GGSIPU Mathmatics 2004

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Cory Blankenship
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1 GGSIPU Mathmatis If the angles between the pair of straight lines represente by the equation X 2 3xy + l y 2 +3x-5y + 2 = 0 is tan - 1. Where l is a non-negative real number,then l i s : a 2 b The istane of the line 2x-3y = 4 from the point 1,1 measure parallel to the line x+y = 1 is : a b 5 / 1 / 6 3. The equations of bisetors of the angles between the lines x = y a r e : a y = ±x an x=0 b x = an y = y =0 an x =0 4. The base of verties of an isoseles triangle PQR are Q 1,3 an R -2,7.The vertex p an be : a 1,6 b, 5, 6 5. The normal at the point 3,4 on a irle uts the irle at the point -1,-2.Then the equation of the irle is : a x 2 + y 2 + 2x- 2 y 13 = 0 b x 2 + y 2-2x- 2 y 11 = 0 x 2 + y 2-2x + 2y + 12 = 0 x 2 + y 2-2x- 2y + 14 = 0 6. If os P = an os Q = where P an Q both are aute angles. Then the value of P-Q is : a b 6 0 0

2 The equation 3 os x + 4 sin x = 6 has.. solution a finite one b infinite no 8. If se -1 x = ose - 1 y,then os -1 + os -1 is equal to : a p b p / 4 - p /2 p /2 9. If n be any integer,then nn+1 2n+1 is : multiple of 6 neessarily have any of the foregoing proof a o number b integral perfet square oes not 10. If tan q = -, than the value of sin q i s : a - but ¹ b - o r but ¹ If = 2 os q,then the value of the eterminant = is : a q q b q q 4os 2 q 2 osq the set of values of x for whih the inequality x-1 + x+1 < 4 always hols true is : 2, a -2,2 b -, 2 È of these. -, 1 ] È [ 1, none

3 13. The equation of the parabola whose vertex is -1,-2, axis is vertial an whih passes through the point 3,6,is : 14. The length of the axis of the oni 9x 2 +4y 2-6x+4y+1 = 0 are : a x 2 + 2x - 2 y -3 = 0 b 2 x 2 = 3y x 2-2x+2y-3 = 0 x 2-2x-2y- 3 = 0 a, 9 b 3, 1, 3, If fx = ot -1 an gx = o s -1, then,0<a<, is : a b If f(x =, then : = 1 = 1 not ifferentiable at x = 1 a f is isontinuous at x b f is ifferentiable at x f is ontinuous but 17. lim is equal to : x a 0 b -

4 x = 0,if : 18. Let fx = x p os, when x ¹ 0 an f(x = 0,when x = 0.then f(x will be ifferentiable at a p > 0 b p > <p < 1 < p < 19. The erivative of f(x = 3 2+x atv the point x 0 = -3 is : a 3 b -3 of these 20. Derivative of the funtion f(x = x, x>7 is : 0 none a b 21. If z = x+iy, z 1 / 3 = a ib,then - = k a 2 b 2, where k is equal to : a 1 b The number of real solutions of the equation 1+ e x 1 = e x e x 2 is : a 1 b The points of extrema of f(x= t in a omain x>0 are : 1,2,.. 1,2,.. a 2n+1 b 4n+1 p, n = p, n =

5 1,2,.. 2n+1 p, n = n p,n =1,2, 24. If i=x 2 + y 2 an x=s+3t,y=2s-t,then is equal to : 25. If the equation x 2 +qx+p = 0 have a ommon root then p+q+1 is equal to : a 12 b a 0 b The value of aa b for whih the sum of the ubes of the roots of x 2 - a -2 x+ a -3 = 0 assumes the last value is : a 3 b 4 none of these Let z 1,z 2,z 3 be three verties of an equilateral triangle irumsribing the irle z =. If z 1 = + an z1,z 2,z 3 were in antilokwise sense,then z 2 is : 1- a 1 + b If z=, then the value of arg z is : p /3 a p b p /4 2 p /3 29. Let w is an imaginary ube roots of unity,then the value of 21+ w 1 + w w +1 2 w n+1 n w +1 n w is :

6 a + n b n 30. The lous of the point z satisfying arg = k,where k is non zero is : entre on y-axis entre on x-axis parallel to x- a x i s making an angle 60 0 with the x-axis a a irle with b irle with a straight line a straight line 31. If 3,4,5,Q(4,6,3,R -1,2,4,s1,0,5,then the projetion of RS on PQ is : 4/3 a -2/3 b - ½ If a line makes a, b, g with the positive iretion of x,y,z-axes respetively.then os 2 a+os 2 b+ o s 2 g is equal to : a ½ b -1/ The projetion of a line on o-orinate axes are 2,3,6.Then the length of the line is : a 7 b The eimal equivalent of the binary number is : a b The binary represents of 60 is :

