MOCK TEST - 0 COMMON ENTRANCE TEST 0 SUBJECT: MATHEMATICS Time:.0Hrs Max. Marks 60 Questios 60. The value of si cot si 3 cos sec + + 4 4 a) 0 b) c) 4 6 + x x. If Ta - α + x + x the x a) cos α b) Taα c) si α cot α 3. If 3 si si x+ y+ si z 0 0 0 9 the the value of ( x + y + z ) 03 03 03 ( x + y + z ) a) b)0 c) 3 4 + cos x+ cos x+... 4. If 4 the the values of x are a) & b) & c),& & 3 3 4 4 6 6 5. The Geeral solutio of 9 six.3 six + 0 is a) b) c) + ( ) ± 0 6. The value of k k si + i cos k 03 03 is a) b) i c) i 7. If p is the poit represeted by the complex umber Z rotate OP (O is the origi) through / i the aticlockwise directio. The the ew positio of the complex umber is represeted by a) z + i b) iz c) z - i z i 8. The cotiued product of the cube roots of 3 + i is a) 3 + i b) 3 + i c) 3 i 3 i 9. If i + i 00 a+ ib the (a,b)
a) (,-) b) (,0) c) (0,) (-,) 0. The umber (49 4) (49 3 49) is divisible by a) 5! b) 6! c) 7! 9! ( + x + x )( + y+ y )( + z+ z ). For all positive values of x,y & z the value of xyz be less tha a)8 b) 9 c) 7 3. The digit i the uit place of the umber (009)!+3 7886 is a) b) 7 c) 3 9 4 3. If A the A a)6a b)64a c)3a 4A cos si 4. If A θ θ the (adj A) - is equal to siθ cosθ a) A b) A c) A - adj A will ot 0 0 3 0 4 5 6 5. The characteristic roots of the matrix are a),,4 b) 4,5,6 c),3,6,4,6 a b 6. If for a triagle ABC c a 0 the the value of si A +si B+ si C is b c a) 3 3 b) 4 9 c) 9 4 7. The idetity elemet i the group x M, x R& x 0 with respect to matrix x x multiplicatio is a) 0 0 b) c) 0 0 8. I the group G{0,,,3,4,5} uder additio modulo 6, a sub group is a){0,,3} b){0,,4} c){0,3,5} {0,4,5}
9. Which of the followig statemet is ot true a)the idetity elemet i a group is uique b)i a group of eve order there exists a elemet a e such that a - a i 3 + i 3 c)the cube roots of uity are,,, I a abelia group, (ab) a b for all a,b G 0. If,, The uuur uuur uuur uuur. If the volume of the parallelepiped with, & uuur uuur uuur uuur 6 a b 4 ab 6 a b 4 a b a) b) c) uuur uuur uuur ab c as co-termial edges is 40 ur ur ur ur ur ur cubic uits. The the volume of the parallelepiped havig b + c, c + a & a + b as cotermial edges i cubic uits is a) 60 b) 40 c) 80 0. The sum of two uit vector is a uit vector. The the magitude of their differece is a) b) 3 c) 3. If u r, v r, w r r be such that, r u v, & r w 3. If the projectio of r r r the projectio of alog u. ad If v & w r r r are perpedicular to each other the. u v + w a) 7 b) 4 c) 4 f x ( ) ( )( ) 3 + x+ x + x +... + x The f ( ) 6 a) ( ) b) ( ) - c)( ) - ( ) - 4. If ( ) 5. If 3x 3x d y y cos si the is dx a) 3 y b)9y c)-9y 3 y 6. 6. If si(x + y) + cos(x + y) log(x + y) the a)0 b) d y dx y c) - x
x x e + e dy 7. If y the x x e e dx a) sec hx b) cosech x c) cosech x sec hx 8. If 3 x x x dy x y + x+ + +... + the +! 