TEST PAPER 6 Total Questions: 60 Time allotted 75 minutes Q.) d equal to + e (a) log + + c log + e + c + e + c (b) ( e ) (c) log ( + e ) + c (d) ( ) Q.) π / sin e cos d equal to 0 (a) e + (b) e (c) e + (d) e Q.3) The area bounded by the coordinate aes and the curve + y = equal to (a) (b) (c) 3 (d) 6 π / Q.4) The value of ( ) log tan d equal to 0 π (a) (b) 0 (c) 4 π (d) 8 π Q.5) Q.6) Q.7) dy dy The degree of the differential equation = y d d (a) (b) 3 (c) 4 (d) 5 y A cos ωt + sin ω t a solution of the differential equation d y d y (a) ω y = 0 (b) ω y = 0 dt dt (c) d y ω y 0 dt + = (d) d y + ω y = 0 dt dy 3y 4 4 The differential equation 3 + = y not linear. The integrating factor to solve th equation d (a) (b) 3 4 (c) (d) 4 4
dy Q.8) The general solution of y sin d + = (a) y = ce + sin cos (b) y = ce + sin cos 4 3 (c) y = ce + sin (d) y = ce Q.9) Q.0) Q.) The solution of dy y y d = + (a) sin y sin + c (b) sin y = + sin + c (c) sin y = + sin + c (d) sin y = + cos + c 4 Which one of the following pairs not correctly matched? Differential Equations Their Solutions (a) dy P( ) y 0 d + = P d y = ce (b) dy yd y + a d = 0 tan + a = c + y dy yd (c) = 0 y log ( + y) + c (d) yd+ dy= 0 y = c The differential of the system of circles touching the y-a at the origin, given by dy dy (a) + y y = 0 (b) + y + y = 0 d d (c) dy + = 0 (d) y y d dy = 0 y y d Q.) The rate at which bacteria multiply proportional to the instantaneous number present. If the original number doubles in hours, then they will triple in log log (a) 4 hours (b) 5 hours log 3 log 3 (c) log hours (d) log log 3 log 3 hours Q.3) If b r a unit vector in the y-plane making an angle of 4 π with the -a, then b r equal to (a) iˆ+ ˆj (b) iˆ ˆj iˆ ˆ j / iˆ ˆ j / (c) ( + ) (d) ( ) Q.4) Dtance between two points whose position vectors are 3iˆ+ ˆj kˆ and iˆ 3ˆj+ 5kˆ (a) 69 units (b) 69 units (c) 3 units (d) 9 units ur ur Q.5) If A O and both the conditions
uurur uurur ur ur ur ur (i) A. = AC. and (ii) A = A C hold simultaneously, then ur ur ur (a) = C = O ur ur (c) C Q.6) α, βξηare,, non-empty sets then (a) ( α β) ( ξ η) = ( α β) ( ξ η) (b) ( α β) ( ξ η) = ( α ξ) ( β η) (c) ( α β) ( ξ η) = ( α ξ) ( β η) (d) ( α β) ( ξ η) = ( α η) ( β ξ) ur ur (b) = C ur ur ur ur (d) O, C O Q.7) Q.8) There are 600 students in a school, If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi are (a) 00 (b) 00 (c) 300 (d) 400 In a Euclidean plane, which one of the following not an equivalence relation? (a) Parallelm of lines (a line being deemed parallel to itself) (b) Congruence of triangles (c) Similarity of triangles (d) Orthogonality of lines Q.9) The modulus and principle amplitude of ( i 3) +, respectively are π π (a), (b) 4, 3 5 4 3π (c),tan (d) 4, 8 3 4 Q.0) If, ω, ω are the cube roots of unity, then value of ( y) (a) y (c) 6y (b) 3y (d) 9y + to ( ω yω ) ( ω yω) + + + equal to Q.) 3n 3n + i 3 i 3 The value of + equal to (a) 3 (b) 3/ (c) 0 (d) Q.) i z The comple number z, satfying the equation i+ z = lies on (a) a circle with the centre (0, 0) and radius (b) the -a (c) the y-a (d) the line y = + Q.3) The binary number 00 + 00 written in decimal system as (a) 98 (b) 99 (c) 00 (d) 0
Q.4) The binary equivalent to the decimal number 0.35 (a) 00 (b).00 (c).00 (d).0 Q.5) Q.6) The binary number 000000 in decimal system (a) 44 (b) 44 (c) 4 (d) 4 The the mth and the nth terms of an H.P. are n and m respectively, then the mnth term (a) 0 (b) (c) (d) Q.7) If a, b, c are in G.P., then + a b b (a) (b) c b b c (c) (d) c a b a Q.8) The value of (a) 0 9 3 + =... equal to 3 9 (b) 9 0 (c) 9 4 (d) 4 9 Q.9) If ( )( + 6) 0, then the solution set (a) ( : ) (b) ( : 6) (c) ( : 6) (d) ( : or 6) Q.30) The value of 6+ 6+ 6 +... equal to (a) (b) 3 (c) 6 (d) 6 Q.3) If the equations p+ q = 0 and + q p = 0 have a common root, then which one of the following will hold true? (a) p = q (b) p + q = (c) p + q = (d) p q = Q.3) Q.33) The number of words that can be formed from the letters of the word INDRAPRASTHA when the vowels are never separated (a) 77560 (b) 75760 (c) 75760 (d) 75760 The number of -digit even numbers that can be formed from the digits,, 3, 4 and 5, repetition being not allowed, (a) 5 (b) 5! (c)6 (d) 8