7 Whih of the following statement is not tautology? a b b p q p a ~ p q p ~ p q Ç ~ p p q ~ p q 37. The perio of f(x = sin + os, nî z,n>2 is : b 4nn -1 a 2rn n -1 2 n n The raius of the irle whose ar of length 15 km makes an angle of raian at the entre,is : b 20 m a 10 m 11 m 2 2 m 40. If f n x = e,for all n Î N an f 0 x = x,then {f n x} is equal to : b f n x {f n+1 9x} a f n x f n-1 x. f 2 x f 1 x 41. if 3 x x ³5 x, then the solution set for x is : f n x f n-1 x b [2, a -, 2 ]

8 { 2 } [0,2] 42. The number of integral solution of > is : b 2 a The value of k for whih the equation k - 2 x 2 + 8x + k +4 = 0 has both real,istint an v e, i s : b 2-4 a The triangle PQR of whih the angles P,Q,R satisfy os P = : b right angle isoseles a equilateral any triangle 45. If fx = a -x n 1 / n, where a>0 an n is a positive integer, then f[f x] is equal to : b x 2 none of tese a x 3 x 46. The funtion f(x = [x] 2 [x 2 ] where [y] is the gretest integer less then or equal to y is isontinuous at : a all integers exept 0 an 1 b all integers

9 exept 0 exept 1 all integers all integers 47. the funtion fx = p x - q + r x, x Î -, where p>0,q.0,r>0 assumes its maximum value only at one point,if : q¹r p=q=r a p ¹q r ¹p b 48. A funtion f(x = i s : x= -3 a t x = -3 an maximum at x= 1 a maximum at b maximum x= 1 maximum at inreasing in its omain funtion is 49. The lous of the point px,y satisfying the relation = 6 is a b Straight line Pair of straight lines Cirle Ellipse 50. If z 1, z 2 an z 3 are omplex number suh that z 1 = z 2 = z 3 = + + = 1 then z 1 + z 2 + z 3 is : a equal to 1 b less than 1

10 than 3 greater equal to Let a 1,a 2,a 3 be any positive real numbers, then whih of the following statement is not true? a 3 a 1 a 2 a 3 a a a 3 3 b + + ³ ³ 9 a 1 a 2 a a 1 a 2 a If ab = 2a +3b,a>0,b<0,then the minimum value of ab is : b 24 a Let N be +ve integer ¹ 1, then none of the numbers 2,3,,N is ivisor of N! -1.So we an onlue that N! -1 is : number one of this number N+1, N+2,.,N! 2 is ivisor o f N! 1 smallest numbers between N an N! whih is ivisor of N! -1 is pr ime number these a prime b at least The none of 54. If f(x = os [ p 2 ] x+os [- p 2 ] x,then : a f p /4=2

11 b f -p = 2 f p = 1 f p /2= let fx =, for x > 2,then the funtion f : -,-2]È [ 2, -1,1 is : one into b one -one onto a one - one into many-one onto m a n y The funtion f(x = sin log x+ + is : funtion b o funtion even nor o perioi funtion a even b neither 57. The range of f(x = se p, - < x < i s : b [ 1, 1]È [ 1, ] -, 1 ] È [1, a [ 1, ] [ -,- 58. For any three sets A 1,A 2,A 3.Let B 1 = A 1, B 2 = A 2 -A 1 an B 3 = A 3 A 1 È A 2,then whih of the following statement is always true? A 2 È A 3 É B 1 È B 2 È B 3 A 2 È A 3 = B 1 È B 2 È B 3 A 2 È A 3 Ì B 1 È B 2 È B 3 a A 1 È b A 1 È A 1 È of these none 59. the omain of the funtion f(x = i s :

12 b 3, 4 ] -,3 È [ 2, a [2,4] [2, 60. The remainer obtaine when 1! + 2! ! Is ivie by 14 is : b 4 a 3 5

Q.B.- Maths I + II - FYJC - Ver

Q.B.- Maths I + II - FYJC - Ver -709 Q Find the equation of lous of a point, whih moves suh that the ratio of its distanes from (,0) and (, ) is :. ( : 9x + 9y + x - 0y + 86 0) Q Q Find the equation of