3!! dx! a)x b) x c)y y 9. If a) dy y si x ax a ax the dx x x b) si a ax si xsi c) 0 a 30. A stoe is throw vertically upwards from the top of a tower 64 meters high accordig to the law s 48t 6t. The greatest height attaied by the stoe above the groud is a) 00mts b) 64mts c) 36mts 3mts 3. The taget & the ormal draw to the curve yx -x+4 at the poit p(,4)cuts the x- axis at A & B respectively. The the area of the triagle PAB i square uits is a)3 b)4 c)6 8 3. The rate of chage of the surface area of a sphere of radius r whe the radius is icreasig at the rate of cm/sec is proportioal to a) b) c) r r r r 33. e x.x 5 dx is a) e x [x 5 + 5x 4 + 0x 3 + 60x + 0x + 0] + c b) e x [x 5-5x 4-0x 3-60x - 0x - 0] + c c) e x [x 5-5x 4 + 0x 3-60x + 0x - 0] + c e x [x 5 + 5x 4 + 0x 3-60x - 0x + 0] + c 34. The value of ax3 + bx+ c dx depeds o the 35. a) value of b b) value of c c) value of a values of a & b dx 0 + ta ( x) 0
a) b) 3 c) 4 0 36. The area of the ellipse 37. x y + is 64 36 a)64 b)36 c)48 6 cos xdx cos x α ( ) a)x cos α + siα log cos (x - α) b)x siα + cos α log cos(x - α) c)x si α - si α log cos (x - α) x cos α - siα log si (x - α) 5 3 dy d y 38. The order & degree of the differetial equatio + are respectively dx dx a)&5 b)& c)&5 &3 dy 39. The solutio of x y x y dx + is a) si y si x+ c b) si - yx y +c c)si - yx x +si - x+c cos - yxcos - x+c 40. If 3x+y+k0 is a taget to the circle x +y 0,the the values of k are a)±7 b)±5 c)±0 ±9 4. If (x, 3) ad (3, 5) are the ed poits of the diameter of a circle with cetre at (, y) the the value of x ad y are: a) x, y 4 b) x 4, y c)x 8, y - x -8, y - 4. The area of the circle x+3cosθ & y3siθ- is a)9sq.uits b)4sq.uits c)6sq.uits sq.uits 43. The umber of values of C such that the lie y 4x + c touches the ellipse x + y is 4 a) ifiite b) 0 c)
44. The equatio x y λ λ 0 5 represets a ellipse if a) λ>5 b) λ < c) < λ < 5 > λ > 5 45. If the distace betwee the foci & the distace betwee the directrices of the x y hyperbola are i the ratio 3: the a:b is a b a) 3: b) : c) : : 46. The focus of the parabola y + 6x 0 is a) (6, 0) b) (-6, 0) c) (4, 0) (-4, 0) 47. The agle betwee the pair of lies x + xy y 0 is : a) 0 b) c) 3 6 48. If the area of the triagle with vertices (x,0) (,) & (0,) is 4 square uits. The the value of x is. a) - b) -4 c) -6 8 49. If p is the legth of the perpedicular from the origi o the lie whose itercepts o the axes are a&b the. a) p a +b b) p a -b c) + p a b p a b 3. 4.5 50. lim x 5. + 7.5 0 a) 7 + + b) 0 c) 3 5 4 5 5. The fuctio f ( x) ( + ax) ( bx) log log is ot defied at x 0. The value which x should be assiged to f at x 0 so that it is cotiuous at x 0 is a) loga + logb b) 0 c) a b a + b 5. si 7.5 0 + si 7.5 0 is equal to a) cos 90 0 b)ta 45 0 c)cos 30 0 si 45 0 53. OA & OB are two roads eclosig a agle of 0 0. X & Y start from O at the same time. X travels alog OA with a speed of 4 km/hr & Y travels with a speed of
3km/hr. The rate at which the shortest distace betwee X & Y is icreasig after hour is a) 37 km / hr b)37 km/hr c)3 km/hr 3 km / hr 54. If A+B+C80 0 the cos A + cos B +cos C a) --4cosA cosb cosc b) 4cosA cosb cosc c) +4cosA cosb cosc -+4cosA cosb cosc 3 5 7 55. The value of si si si si + + + 8 8 8 8 is a) b) c) 8 8 56. If A{,,3,4,5,6} how may subsets does the set A have a) 64 b) 63 c) 30 6 57. If 00 the + + +... +... log log3 log4 log00 a) 00 b) 0 c) 00 58. If p (q r) is false the the truth value of p,q,r, are respectively a)tff b)fff c)ftt TTF 59. The 9 th term of the expasio 3x x is a) b) 9 9 5x 5x 8 c) 8 56x 8 56x + x 3x is 60. The sum of the coefficiets i the expasio of ( ) 348 a) 8 b) 7 c)