STD XII TIME 1hr 15 mi SLIP TEST Chapter 2, ad 6 Max.Marks 5 Part A Aswer all the questios Each questio carries 1 mark 1 x 1 =1 1. The equatio of the plae passig through the poit (2, 1, 1) ad the lie of itersectio of the plaes r (i + j k ) = 0 ad r (j + 2k ) = 0 (1) x + 4y z = 0 (2) x + 9y + 11z = 0 () 2x + y z + 5 = 0 (4) 2x y + z = 0 2.If the magitude of momet about the poit j + k of a force i + aj k actig through the poit i + j is 8 the the value of a is (1) 1 (2) 2 () (4) 4. If x = r cos θ, y = r si θ, the r is equal to x (1) sec θ (2) si θ () cos θ (4) cosec θ 4. If a = cos α i si α, b = cos β i si β ad ; c = cos γ i si γ the a2 b 2 c 2 is (1) cos 2(α β + γ) + i si 2(α β + γ) (2) 2 cos(α β + γ) () 2i si(α β + γ) (4) 2 cos(α β + γ) 5. The polar form of the complex umber (i 25 ) is abc (1) cos π 2 + i si π 2 (2) cos π + i si π () cos π i si π (4) cos π 2 i si π 2 6. Which of the followig is icorrect? 1 Multiplyig a complex umber by i is equivalet to rotatig the umber couter clockwise about the origi through a agle of 2 Multiplyig a complex umber by -i is equivalet to rotatig the umber clockwise about the origi through a agle of Dividig a complex umber by i is equivalet to rotatig the umber couter clockwise about the origi through a agle of 4 Dividig a complex umber by i is equivalet to rotatig the umber clockwise about the origi through a agle of 7..
. Part B Aswer ay five questios Each questio carries 2 marks 2 x 5 =1 11. Show that the vectors 2i j k, i j 5k, i 4 j 4k form the sides of a right agled triagle 12. A force give by i 2 j 4k is applied at the poit (1,-1,2). Fid the momet of the force about the poit (2,-1,) 1. P represets the variable complex umber Z Fid the locus of P if 2Z 1 Z 2 14. If U = (x-y) (y-z)(z-x) the Show that U x + U y+ U z = 0 15. Show that a b, b c, c a 0 16. For ay two complex umbers Z 1 ad Z 2 Prove that a) Z1Z 2 Z1 Z 2 b) arg (Z 1Z 2)= arg (Z 1) + arg (Z 2) 17. If w= x+2y+z 2 ad x=cost y=si t z=t fid dw dt Part C Aswer ay five questios Each questio carries marks x 5 =15 18. Solve x 4 +4 =0 if 1+i is oe of the roots. 19. Fid all the values of i 1/ 20. The edge of a cube was foud to be cm with a possible error i measuremet of.1 cm. Use differetials to estimate the maximum possible error i computig 1 the volume of the cube ad 2 the surface area of a cube x y u u 21. u log e e Fid x y 22. Fid the vector ad Cartesia equatio of a sphere with cetre havig positio vector 2i j k ad radius 4 uits.
