Math Bank - 9. If cos ecθ= + then the value of cos ecθ + cot θ - / (d) -/. If sin ( A + B + C) =, tan ( A B) = and ( ) 0 0 0 A= 90,B= 60,C= 0 0 0 0 A = 0,B = 60,C = 0 0 0 0 A= 60,B= 0,C= 0. 9 5 The value of cos cos + cos + cos 0 - sec A + C =, then. The solution of the equation cos θ + sin θ+ = 0, lies in the interval.,, 5 5 7, (d), 5. Solution of the equation cos θ = cot θ tan θ θ= n± θ = n± θ= n± 6. The value of tan + tan 6 (d) 0 7. ( ( ) )( ( )) sin cos sin + cos sin cos equal to (d) 0 5 8. If ( sin ) ( cos ) + =, then equal to 8
, -,, (d),0 9. The angle C of the triangle ABC in which ( c+ a+ b)( a+ b c) = ba (d) 6 0. In any ΔABC, abc Δ Δ A B C Ssin sin sin = Δ. A person, standing on the bank of a river observes that the angle subtended by a tree on the opposite bank 60 0,when he retreats 0m from the bank, he finds the angle to be 0 0. The height of the tree and the breadth of the river are 0 m,0m 0 m,0m 0 m,0m. At the foot of the mountain the elevation of its summit 5 0, after ascending 000m towards the mountain up a slope of 0 0 inclination, the elevation found to be 60 0. The height of the mountain + m + m m. If α, β, γ are the real roots of the equation P + q = 0, then the centroid of the triangle having vertices α,, β, and γ, α β γ (P, q) (P, -q) (-P, q) (d) (-P, -q). The equation of the straight line, passing through the point (, -) and perpendicular to the line 8 y + 7 = 0 + y+ 6= 0 y+ 6= 0 + y + 6 = 0 (d) y + 6 = 0 5. If the lines y 6 = 0, + y = 0 and λ + y+λ = 0 are concurrent, then λ = λ = - λ = 6. If the ratio of gradients of the lines, represented by the ratio h : ab a + hy + by = 0 :, then the value of (d)
7. If the angle between the two lines represented by + 5y + y + 6 + 7y + = 0 then m = 5 tan m, 7 5 (d) 7 8. The equation of that diamenter of the circle origin, y = 0 + y = 0 y = 0 9. If the line y + k = 0 a diameter of the circle 9 6 (d) + y 6+ y 8= 0, which passes through the + y + 6 6y+ 5= 0 then k equal to 0. The locus of a point whose sum of the dtances from the origin and the line = units y = ( ) y = ( ) y = y = ( ) (d) ( ). In an ellipse the dtance between its foci 6 and length of its minor a 8. Then its eccentricity 5 5 (d) 5 999 y =. The eccentricity of the hyperbola ( ) (d). Equation of the tangent to the hyperbola y = + 5 y = 5 y = + 5 and y = 5. The mirror image of the directri of the parabola y ( ) = - y = 6 y + 6 = 0 y = 6 which parallel to the line y = + = + in the line mirror + y = 5. If the dtance of a point on the ellipse angle 6 (d) + = from the centre, then the eccentric 6 y 6. The domain of the function f ( ) = + 5
[, ) (,5) (, 5 ) (d) [, 5 ] 7. The period of the function f( ) = sin + cos 8 = = + + f() f() f() (d) f() 8. If f ( ) log,thenf 9. The value of lim 0 ( ) e + 0 (d) 0. The value of 8 + + lim + 5 e 8 e -8 e (d) e -. + lim equal to X / / / (d) /. If f ( ) sin, < cos = b ( sin), > ( ) Then f() continuous at a =,b= a =,b = 8 a =,b = 8. The function f ( ) = = u + u, where u = dcontinuous at the points = -,, / = ½,, =, 0. If ( ) ( ) f =, where [.] denotes the greatest integer Function, then
f() continuous for = n,wheren f( ) = f ( ) = 0 for < < 5. If f ( ) = cos, then f equal to d dy equal to 5 5cos cos 5 5cos + cos 5 cos 5cos 7 6. If y = sin, then ( cos ) 7. If f() = and φ () = (fof)(), then for > 0, φ () equal to 0-8. The equation of the normal to the curve e e + y = e = ( ) e( e y) = e e( e ) = e y= e at the point where the curve cuts the line 9. The maimum value of log e e (d) d = e 0. If y = f() be the equation of an ellipse to which the line y = + a tangent at the point where =, then f () = f ( ) = f () f + f + f = ( ) ( ) ( ) ( ). The value of d
