Contact www.solvedhub.com for best and lowest cost solution or email solvedhub@g mail.com Business Mathematics ADL 22 V1 ASSIGNMENT A 1.
(A) Simplify: [(a+x)1/2 + (a-x)1/2] / [(a+x)1/2 (a-x)1/2] = a / x
1 1/ 2
(B) Prove by way of Mathematical Induction : 13+23+33+43+ - - - - - - - - - - - - - - - - - + n3 = [n2(n+1)2] / 4 11/2 2. 3
Prove the following Trigonometric Identity: 2(Sin6A + Cos6A) 3(Sin4A + Cos4A) + 1 = 0
3. Draw Draw the the Grap Graph h of the the foll follow owin ing g In-E In-Equ quat atio ions ns and and find find the the Comm Common on Feas Feasib ibl l e Solution along with the Vertices : x+y <= 4 ; 3x+y >= 3 ; x+4y >= 4 ; x <= 3 ; y >= 2 3 4.
(A)
Show whether the following is a Tautology or a Contradiction ? ((p ? q) ? (q ? r)) ? (p ? r) 11/2
(B) For what values of k the terms : 1 + k , 5/6 + k , 13/18 + k are in Geometric Progression ? 11/2 5.
Find dy/dx if : (tan-1x)y + (y)cotx = 1
3
ASSIGNMENT B
1.
(A)
If a , b , c are in Arithmetic Progression prove : 21/2 1 / (b1/2+c1/2) , 1 / (c1/2+a1/2) , 1 / (a1/2+b1/2) are also in A
.P. (B) Integrate the following function : 21/2 (x) / [(x+1)(x-1)3] 2. The angle of elevation of a jet plane from a point A on the groun d is 60* . After a f flig ht of 15 seconds, the angle of elevation changes to 30* . If the jet plane is f l flying at a constant height of 1500?3m, find the Speed of the jet plane. 5 4. 21/2
(A)
Solve the following System of Equations in Matrix Form : 2/x + 3/y + 10/z = 4 4/x 6/y + 5/z = 1
6/x + 9/y 20/z = 2 (B) A survey has been taken on methods of computer travel. Each respondent was Asked to check BUS, TRAIN, or AUTOMOBILE as a major method of traveling to work. More than one answer was permitted. The results reported was as follows : BUS 3 0 people; TRAIN 35 people; AUTOMOBILE 100 people; BUS and TRAIN 15 people; BUS a nd AUTOMOBILE 15 people; TRAIN and AUTOMOBILE 20 people; and all three methods 5 people. How many people completed the survey form. 21/2
ASSIGNMENT C OBJECTIVE TYPE QUESTIONS 1. If in a G.P. a = 4 , r = 5 then S6 = ? a. 15 2 65 c. 15 5 62 2. a. b. c. d.
b. d.
1 5 62 5 1 5 22 5
The Disjunction of p and q is true if : Both p and q are true When p is true and q is false When p is false and q is true When p or q is true 3.
Value of the Determinant b.
4.
a. 1
Cosx -Sinx
S in x
is :
C o sx
Cos2x Sin2x d.
b. 0 Cosx + Sinx
Derivative of x + (1/x) w.r.t x is equal to : a. 1 x b. 1 1/x2 b. 1 + ( 1 /x ) d. 1 + 1 / x2
5. Sum of money will double itself at 10% per year Simple Interest in : a. 5 yr s b. 2 yrs c. 20 yrs d. 10 yrs 6. a. b. c. d.
In an In-Equation x <= 2; solution for x is = ? All real values less than 2. Value equal to 2. All real values less than and equal to 2. All real values other than 2.
