81279 + Interview Questions in Mathematics QA in Mathematics

1.	95. Prove that : ०० 6+0००5९८6-1 _ l+cosA" cotA—cosecA+l sinA
Answer»

Discussion

2.	Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.7.
Answer» Draw a trapezium say abcd and join the diagonals you will obtain two triangle draw two perpendiculars on diagonals from both parallel sidesnow area of quadrilateral(trapezium)=sum of area of both the triangles let a and b be two parallel sides and h be the perpendicularsarea of 1st triangle=1/2 x a x h ....1area of 2nd triangle=1/2 x b xh .........2 sum of 1 and 2 = area of quadrilateral(trapezium)1/2 x a x h +1/2 x b xh= area of trapezium 1/2 x (a+b) x h= area of trapezium (taking out 1/2 as common) thus proved............

2.

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.7.

Answer»

Draw a trapezium say abcd and join the diagonals you will obtain two triangle draw two perpendiculars on diagonals from both parallel sidesnow area of quadrilateral(trapezium)=sum of area of both the triangles let a and b be two parallel sides and h be the perpendicularsarea of 1st triangle=1/2 x a x h ....1area of 2nd triangle=1/2 x b xh .........2 sum of 1 and 2 = area of quadrilateral(trapezium)1/2 x a x h +1/2 x b xh= area of trapezium 1/2 x (a+b) x h= area of trapezium (taking out 1/2 as common)

thus proved............

Discussion

3.	Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.1
Answer» Let ABCD be a parallelogram, and BD be the diagonal forming two triangles ABD and BCD.Let DE be the height of trapezium ABCD.Area of trapezium ABCD=Area of tr. ABD+Area of tr. BCDSo, area of tr. ABD= 1/2×base×height=1/2×AB×DE..(i) Similarly, area of tr. BCD=1/2×DC×DE ..(ii) [Both triangles will have the same height as they lie between the same parallel lines]Now, area of trap.= sum of eq(i) and (ii)So, (1/2×AB×DE) + (1/2×DC×DE)1/2×DE(AB+DC)Hence, proved

3.

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.1

Answer»

Let ABCD be a parallelogram, and BD be the diagonal forming two triangles ABD and BCD.Let DE be the height of trapezium ABCD.Area of trapezium ABCD=Area of tr. ABD+Area of tr. BCDSo, area of tr. ABD= 1/2×base×height=1/2×AB×DE..(i)

Similarly, area of tr. BCD=1/2×DC×DE ..(ii) [Both triangles will have the same height as they lie between the same parallel lines]Now, area of trap.= sum of eq(i) and (ii)So, (1/2×AB×DE) + (1/2×DC×DE)1/2×DE(AB+DC)Hence, proved

Discussion

4.	7. Prove that the area of a trapezium is halfthe sum of the parallel sides multiplied by thedistance between them.
Answer» Let ABCD be a trapezium in which AB\|\|CD.Draw CE⊥ AB and AF⊥ CD (Extended).Let AB = a, CD = b and CE = AF = h.Hencearea of trapezium ABCD = area of triangle ABC + area of triangle ADC= (1/2) ah + (1/2) bh= (1/2) h[a + b] sq units.

Discussion

5.	Jлитипотрессгосту. І пти Чл.12. Find the zeroes of the quadratic polynomial 6x2 – 7 – 11x.13 Show that the saare of any nositive integer is either of the form 22
Answer» x=-b+-√b^2-4ac/2ax=11+-√121+168/12x=11+-√289/12x=11+-17/12x=7/3,-1/2

Discussion

6.	\frac{4}{3} \tan ^{2} 60^{\circ}+3 \cos ^{2} 30^{\circ}-2 \csc ^{2} 60^{\circ}-\frac{3}{4} \cot ^{2} 45^{\circ}
Answer» tan60tan60 = 3 cos30cos30 = 3/4 cosec60cosec60 = 4/3 cot45cot45 = 1 4/3 (3) + 3(3/4) - 2(4/3) - 3/4(1) = 4+9/4-8/3-3/4 = (48+27-32-9)/12 = 34/12 = 17/6

Discussion

7.	Be sin A = L then what is the valueof cosa?
Answer» if sinA=1then the value of COSA=0 sin A = 1sin A = sin 90A= 90therefore, cos A=cos90=0. Considering the period of [0,2π], the value of sinA is 1 only at A=π/2.Hence, A=π/2cosA=cosπ/2=0.

