Math Bank - 9. If cos ecθ= x + then the value of cos ecθ + cot θ is. (a) 2x (b) -2x. = and ( ) sec A + C = 2, then. (b), (c), (d) None of these

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1 Math Bank - 9. If cos ecθ= + then the value of cos ecθ + cot θ - / (d) -/. If sin ( A + B + C) =, tan ( A B) = and ( ) A= 90,B= 60,C= A = 0,B = 60,C = A= 60,B= 0,C= 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) If ( sin ) ( cos ) + =, then equal to 8

2 , -,, (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 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)

3 7. If the angle between the two lines represented by + 5y + y y + = 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) 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

4 [, ) (,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 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

5 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

6 c ( ) 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 α [ 0.] 5. The value of α which satfies cos d = cos α, 6 α 0

7 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 (d) If () () = ( ) 5, then Given A = {,, }, B = {, }, C = {, 5, 6}, then (A B) (B C) A null set of ordered pairs {(, )} {(, )} (d) {(, ),(,)}

8 56. Value of ( i)( i)( i)( i) The multiplicative inverse of the comple number z = i i + i + i (d) i 58. If ( + iy)( i ) = + i, find ( + y) ( y ) The conjugate of ( + i ) i 9 i 9 i i 9 (d) 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 = = = 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:

9 65. The value of m for which the equation m + = 0has two roots equal in magnitude but opposite in sign (d) T n of an A.P. 5 6n. The value of S n of the same A.P. : n n n n ( ) ( ) ( n n ) If in an A.P. the sum of 0 items, and the sum to terms 9 then the sum of 0 terms : (d) If 9 th terms of an A.P. zero, and 9 th term n times, the 9 th term, then value of n : (d) An A.P. consts of 60 items. If the first and the last term be 7 and 5 respectively its nd term : (d) 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 : (d) 0 7. Number of different signals can be given using any number of flags from 5 flags of different colour? In how many ways a committee of 5 members can be selected from 6 men and 5 women, consting of men and women? If nc = nc8, then n has the value 0 6 (d) 0

10 ANSWER KEYS.... (d) (d) (d) (d) (d) (d) (d)

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz 318 NDA Mathematics Practice Set 1. (1001)2 (101)2 (110)2 (100)2 2. z 1/z 2z z/2 3. The multiplication of the number (10101)2 by (1101)2 yields which one of the following? (100011001)2 (100010001)2 (110010011)2