Q.34) The number of ways in which 6 people can be seated at a round table (a) 6 (b) 60 (c) 0 (d) 70 Q.35) The coefficient of the middle term in the epansion of ( + 3) 4 (a) 6 (b) 5! (c) 8! (d) 6 Q.36) If in the binomial epansion of ( + ) n when n a natural number, the coefficients of the 5 th, 6 th and 7 th terms are in A.P., then n equal to (a) 7 or 3 (b) 7 or 4 (c) 7 or 5 (d) 7 or 7 Q.37) If log8 m + log g =, then m equal to 6 3 (a) 4 (b) 8 (c) (d) 4 Q.38) Q.39) Q.40) Q.4) y z If a = b = c, and logb a = logcb, then which one of the following will hold true? (a) y = z (b) = yz (c) z = y (d) y = z 6 If + = 3, then + 6 equal to (a) 97 (b) 44 (c) 364 (d) 3 3 0 4 3 The rank of the matri equal to 3 3 6 8 7 5 (a) (b) (c) 3 (d) 4 0 If A = 0 and =, the ( A + ) not equal to (a) A + A + A + (b) A + A + (c) A + A + A + I (d) A I + A+ A+ 0 0, then the value of α and β are given by (a) α =, β = (b) α =, β = (c) α = β = ± (d) α = β =± Q.4) If A = = ( α+ βa) Q.43) If A be an n n matri and C any scalar, then CA C n (a) n A (b) C A
(c) nc A (d) CA Q.44) 0 7 4 The matri 7 0 5 4 5 0 (a) symmetric (c) non-singular (b) skew symmetric (d) orthogonal Q.45) 3i If = y i = 6+ i, then 0 i i (a) = 3, y = 4 (b) = 3, y = 4 (c) = 3, y = 4 (d) = 3, y = 4 Q.46) If A = 3 4, then A - equal to (a) 3 (c) 3 (b) (d) 3 3 Q.47) The epansion of the determinant y 3 5y 9 contains which one of the following as a factor? 0y 7 3 3 5 (a) 3 (b) y (c) 3 3 y 3 y (d) ( )( ) a h g f Q.48) The value of the determinant 0 0 b c e 0 d k 0 0 0 l (a) gfkl (b) abhg (c) abdl (d) ablc Q.49) If A 3 = and = 3 4, then (a) both A and A et (b) neither A nor A ets (c) A ets but A does not ets (d) A does not et but A et Q.50) The solution of equations 3+ y+ z = 3; 3y z = 3and + y+ z = 4 (a) = 3, y =, z = (b) =, y =, z = 3
(c) =, y =, z = (d) =, y =, z = Q.5) The adjoint of sinθ sinθ (a) sinθ sinθ (c) sinθ sinθ equal to (b) cos θ sinθ (d) cos θ sinθ sin θ sin θ Q.5) Q.53) The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their angles 9 0. Which one of the following correct? (a) One of them a pentagon and the other a rectangle. (b) One of them must be a heagon. (c) One of them an octagon. (d) One of the has 0 sides and the other has 6 sides. o o o o The value of tan3.tan3.tan3.tan33...tan59 equal to (a) - (b) 0 (c) (d) Q.54) π π The number,tan 6 4 and 83π cot are in 6 (a) A.P. (b) G.P. (c) H.P. (d) none of the above Q.55) The correct value of the parameter t of the identity ( 6 6 ) t( 4 4 ) (a) 0 (b) - (c) - (d) -3 Q.56) If w= + y+ z, then sin + sin y+ sin z sinω equal to y+ z z+ + y y+ z z+ + y (a) 4sin sin sin (b) 4cos cos cos y+ z z+ + y y+ z z+ + y (c) 4tan tan tan (d) 4cot cot cot sin + cos + sin + cos = Q.57) To derive the tangent formula, the following steps are given: sin Acos cos Asin +. tan ( A+ ) = cos Acos cos Acos cos Acos sin Asin + cos Acos cos Acos sin ( A + ). tan ( A+ ) = cos A + 3. tan ( A ) 4. tan ( ) ( ) sin Acos + cos Asin + = cos Acos sin Asin tan A + tan A+ = tan A tan Their correct and proper sequential form to derive the formula (a), 4, 3, (b),, 3, 4
(c), 4,, 3 (d), 3,, 4 Q.58) Consider the following:. If cotθ, then + = secθcosecθ.. If + = sinθ, then + = sin θ 3. If = psecθ and y = qtanθ, then q y p = p q. 4. The maimum value of 3 sinθ 3. Which of these are correct? (a) and (b) and 3 (c) 3 and 4 (d), and 3 Q.59) If + =, then 3 + equal to 3 (a) (c) cos3θ (b) cos θ (d) 3 cos 3θ 3π π (a) sin α + sin 3α (b) 3 (c) (d) 0 Q.60) The epression 3{sin 4 α + sin 4 ( 3 π α) } {sin 6 α + sin 6 ( 5π α) equal to
ANSWER KEYS. (c). (b) 3. (d) 4. (b) 5. (d) 6. (d) 7. (b) 8. (b) 9. (c) 0. (c). (d). (c) 3. (c) 4. (b) 5. (b) 6. (d) 7. (a) 8. (d) 9. (b) 0. (c). (d). (b) 3. (c) 4. (c) 5. (b) 6. (b) 7. (b) 8. (c) 9. (a) 30. (b) 3. (d) 3. (b) 33. (d) 34. (c) 35. (d) 36. (b) 37. (a) 38. (a) 39. (d) 40. (c) 4. (b) 4. (c) 43. (d) 44. (b) 45. (a) 46. (a) 47. (a) 48. (c) 49. (c) 50. (c) 5. (a) 5. (c) 53. (c) 54. (b) 55. (d) 56. (a) 57. (d) 58. (d) 59. (c) 60. (c)