Amity School of Distance Learning Business Mathematics ADL - 22 ASSIGNMENT – A
Answer any five questions 1.
Max. Marks : 15
(A) Simplify: [(a+x)1/2 + (a-x)1/2] / [(a+x)1/2 – (a-x)1/2] = a / x
11/2
(B) Prove by by way of Mathema Mathematical tical Induction Induction : 3 3 3 3 1 +2 +3 +4 + - - - - - - - - - - - - - - - - - + n3 = [n2(n+1)2] / 4 2.
3. s 4.
Prove the following Trigonometric Identity: 2(Sin6A + Cos6A) – 3(Sin4A + Cos4A) + 1 = 0
11/2 3
Draw the Graph of the following following In-Equatio In-Equations ns and find the Common Common Feasible Feasible Solution along with the Vertices : x+y <= 4 ; 3x 3x+y >= 3 ; x+ x+4y >= 4 ; x <= 3 ; y >= 2 3 (A) Show whether the following is a ‘Tautology’ or a ‘Contradiction’ ? ((p → q) ∧(q → r)) → (p → r) 11/2 (B) For what what value valuess of ‘k’ the terms terms : 1 + k , 5/6 + k , 13/18 + k are in Geometric Progression ?
1 1/2
5.
Find dy/dx if : (tan-1x)y + (y)cotx = 1
3
6.
Prove by applying the properties of Determinants :
3
x y z 2 2 2 x y z yz zx xy
=
1 x2 x3
1 1 y2 z2 y3 z3
= (y – z)(z – x)(x – y)(yz+zx+xy)
ASSIGNMENT – B
Answer any Three questions 1.
(A)
If a , b , c are in Arithmetic Progression prove : 1 / (b1/2+c1/2) , 1 / (c 1/2+a1/2) , 1 / (a 1/2+b1/2) are also in A.P.
21/2
(B)
Integrate the following function : (x) / [(x+1)(x-1)3]
21/2 •
2.
The angle of elevation elevation of a jet plane from a point A on the ground ground is 60 . After a • flight of 15 seconds, the angle of elevation changes to 30 . If the jet plane is f flying at a constant height of 1500 √3m, find the Speed of the jet plane. 5
f l 3.
4.
Max. Marks : 15
(A)
Kamla borrowed from Ratan a certain sum at certain rate for two years Simple Interest. She lent this sum at the same rate to Hari for two years Compound Interest. At the end of two years, she received Rs. 210 as compound Interest, But paid Rs. 200 only as a Simple Interest. Find the Sum and the Rate of Interest.
5
2 1/2
(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 surv survey ey has has been been taken taken on on meth method odss of of compu computer ter travel travel.. Each Each resp respond ondent ent was Aske Asked d to chec check k BUS, BUS, TRAI TRAIN, N, or AUTO AUTOMO MOBI BILE LE as a majo majorr meth method od of traveling to work. More than one answer was permitted. The results reported was as follows : BUS – 30 people; TRAIN – 35 people; AUTOMOBILE – 100 people; BUS and TRAIN – 15 people; BUS and AUTOMOBILE – 15 people; TRAIN and AUTOMOBILE – 20 people; and all three methods – 5 people. How many people completed the survey form. 2 1/2
ASSIGNMENT – C OBJECTIVE TYPE QUESTIONS Tick Mark (√ ) the most appropriate answer 1.
2.
3.
If in a G.P. a = 4 , r = 5 then S 6 = ? a. 15265 c. 15562
Max. Marks : 10 b. 15625 d. 15225
The Disjunction of ‘p’ and ‘q’ is true if : a. Both Both p and and q are are true true b. b. When When p is tru truee and and q is is fals falsee c. When When p is is fal false se and and q is true true d. When When p or or q is true true Value of the Determinant a. Cos2x – Sin2x b. 1
Cosx -Sinx
Sinx is : Cosx b. 0 d. Cosx + Sinx
4.
Derivative of x + (1/x) w.r.t x is equal to : a. 1 – x b. 1 – 1/x 2 b. 1 + (1/x) d. 1 + 1/x2
5.
Sum Sum of of mon money ey will will doub double le itse itself lf at 10% 10% per per year year Simp Simple le Inte Intere rest st in : a. 5 yrs b. 2 yrs c. 20 yrs d. 10 yrs
6.
In an In-E In-Eq quation x <= 2; 2; so solution fo for x is = ? a. All All real real valu values es less less than than 2. b. b. Valu Valuee equ equal al to 2. c. All real real values values less less than than and and equa equall to 2. d. All All real real val value uess othe otherr than than 2. 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 A={1,2 ,2,3 ,3,,4} , B={ B={2, 2,4 4,6,8 ,6,8} } , C={ ={3, 3,4, 4,5, 5,6 6} the then n A’ 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 value of k will be = ? a. k = 0 c. k = -6
and
kx + ky = 12 has Infinite Infinite Many Solutions Solutions,, then b. k = 6 c. None of the Above
10.