7. If a + b + c = 0, value of x(a.a) / bc . x(b.b) / ac. x(c.c) / ab is = ? a. x b. x3 b. x0 d. xabc 8. If A={1,2,3,4} , B={2,4,6,8} , C={3,4,5,6} then A?B is equal to : a. A?B b. A?B c. (A?B) d. (A?B)
9. If the two Linear Equations : (k 3)x + 3y k = 0 and
kx + ky = 12 has Infinite Many Solutions, then val
ue of k will be = ? a. k = 0 b. c. k = -6 c.
k = 6 None of the Above
10. If the value of (7+3?5) / (7-3?5) / (3-?5) a. (3+? (3+?5) 5) / c. (3-? (3-?5) 5) /
(3+?5) is equal to (3+?5) / 2 then the value of is equal to : 2 b. 3?5 3?5 2 d. 7?5 7?5
11. What will be the value of A ? B if A = 1 1 0 B = 1 0 1 0 1 1 0 0 0 1 a.
1
1
1
1
0
b.
0 0 1
0 1 0
1
0 1 1
1
0 1 1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1 1
0
1
1
1
1 0
1 0
1 1
0 0
1
0
1
1
0
1
1 c. 1 1
d.
0
1
0
1 1
1
1
0
0 1
12. A tower is 100?3m high. What will be the angle of elevation if its top from a point is 100m away from its foot. a. 30 b. 0 c. 90 d. 60 13. 13. If U be be the the set set of of all all tria triang ngle les s in in a plan plane, e, and and A is the the set set of all triangles with at least one angle different from 60 then A is :a. All triangles in a plane b. Set of all equilateral triangles c. Set of all triangles except equilateral triangle d. None of the above a. c.
14 Integration of Cosec(ax+b)Cot(ax+b) is = ? b. Cot(ax+b) Cosec(ax+b) d. [Cosec(ax+b)] / (ax+b) [Cosec(ax+b] / a
a. c.
15 50 0 55 0
Sum of of th the Se Sequence 15 15+24+ 24+33+42+51+60+69+78+87+96 is is b. 50 5 d. 55 5
a. c.
16 Re a l Im a gi n ar y
In a quadratic eq equation if if b2 b2 < 4ac th the ro roots ar are : b. E qu a l d. Un e qu a l
17. 17. . . Cos180 is a. 0 c. 1/ ? 2
Valu Value e of of Cos Cos1. 1.Co Cos2 s2.C .Cos os3. 3.Co Cos4 s4 . . . . . . . . . . . . . . . . . .
18. 18. alue of the
If any any two two rows rows or colu column mns s of of a Dete Determ rmin inan ant t are are iden identi tica cal, l, the the V D e Determinant becomes a. 1 b. 0 c. No Change d. 1
a. c.
19. 19. 50 . 36 50 . 45
20. 20. Tennis. How a. 25 c. 65 a. b. c. d.
Is a Is a Is a None
b.
1 d.
? 3/ 2
101t 101th h ter term m of of an an A.P A.P. . of of the the func functi tion on [n(n [n(n+1 +1)] )] / (2n (2n-1 -1) ) is is : b. 5 0 .2 4 d. 5 0 .1 3 In a gro group up of 65 peop people le, , 40 40 lik like e Cri Crick cket et, , 10 10 lik like e bot both h Cri Crick cket et & many of them like only Tennis and not Cricket? b. 35 d. 40
21 . Do you speak English? Statement. Declarative Sentence and Statement. Declarative Sentence but not a Statement. of the Above. 22 .
Differentiation of Cos3x is is a. 3Cos2xSinx c. 3C o s2 x Si n x
d.
b. 3 Co s 2x 3CosxSinx
23. Simple Interest on Rs. 650 for 8 Months at the rate of 5 paise p er rupee per month is a. 65 / 3 b. 26 0 c. 28 0 d. 36 0 24. 24. For For an A.P. A.P., , a1,a a1,a2, 2,a3 a3,a ,a4, 4,- - - - - - - - - -if -if en a6 / a8 will be : a. 3/ 2 c. 5/ 4 25 .
Value of 15 . 17 . 1-3 . 1-8 is : a. 0 c. 1
b. d.
a4 / a7 = 2/3 2/3 th b. d.
