K.S.E.E.B., Malleshwaam, Bangaloe SSLC Model Question Pape-1 (015) Mathematics Max Maks: 80 No. of Questions: 40 Time: Hous 45 minutes Code No. : 81E Fou altenatives ae given fo the each question. Choose the coect altenative and wite the complete answe along with its alphabet in the space povided. 1 mak 8 = 8 1. Which one of the following is a coect elationship? (a) np nc! (b) nc np! (c) np nc! (d) nc np!. Pobability of getting 3 heads o 3 tails in tossing a coin 3 times is, (a) 1 8 (b) 1 (c) 3 8 (d) 1 4 3. The sides of two simila tiangle ae in the atio : 3. Then thei aeas ae in the atio (a) 9 : 4 (b) 4 : 9 (c) : 3 (d) 3 : 4. If A B then, A B is (a) A B (c) B (b) B A (d) A 5. Mean and standad deviation of a data ae 48 and 1 espectively. The coefficient of vaiation is, (a) 48 (b) 4 (c) 15 (d) 5 K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 1
6. If ax bx c 0 has equal oots. Then c is equal to (a) (c) b 4a b a (b) (d) b a b 4a 7. In the adjoining figue, D and E ae the mid points of AB and AC espectively. If DE = 4 cm, then BC is equal to (a) 4 cm (b) 6 cm (c) 8 cm (d) 1 cm 8. 1 tan 60 is equal to (a) 1 (b) (c) 16 (d) 4 II 1 mak 6 = 6 9. Expess 676 as the poduct of pime factos. 10. Find the zeoes of the polynomial 4a 49. 11. Fo the equation 143 x 1, find the value of x. 1. Fom the quadatic equation whose oots ae 3 and 5. 13. In ABC. ABC 90 and BD AC. If BD = 8 cm and AD = 4 cm, find CD. K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1
14. O is the cente of the cicle. P is extenal point. If AP = 8 cm, AP = BP and APB 60 then find the length of the chod AB. III maks 16 = 3 15. In a school, the stength of 8 th, 9 th and 10 th standads ae espectively 48, 4 and 60. Find the least numbe of books equied to be distibuted equally among the students of 8 th, 9 th and 10 th standad. 16. In a town 85% of the people speak English, 40% speak Kannada and 0% speak Hindi. Also 4% speak English and Kannada, 3% speak Kannada and Hindi and 10% speak English and Hindi. Find the pecentage of people who can speak all the thee languages. 17. Find the sum of all natual numbes between 1 and 01 which ae divisible by 5. 18. The 10 th tem of a G.P. is 30 and 6 th tem is 0. Find the pogession. 19. It is equied to seat 5 men and 4 women in a ow so that the women occupy the even places. How many such aangements ae possible? 0. How many maximum diagonals that can be dawn in a octagon? Eveybody in a function shakes hand with eveybody else. The total numbe of handshakes is 45. Find the numbe of pesons in the function. K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 3
1. Thee ae ed and yellow flowes in a basket. A child picks up at andom thee flowes. What is the pobability of picking up both the yellow flowes?. Rationalise the denominato and simplify: 4 3. 3 3. Multiply: 3 4 5. 4. Solve by using fomula: 15m 11m 0. 81E If one oot of the equation 3p 16q. x px q 0 is 3 times the othe, then pove that 5. Find the value of sin30 tan 45 cosec60 sec30 cos60 cot 45. 6. Find the slope of the line pependicula to the line joining the points (1, 7) and ( 4, 3). 7. A point P (, 1) is equidistant fom the points (a, 7) and ( 3, a). Find a. 8. Daw a cicle of adius 4 cm and constuct a pai of tangents such that angle between them is 50. 9. Daw the gaph (netwok) fo the following: Nodes = 7, Regions = 5, Acs = 10. 30. Daw a plan fo the ecodings fom the suveyo s field wok book given below: (Scale 5 m = 1 cm) To D metes 300 00 100 to C to E 50 150 75 to B 100 Fom A K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 4
IV 3 maks 6 = 18 31. Daw Pie chat to epesent the following data: 81E Name of the spot Numbe of students Foot ball 35 Tennis 14 Volley ball 16 Hockey 7 3. Find the diviso g(x), when the polynomial 3 P x 4x x 10x is divided by g(x) and the quotient and emainde obtained ae x 4x 1 and 5 espectively. If the quotient obtained on dividing 4 8x x 6x 7 by x 1 is 3 4x px qx 3 then find the value of p, q and also the emainde. 33. If two cicles touch each othe intenally thei centes and the point of contact ae collinea. Pove. 34. In the tapezium ABCD, AB DC and AED BEC. The pove that AD = BC. D, E and F ae the mid-points of sides of ABC. P, Q, R ae the mid points of sides DEF. This pocess of making the mid-points and foming a new tiangle is continued. How ae the aeas of these tiangles elated? K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 5
35. Show that: tan 1 tan cot 1. Show that sec A 1 sin A sec A tan A 1. 36. A medicine capsule is in the shape of a cylinde with two hemisphees stuck to each of its ends. The length of the capsule is 14 mm and the width is 5 mm. Find the suface aea. The diamete of the intenal and extenal sufaces of a hollow hemispheical shell ae 6 cm and 10 cm espectively. It is melted and ecast into a solid cone of diamete 14 cm. Find the height of the cone. V 4 maks 4 = 16 37. In an A.P. whose fist tem is the sum of fist five tems is one fouth the sum of the next five tems. Show that T 0 11 and also find S 0. Sum of thee tems in a G.P. is 31 and thei poduct is 15. Find the numbes. 38. A man tavels a distance of 196 km by tain and etuns in a ca which tavels at a speed of 1 km/hou moe than the tain. If the total jouney takes 11 hous, find the aveage speed of the tain and the ca espectively. 39. In a ight angled tiangle, the squae on the hypotenuse is equal to the sum of the squaes on the othe two sides. Pove. 40. Constuct a tansvese common tangent to two cicles of adii 4 cm and cm having thei cente 10 cm apat. Measue the length of the TCT and veify by calculation. * * * K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 6