If the value of (7+3√5) / (3+ √5) is equal to (3+ √5) / 2 then the value of (7-3√5) / (3-√5) is equal to : a. (3+√5) / 2 b. 3√5 c. (3-√5) / 2 d. 7√5
11.
What will be the value of A ⊕ B if A= 1 1 0 B= 0 1 0 1 1 0 0 0 1
1 0 0 0 0 1 1 0 1 0 1 1
a.
b.
1 0 1 1
1 1 1 0
1 1 1 1
0 0 0 1
1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1
c.
12. a. 30 c. 90
d.
1 0 1 1
1 1 0 0
1 1 1 1
0 0 1 1
1 0 1 1
0 1 1 0
1 0 1 1
1 1 0 1
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. b. 0 d. 60
13.
If U be the set of all triang triangles les in a plane plane,, and and A is the the set set of of all all trian triangle gless with with at least one angle different from 60 then A’ is :a. All All tria triang ngle less in a plan planee b. Set of all equila equilatera terall trian triangle gless c. Set of of all trian triangle gless except except equil equilate ateral ral trian triangle gle d. None None of the the abo above ve
14
Inte Integ grati ratio on of of Co Cosec(a ec(ax+ x+b) b)Co Cot( t(ax ax+b +b)) is is = ? a. –Cosec(ax+b) b. –Cot(ax+b) c. –[Cosec(ax+b)] / (ax+b) d. –[Cosec(ax+b] / a
15
Sum Sum of the the Seq Seque uenc ncee 15+2 15+24+ 4+33 33+4 +42+ 2+51 51+6 +60+ 0+69 69+7 +78+ 8+87 87+9 +96 6 is
a. 500 c. 550
b. 505 d. 555
16
In a qu quadratic eq equation if if b2 < 4ac the roots are : a. Real b. Equal c. Imaginary d. Unequal
17. 17.
Valu Valuee of Cos Cos1. 1.Co Cos2 s2.C .Cos os3. 3.Co Cos4 s4 . . . . . . . . . . . . . . . . . . . . Cos Cos18 180 0 is a. 0 b. 1 c. 1/√2 d. √3/2
18.
If any any two rows rows or or colum columns ns of a Determ Determina inant nt are are iden identica tical, l, the the Valu Valuee of of the the Determinant becomes a. 1 b. 0 c. No Change d. –1
19. 19.
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 : a. 50.36 b. 50.24 c. 50.45 d. 50.13
20.
In a grou group p of 65 peop people, le, 40 like like Crick Cricket, et, 10 10 like like both both Crick Cricket et & Tenn Tennis. is. How How many of them like only Tennis and not Cricket? a. 25 b. 35 c. 65 d. 40
21.
Do yo you speak En English? a. Is a State tatem ment. ent. b. Is a Decla Declarati rative ve Senten Sentence ce and and Statem Statement. ent. c. Is a Decla Declarati rative ve Senten Sentence ce but but not a State Statemen ment. t. d. None None of the the Abo Above ve..
22.
Differentiation of Cos3x is a. –3Cos2xSinx c. 3Cos2xSinx
e
b. 3Cos 2x d. –3CosxSinx
23.
Simple Interest on Rs. 650 for 8 Months at the rate of 5 paise per rupee per month is a. 65 / 3 b. 260 c. 280 d. 360
24. 24.
For For an A.P. A.P.,, a1,a a1,a2, 2,a3 a3,a ,a4, 4,-- - - - - - - - - -if -if a4 / a7 = 2/3 2/3 the then n a6 a6 / a8 a8 wil willl be : a. 3/2 b. 4/6 c. 5/4 d. 4/5
25.
Value of –15 . 17 . –1-3 . 1-8 is :
D
a. 0 c. –1
b. 1 d. Infinity
26.
A soft softwar waree firm firm prov provide idess the the foll followi owing ng three three char characte acterist ristics ics for each each progr program am 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 Real Real and and Equ Equal al Root Rootss the the valu valuee of of the the Deter Determi mina nant nt : a. D > 0 b. D< 0 c. D != 0 d. D = 0
28. 28.
For For wha whatt val value uess of of ‘a’ ‘a’ doe doess the the Line Linear ar Equ Equat atio ion n: ax + 8y + 6 = 0 & 2x + (a-1)y – 7 = 0 have Unique Solution? a. Valu Values es 4, 17, 17, -4 -4 b. b. Valu Values es betw betwee een n –4 and and 17 17 c. Valu Values es othe otherr than than 4, -4, -4, 17 17 d. None None of the the Abo Above ve
29. 29.