4/ 6 4/ 5
1 I n fi n it y
26. 26. A sof softw twar are e fir firm m pro provi vide des s the the foll follow owin ing g thr three ee char charac acte teri rist stic ics s for for each program that it sells: Language : FORTRAN (f) ; PASCAL(p) ; LISP(l) Memory : 2meg(2) ; 4meg(4) ; 8meg(8) Operating System: UNIX (u) ; DOS (d) The number of Categories in this Classification is : a. 18 b. 19 c. 7 d. None of the Above 27. 27.
For For Rea Real l and and Equa Equal l Roo Roots ts the the val value ue of the the Det Deter ermi mina nant nt : a. D > 0 b. D< 0 c. D ?= 0 d. D = 0
For what values of a does the Linear Equation : ax + 8y + 6 = 0 & 2x + (a-1)y 7 = 0 have Unique Solution? a. Values 4, 17, -4 b. Values between 4 and 17 28 .
c. Values other than 4, -4, 17 d. None of the Above 29. 29. 0
If A = {a, {a, b, b, c, c, d} d} and and R be be the the Rela Relati tion on on A, whos whose e Mat Matri rix x is is : 1 0 0 then R will be: 0 1 0 0 a. {(a,a),(a,b),(a,c)(a,d),(b,b),(c,c),(d,d)} 1 1 1 0 b. {(a,a),(a,c),(b,b),(b,c),(c,c),(d,d)} 0 1 0 1 c. {(a,a),(a,c),(b,b),(b,c),(b,d),(c,c),(d,d)} d. {(a,a),(a,c),(b,b),(b,c),(b,d),(c,c),(c,d),(d,d)} 30 .
Which term in the given Seq Sequence is wrong? 10, 20, 40, 70, 120, 160 a. 40 b. c. 16 0
120 d.
70
31. 31. A Sum Sum of Rs. Rs. 200 2000 0 is is inv inves este ted d at at 16% 16% rate rate of inte intere rest st per per ann annum um. . What will be the Amount after 2 years if the interest is Compounded Semi annual ly? a. Rs . 23 6 1. 2 0 b. Rs . 2 16 3 .2 0 c. Rs . 21 3 6. 2 0 c. Rs . 2 61 3 .2 0 e. Rs. 2720.98 32 .
33 .
If A = {a, e, i, o, u} a. a ? A c. a ? A
b. c.
a ? A No None of the Above
Integration of e5x a. 5e 5 x c. e5x / 5
d.
b. e5 x
5 e4 x
34. 34. If the the Grap Graph h of two two Line Linear ar Equa Equati tion ons s repr repres esen ents ts a Sing Single le Line Line t hen the Solution for the graph is a. Co n si s te n t b. In c o ns i st e n t c. Un Unique d. No None of the Above 35 .
Value of of 2 Sin2? + Cos2? is is = ?, wh where 45 45º a. 3 / 2 c. 2 / 3
b. d.
2 3 / ?2
36. 36. If the the dif diffe fere renc nce e bet betwe ween en Simp Simple le and and Com Compo poun und d Int Inter eres est t on on a Sum Sum of Money for 4 years at 5% per annum is Rs. 150 the Sum will be: a. Rs . 96 3 7. 5 2 b. Rs . 9 76 3 .2 5 c. Rs . 93 6 7. 2 5 d. Rs . 9 67 3 .5 2 37 .
If
A =
5
4 7
a.
5
7 4
A-1 will be equal to 6 b.
3
7/2
6
2
-5/2 c.
3
7 /2
d.
3
-7
-2
5
/2 2 /2
5/2
38 .
39 .
a. b. c. d.
Differentiation of a. ta n 2x c os 2 x c. sec4x
tan2x w.r.t. cos2x is: b. d.
Value of (81 / 256)-5/4 is: a. 3 / 2 c. 1024 / 243
d.
se c 4 x t a n 2x / co s 2x b. 3/2
1024 / 243
40 . Integration of (2x-3)2 4/3x3-6x2+9x 4/3x2-6x+9 3/4x3-6x2+9x 3/4x3-6x2+9
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