2. Fid the meetig poit of the lie r 2i j k t 2i j k ad the plae x-2y+x+7=0 24. Prove by vector method the Diagoals of a rhombus are at right agles Part D Aswer ay questios Each questio carries 5 marks x 5 =15\ 25. Fid the vector ad Cartesia equatio of the plae cotaiig the lie Ad passig through the poit -1,1,-1 x 2 y 2 z 1 2 2 Fid all the values of 1 i 2 2 4 ad hece prove that the product of the values is 1 26. If ad are the roots of x 2 1 9 9-2x+4=0 Prove that i2 Si ad deduct Fid the approximate value for 27. 65 x 1 y 1 z 1 x 4 y z 1 Show that the lies, ad 1 0 2 0 poit of itersectios. itersect ad hece fid the Trace the curve y =x +1 ---------------------------------------------------------------------------------------------------------------------------------- Prepared by G NARASIMHAN. M.Sc.,M.Ed.,PGDCA Retired Head Master, J.G. Natioal Hr Sec School, East Tambaram. Residetial address: No. 40/28 Buddhar Street East Tambaram, Cheai -59 Phoe Number: 9884588989
SLIP TEST 4 XII STD MATHEMATICS MAX MARKS : 50 TIME 1HR 15 MIN part A Aswer ay 10 questios Each questio carries 2 marks 2 x 10 =20 1 1 1. Fid the cojugate of 1i 1i 2. Fid the real part ad imagiary part of. Fid the multiplicative iverse of 1+i i i 20 19 2i 1 4. Compute the square roots of Z = - 1-i 5. Compute the real ad imagiary part of Z = i 4 2i 6. Fid the coditio that y = mx +C may be a taget to the parabola y 2 =4ax 7. Solve x -1 = 0 8. Fid the equatio of the parabola, if the curve is ope rightward, vertex is (2,1) ad passig through the poit (6,5) 4 cos i si 9. Simplify 5 si i Cos 10. Fid the equatio of chord of cotact of tagets from the poit (2,4) to the ellipse 2x 2 +5y 2 =20 11. If the ceter of the ellipse is (4,2) ad oe of the focus is (4,2) fid the other focus. 12. Defie Asymptote Part B Aswer ay 5 questios Each questio carries marks x 5 =15 1. A arch is i the form of a semi ellipse whose spa is 48 feet wide. The height of the arch is 20 feet. How wide is the arch at a distace of 10 feet above the base? 14.A satellite is travellig aroud the earth i a elliptical orbit havig the earth at a focus ad of eccetricity ½.The shortest distace that the satellite gets to the earth is 400kms. Fid the logest distace that the satellite gets from the earth. 15. If 1 i 1 i 100 a ib, the fid (a,b) 16 A reflectig telescope has parabolic mirror for which the distace from the vertex to the focus is 9 mts If the distace across ( diameter ) the top of the mirror is 160 cm. how deep is the mirror at the middle? 17. Fid the vertex, focus ad equatio of directrix of the parabola (y+2) 2 = -8 (x+1)
18. Solve 6x 4-25x +2x 2 +x-10 =0 give that oe of the roots is 2-i 1 i 19. Fid all the values of 2 Part C Aswer ay three questios Each questio carries 5 marks 5 x =15 y y Si 20. If α ad β are the roots of x 2-2x+2=0 ad Cot =y+1 Show that Si 21. If P represets the variable complex umber Z Fid the Locus of P if z 1 arg z 1 22.A cable of a suspesio bridge hags i the form of a parabola whe the load is uiformly distributed horizotally. The distace betwee two towers is 1500 ft. the poits of support of the cable o the towers are 200 feet above the road way ad the lowest poit o the cable is 70 feet above the road way. Fid the vertical distace to the cable from the pole whose height is 122 feet. 2.The ceilig i a hallway 20 feet wide is i the shape of a semi ellipse ad 18 feet high at the ceter. Fid the height of the ceilig 4 feet from either wall if the height of the side walls is 12 feet. 24.O lightig a rocket cracker it gets projected i a parabolic path ad reaches a maximum height of 4 mts whe it is 6 mts away from the poit of projectio. Fially it reaches the groud 12 mts way from the startig poit fid the agle of projectio ----------------------------------------------------------------------------------------------------------------------------- --------------- Prepared by Mr. G NARASIMHAN M.Sc., M.Ed., PGDCA. Retired Head Mater, J.G. Natioal Hr. Sec. School., East Tambaram. Cheai 59. Part Time P.G.T i Sita Devi Garodia Hidu Vidhyalaya, East Tambaram. Cheai -59 Residetial address: No. 40/28 Buddhar Street., East Tambaram. Cheai 59