c 8 + + ( ) c 8 + ( ) + c 8. The value of d + + + n + c + + + In + c + + + + c (d) + + c + +. The antiderivative of the function ( + ) sin, where 0 < <, given by sin + cos ( ) sin + ( + ) cos sin + ( + ) cos. 6 sin cos d 0 equal to 5 56 0 α [ 0.] 5. The value of α which satfies cos d = cos α, 6 α 0
6. d ( ) 0 a + b ab b/a equal to a/b (d) /ab 7. The degree of the differential equation of which y = a( + a) a solution, 8. Integrating Factor of differential equation sin sec tan (d) cos dy cos. ysin d + = 9. dy The solution of the differential equation y d = represents circles straight lines ellipse (d) parabola ( a+ ib ) ( a ib ) 50. If a ib a+ ib = + iy, then b 6a b a + b a + b ( ) 0 ( ) 5. If set A = {5, 5, 0, 0} and B = {, 5, 5, 8, 0} then A B {, 5, 5, 8, 0, 0} {, 8, 0} {, 5, 5, 8, 0} (d) {5, 5, 0} 5. In a group of people 65% speak German and 5 speak French. If 5% of the people speak neither French nor German, then the percentage of people who can speak both German and French 5% 0% 5% (d) 0% 5. Convert 0 of base to a number of base 0 0 0 (d) 00 5. If () () = ( ) 5, then 0 9 55. Given A = {,, }, B = {, }, C = {, 5, 6}, then (A B) (B C) A null set of ordered pairs {(, )} {(, )} (d) {(, ),(,)}
56. Value of ( i)( i)( i)( i) + + + + + + + 57. The multiplicative inverse of the comple number z = i i + i + i (d) i 58. If ( + iy)( i ) = + i, find ( + y) ( y ) 9 9 9 59. The conjugate of ( + i ) i 9 i 9 i 5 5 5 5 9 5 5 i 9 (d) 5 + 5 i 60. If ω the cube root of unity then ( + ω ω ) 7 equals 8 ω 8 ω 8 ω (d) 8 ω n 6. The smallest positive integer for which ( i) ( i) 8 (d) n + = 6. If α + β =, α + β = 7, then α and β are the roots of + 9+ 7 = 0 9 7+ 0= 0 6+ 5= 0 6. If one root of the equation i ( i ) ( i) + + = 0 i, then P + q the other root : q P i + i i (d) i 6. If the ratio of the roots of the equation n 0 l n (d) l l n l n n + + = 0 be P: q, then equal to:
65. The value of m for which the equation m + = 0has two roots equal in magnitude but opposite in sign (d) 5 66. T n of an A.P. 5 6n. The value of S n of the same A.P. : n n n n ( ) ( ) ( n n ) + 67. If in an A.P. the sum of 0 items, and the sum to terms 9 then the sum of 0 terms : -0 0 0 (d) -0 68. If 9 th terms of an A.P. zero, and 9 th term n times, the 9 th term, then value of n : (d) 5 69. An A.P. consts of 60 items. If the first and the last term be 7 and 5 respectively its nd term : 6 65 66 (d) 69 70. Let S n = denote the sum of first n terms of an A.P.. If Sn = Sn then the ratio S n / S n equal to 6 8 (d) 0 7. The sum of the first four terms of an A.P. 56. The sum of the last four terms. If its first term, the number of terms : 0 7. The sum of 0 arithmetic means between 7 and : 60 00 500 (d) 0 7. Number of different signals can be given using any number of flags from 5 flags of different colour? 5 0 0 7. In how many ways a committee of 5 members can be selected from 6 men and 5 women, consting of men and women? 0 00 50 75. If nc = nc8, then n has the value 0 6 (d) 0
ANSWER KEYS.... (d) 5. 6. 7. 8. 9. 0..... 5. 6. 7. 8. 9. 0..... 5. 6. (d) 7. 8. 9. 0..... 5. 6. 7. 8. 9. 0..... 5. 6. (d) 7. 8. 9. (d) 50. 5. 5. 5. 5. 55. 56. 57. 58. 59. 60. (d) 6. 6. 6. 6. 65. 66. 67. (d) 68. 69. (d) 70. 7. 7. 7. 7. 75.