If A = {a, {a, b, c, d} and and R be the the Relat Relatio ion n on A, whos whosee Matr Matrix ix is : then R will be: a. {(a,a),(a,b),(a,c)(a,d),(b,b),(c,c),(d,d)} b. {(a,a),(a,c),(b,b),(b,c),(c,c),(d,d)} c. {(a,a), {(a,a),(a,c (a,c),( ),(b,b b,b),( ),(b,c b,c),( ),(b,d b,d),( ),(c,c c,c),( ),(d,d d,d)} )} d. {(a,a),(a,c),( {(a,a),(a,c),(b,b), b,b),(b,c), (b,c),(b,d) (b,d),(c,c) ,(c,c),(c,d) ,(c,d),(d,d ,(d,d)} )}
30. 30.
Whic Which h ter term m in in the the give given n Seq Seque uenc ncee is is wro wrong ng?? 10, 20, 40, 70, 120, 160 a. 40 b. 120 c. 160 d. 70
31.
A Sum Sum of Rs. 2000 2000 is invest invested ed at at 16% 16% rate of intere interest st per per annu annum. m. What What will will be the Amount after 2 years if the interest is Compounded Semi – annually? a. Rs.2361.20 b. Rs.2163.20 c. Rs.2136.20 c. Rs.2613.20
32.
If A = {a, e, i, o, u} a. a ⊄ A c. a ⊆ A
33.
Integration of e5x
b. a Ε A c. None of the Above
1 0 1 0
0 1 1 1
0 0 1 0
0 0 0 1
a. 5e5x c. e5x / 5
b. 5e4x d. e5x
34.
If the Graph Graph of two Linear Linear Equati Equations ons represe represents nts a Singl Singlee Line Line then then the the Soluti Solution on for the graph is a. Consistent b. Inconsistent c. Unique d. None of the Above
35.
Value of 2 Sin2θ + Cos2θ is = ?, where 45º a. 3 / 2 b. 2 c. 2 / 3 d. 3 / √2
36.
If the the diffe differen rence ce betw between een Simple Simple and Compou Compound nd Intere Interest st on on a Sum of Money Money for for 4 years at 5% per annum is Rs. 150 the Sum will be: a. Rs.9637.52 b. Rs.9763.25 c. Rs.9367.25 d. Rs.9673.52
37.
If A =
5 4 7 6
a.
5 4
7 6
b.
–3 2
c.
3 2
7/2 5/2
d.
3 -7/2 -2 5/2
A-1 will be equal to
7/2 -5/2
38.
Differentiation of tan tan2x w.r.t. cos 2x is: a. tan2xcos2x b. sec4x c. –sec4x d. tan2x/cos2x
39.
Value of (81 / 256)-5/4 is: a. 3 / 2 c. 1024 / 243
40.
Integration of (2x-3)2 a. 4/3x3-6x2+9x b. 4/3x2-6x+9 c. 3/4x3-6x2+9x d. 3/4x3-6x2+9
b. –1024 / 243 d. –3/2
AMITY SCHOOL OF DISTANCE LEARNING Post Box No. 503, Sector 44, Noida 201 303 ASSIGNMENT No. ADL – 22 Subject Name & Code : Business Mathematics Study Centre
:
Enroll No.
:
Date
:
ASSIGNMENT INSTRUCTION a)
Total tal wei weigh ghta tage ge given ven to to th these ese ass assiignm gnment ents is is 30% 30%..
b)
All assignments are to be completed in your own hand
writing. c) d)
All qu questions ar are re required to to be be at attempted. are to be answe nswere red. d. Three Three assignme assignments nts i.e A, B & C are
Assi Assign gnme ment nts s A will will carr carry y Five Five subj subjec ecti tive ve ques questi tion ons s (10 (10 marks). Assignment B will carry three subjective questions wit with a (10 marks) and Assignm gnment C will carry Forty objective type questions (10 marks) e)
All the the three hree assi assign gnm ment ents ar are to to be be com completed eted by d due ue dates ates
(spe (speci cifi fied ed from from time time to time time)) and and mail mailed ed / give given n by hand hand for for evaluation at the ASoDL office Noida / your Study Centre. f)
The eval evalu uated ated ass ssiignm gnment ents can can be col collecte ected d fro from m yo your study tudy
cente centerr / AS ASoD oDL L Offi Office ce afte afterr Six Six week week.. Ther Therea eaft fter er thes these e will will be destroyed at the end of each semester. Signature : Name
:
Date
:
()
Tick mark in front of the assignments submitted
Assignment “A”
Assignment
Assignment
“B”
“C”
