MOCK CSE ORD EXM MTHEMTICS CLSS X (Paper 1) (S PER THE GUIDELINES OF CSE) Time: 3 Hurs Max. Marks: 80 General Instructins 1. ll the questins are cmpulsry. 2. The questin paper cnsists f 30 questins divided int fur sectins,, C, and D. Questins 1-10 carry 01 mark each, questins 11-15 carry 02 marks each, questins 16-25 carry 03 marks each, and questins 26-30 carry 06 marks each. 3. There is n verall chice. Hwever, an internal chice has been prvided in ne questin f 02 marks each, three questins f 03 marks each and tw questins f 06 marks each. Yu have t attempt nly ne f the alternatives in all such questins. 4. Use f calculatrs is nt permitted. NY CNDIDTE GIVING / SEEKING / RECEIVING SSISTNCE FOUND COPYING WILL E IMMEDITELY DISQULIFIED. ll the best! steps.tcynline.cm
M CSE FLT 1 STEPS TCY Prgram 1. State Euclid s divisin lemma. SECTION 2. What is the nature f rts f the quadratic equatin 2x 2 + 5x + 5 = 0? 3. Fr what value f k will the equatins, x + 5y 7 = 0, and 4x + 20y + k = 0 represent cincident lines? 4. Write the plynmial whse zeres are 5 and 4. 5. If cs = 5 3, find 9 ct 2 1. 6. Find the perimeter f the figure. (Take π = 7 22 ) 60 0 7 cm O 7. In the given figure, find the perimeter f C, if P = 10 cm. R C P Q 8. The pint f intersectin f the gives (mre than and less than type) is given by (20.5, 30.4). What is the median? 9. bag cntains 5 red balls, 8 white balls, 4 green balls, and 7 black balls. ball is drawn at randm frm the bag. Find the prbability that it is nt green. 10. Find the ttal surface area f a cubid with dimensins 10 cm, 8 cm and 6 cm. Fr slutins lg n t Steps.TCYnline.cm Page : 1
M CSE FLT 1 STEPS TCY Prgram 11. If sin θ + cs θ = 2sin (90 θ), find ct θ. 12. Slve the fllwing system f linear equatins: SECTION (a b)x + (a + b) y = a 2 2ab b 2, (a + b) (x + y) = a 2 + b 2 13. The line jining the pint (2, 1) and (5, 6) is bisected at P. If P lies n the line 2x + 4y + k = 0 find the value f k. 14. In a C, = C and D is a pint n side C, such that C 2 = C CD. Prve that D = C 15. card is drawn frm a well shuffled pack f 52 cards. Find the prbability that the card drawn is neither a red card nr a queen. Cards marked with numbers 1, 2, 3,, 25 are placed in a bx and mixed thrughly and ne card is drawn at randm frm the bx. What is the prbability that the number n the card is (i) an dd number (ii) neither divisible by 5 nr by 10 SECTION C 16. Find the zeres f the plynmial 6x 2 29x + 28 and verify the relatinship between zeres and its cefficients. Divide x 4 2x 2 + 3x 3 + 7x 2 by x 2 + 2 and verify the divisin algrithm. 17. Find the value f x, if the sum f the first 14 terms f the.p. 2x, 5x, 8x, 11x, is 1505. Find the 22 nd term f an.p whse 15 th term is 138 and the sum f the first 25 terms exceeds the 25 th term by 2772. cs 75 18. Evaluate: 2 sin 15 3 1 tan 80 tan 10 + 5 3 csec 12 sec 88 csec 2 sec 78 19. Draw a triangle C with C = 4 cm, = 4.5 cm, and C = 5 cm. Draw anther triangle similar t C such that the sides f the new triangle are equal t 4 3 f the crrespnding sides f C. 20. Prve that 6 + 2 is irratinal. 21. If ( 1, 3), (1, 1) and (5, 1) are the vertices f a triangle, find the length f the median thrugh (5, 1). Fr slutins lg n t Steps.TCYnline.cm Page : 2
M CSE FLT 1 STEPS TCY Prgram 22. In the figure, O is the centre f the circle and P is a pint 14 cm away frm the centre f the circle where P and P are tangents t the circle frm P. If P = 60, find the perimeter f the shaded regin. O P 23. Find the rati f the areas f an equilateral triangle and a square having equal perimeter. 5 1 24. (3, 2) and ( 2, 1) are tw vertices f a triangle C, whse centrid G has crdinates,. 3 3 Find the crdinates f the third vertex C f the triangle. 25. Frm a bus stand in angalre, if we buy 2 tickets t Malleswaram and 3 tickets t Yeshwanthpur, the ttal cst is Rs 46, but if we buy 3 tickets t Malleswaram and 5 tickets t Yeshwanthpur the ttal cst is Rs 74. Find the fares frm the bus stand t Malleswaram, and t Yeshwanthpur. SECTION D 26. The sum f a tw digit number and the number frmed by interchanging its digits is 110. If 10 is subtracted frm the first number, the new number is 4 mre than 5 times the sum f the digits f the first number. Find the first number. The places and are 100 km apart n a highway. One car starts frm and anther frm at the same time. If the cars travel in the same directin at different speeds, they meet in 5 hurs. If they travel twards each ther, they meet in 1 hur. Find their speeds. 27. 10 m high flagstaff is fixed n the tp f a twer. The angle f elevatin, f the tp f the flagstaff as bserved frm a pint n the grund, is 60. The angle f depressin, f the same pint frm the tp f the twer is 45. Find the height f the twer. 28. (i) Prve the basic prprtinality therem. (ii) Use the abve therem t prve that the diagnals f a trapezium cut each ther in the same rati. 29. If h, c and V respectively are the height, the curved surface and vlume f a cne, prve that 3π Vh 3 c 2 h 2 + 9V 2 = 0 Fr slutins lg n t Steps.TCYnline.cm Page : 3
M CSE FLT 1 STEPS TCY Prgram bucket made up f a metal sheet is in the frm f a frustum f a cne. Its depth is 24 cm and the diameters f the tp and bttm are 30 cm and 10 cm respectively. Find the cst f milk which can cmpletely fill the bucket at the rate f Rs. 20 per litre and the cst f the metal sheet used, if it csts Rs. 10 per 100 cm 2. (Take π = 3.14) 30. The fllwing table gives the prductin yield per hectare f wheat f 100 farms f a village. Prductin yield (in kg/ha) 50 55 55 60 60 65 65 70 70 75 75 80 Number f farms 2 8 12 24 38 16 Change the distributin t a mre than type distributin, and draw its give. Obtain the median prductin yield (kg/ha) frm the graph. Fr slutins lg n t Steps.TCYnline.cm Page : 4