y x xy 1 sinθ 1 + sinθ 1 sinθ 1 sinθ (1 sinθ) 1 sin θ Multiply both sides by 8 xy (1 sinθ) cos θ 10 y xy x xy 8 8 xy xy 8 1 sinθ cosθ 1 sin θ sec θ tan θ cosθ cos θ 10x 8 + 9y 8 1

3 x + y Page 3 of x intersepts (a) 8 10 y intersepts b 8 9 (OR) Total surface area of cylinder 3 CSA of cylinder πr + r 3 πr + r 3 3 r f similarly f 1 3; f 5 ; f 3 7 (i) A set of ordered pairs The given function f can be represented as a set of ordered pairs as f 0,1, 1,3,,5, 3,7 (ii) Table form: Let us represent f using a table as shown below. x f(x) (iii) Arrow Diagram: r r SECTION-C 31. A\ B C A\B (A\C) Let us represent f by an arrow diagram. We draw two closed curves to represent the sets A and B Then each element of A and its unique image element in B are related with an arrow. (iv) Graph: f {(x, f x )/x εa} { 0, 1, 1, 3,, 5, 3, 7 } Now, the points (0, 1), (1, 3), (, 5) and (3, 7) areplotted on the plane as shown below. The totality of all points represent the graph of the function. From (I) and (II) A\ B C A\B A\C is true. 3. f: A B defined by f x x + 1 Given: A 0,1,,3 B{1,3,5,7,9} 33. S n to n terms. 7( to n terms) to n terms] 9

4 7 9 Page of 8 [ (1000 1)+ to n terms 7 9 [ to n terms ( to (10 n 1) n (10n 1) 7n x 3 x 5x n terms)] (AB) T B T A T ( I ) ( ) Thus (1) and () We get (AB) T B T A T 37. Area of the quadrilateral ABCD x 1 is a factor. The other factor is x x 6 x 3 x + i.e., x 3 x 5x + 6 x 1 x 3 x x x + 1 3x 9x 6x 3 + 7x x + 1 9x 6x x -6x 3 + 7x -6x 3 + x 6x x + 1 6x x x x Area of a quadrilateral 1 x 1y + x y 3 + x 3 y + x y 1 1 { (x y 1 + x 3 y + x y 3 + x 1 y ) } { ) - (8+1++7) } 1 {17 93} sq. units 38. Let AD, BE, CF be the altitudes of ABC 36. Given: 9x 6x 3 + 7x x + 1 3x x + 1 AB A 5 5 B Slope of BC y y 1 x x Since the altitude AD is perpendicular to BC Slope of AD 1 [ m 1 m 1]

www.rktuitioncentre.blogspot.in Page 5 of 8 Slope of AC 1 1 0 1 Thus, slope of BE 1 Also Slope of AB 5 3 1 5 Slope of CF 5 3 [ CF AB] [ BE AC] 39.

5 Page 5 of 8 Slope of AC Thus, slope of BE 1 Also Slope of AB Slope of CF 5 3 [ CF AB] [ BE AC] 39. Let ABCD be a parallelogram such that its sides touch a circle with centre O. r 3 3 (18) 3 [ ] r r 16 cm raidus of the third sphere 16 cm. Hemispherical portion : Radius, r 3.5 cm Conical portion : Radius, r 3.5 cm Height, h cm Volume of the wood Volume of the hemisphere + We know that the length of tangents from an external point are of equal length. AP AS, BP BQ, CR CQ, DR DS AP + BP + CR + DR AS + BQ + CQ + DS AP + BP + CR + DR AS + DS + (BQ + CQ) AB + CD AD + BC AB BC [ ABCD is a parallelogram] AB BC [ AB CD and BC AD] 69.5 Volume of the cone 3 πr πr πr r volume of the wood used in the toy 69.5 cu.cm. AB BC CD AD. Hence ABCD is a Rhombus. 0. Refer your text books (example No: 7.18, Page:09) 1. Radius of spherical solid material R 18 cm Let r 1, r, r 3 be the radii of small spheres formed r 1 cm r 1 cm r 3? Volume of the solid sphere volume of 3 small spheres 3 πr3 3 πr πr πr π(18)3 3 π[()3 + (1) 3 + (r 3 ) 3 ] 3. Given that x 35 and n 5. x Let us find x x n , 1 5

6 Page 6 of 8 (x 9) 8 P A B C 8 35 To find (x 18x + 81) 8 x 18 x x x x 307 (x x ), Let us consider (x 9) 8 (x 7 ) 8 [(x 7) ) ] 8 P(A B C) denotes the event that the problem is solved by atleast one of them. To find P A B C : P A B C P A + P B + P C P A B P B C P A C + P A B C P A B C a) All the natural numbers between 00 and 600 which are divisible by 11 07,18, 59 that is S n a 07, d 11, l 59 n l a d + 1 (x x ) 0 + ( 5)8 [ (x x) 0 (x x ) x 307 and (x x ) 6 Hence S n n a + l n 18. Let A denotes the event that A solves the given problem Let B denotes the event that B solves the given problem Let C denote the event that C solves the given problem P A 5 ; P A B 8 15 P B 3 ; P B C 7 P C 3 7 ; P C A 1 35 S b L.H.S 1 x + 1 x 3 1 x 1+x S x 1 + x + 1 x 3 1 x ((1 ) (x ) ) 1 + x + (1 x 3 )(1 x) 1 + x + 1 x 3 1 x

7 Page 7 of 8 (1 + x) + 1 x 3 1 x (iv) Mark a point R distinct from P and Q on the circle so that P, Q and R are in counter clockwise direction. (1 x) (1 + x) 1 + x + 1 x 3 x + x x + 1 x x 6. (b) x + x x + x 3 + x + 1 x x x + x + + x 3 + x 1 + x x + x x 3 + x 1 + x L.H.SR.H.S Section-D R. H. S 6. (a) Refer your text book (example no 9.) 7. (a) Construction (i) With O as the centre, draw a circle of radius 3. cm. (ii) Take a point P on the circle. (iii) Through P, draw any chord PQ.

8 Page 8 of 8 7.(b)

CBSE X Mathematics 2012 Solution (SET 1) Section D

CBSE X Mathematics 2012 Solution (SET 1) Section D Section D Q 9. A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. Let the number of books