7.

Be sin A = L then what is the valueof cosa?

Answer»

if sinA=1then the value of COSA=0

sin A = 1sin A = sin 90A= 90therefore, cos A=cos90=0.

Considering the period of [0,2π], the value of sinA is 1 only at A=π/2.Hence, A=π/2cosA=cosπ/2=0.

Discussion

8.	हि रह आकर:cosa 5100.यदि वसा = हो, तो सिंद्ध कीजिए किcosfsin®B = l+p? g pi ot
Answer»

Discussion

9.	-260^circcosec^2 %2B 3cos(30^circ)^2 %2B (4/3)tan(60^circ)^2 - 3*cot(45^circ)^2/4
Answer» 4/3 (V3)^2+3(V3/2)^2-2(2/V3)-3/4(1)=4/3(3)+3(3/4)-4/3-3/4=4+9/4-4/3-4/3=10 10 is the correct answer of the given question

9.

-260^circcosec^2 %2B 3cos(30^circ)^2 %2B (4/3)tan(60^circ)^2 - 3*cot(45^circ)^2/4

Answer»

4/3 (V3)^2+3(V3/2)^2-2(2/V3)-3/4(1)=4/3(3)+3(3/4)-4/3-3/4=4+9/4-4/3-4/3=10

10 is the correct answer of the given question

Discussion

10.	(2/3)(-sin(45^circ)^4 %2B cos(30^circ)^4) - 3(sin(60^circ)^2 - sec(45^circ)^2) %2B cot(30^circ)^2/4
Answer» trigonometry values yaad karo aur solve karo 2/3 ((V3/2)^4-(1/V2)4)-((sin^2V3/2)-(2)^2)+1/4(V3)2= 2/3(9/16)-1/4)-(3/4-4)+1/4(3)=3/4-1/4- 3/4-4+3/4=1/4

10.

(2/3)(-sin(45^circ)^4 %2B cos(30^circ)^4) - 3(sin(60^circ)^2 - sec(45^circ)^2) %2B cot(30^circ)^2/4

Answer»

trigonometry values yaad karo aur solve karo

2/3 ((V3/2)^4-(1/V2)4)-((sin^2V3/2)-(2)^2)+1/4(V3)2= 2/3(9/16)-1/4)-(3/4-4)+1/4(3)=3/4-1/4- 3/4-4+3/4=1/4

Discussion

11.	& Find two numbers such that one of them exceeds the other by 8 and their sum is 0
Answer» Oooo thanks not 55 there is 44 please help

11.

& Find two numbers such that one of them exceeds the other by 8 and their sum is 0

Answer»

Oooo thanks

not 55 there is 44

please help

Discussion

12.	892 1७98 छेछा2859छु8 ७6 डी -€पक...: छछल9 3७9७७॥28 'छात्छाठ9छ5 कि : BIRILD\| B8 BBS 1098 © 7 +X¢ = (Vd: pI - DBBI
Answer» p(x)=3x+2p(x)=03x+2=03x=-2x=-2/3

Discussion

13.	.. L .Eﬂ रे वर «८४ T W ये दे झरने ये यर 2 o था. © sy ®acB8 RS e X
Answer» 16854-16800= 54

Discussion

14.	2.Form the greatest and smallest numbers using thefollowing digits:(i) 3,7,0,2,8,9,4 (ii) 5,1,6,3,7,2,9
Answer» que 1ans 9874320que 2ans 9765321 98743200234789 97653211235679 i) G -9874320 S-0234789ii) G-9765321 S-1235679 1.98743202.9765321. 1)greatest number = 98,74,320smallest number = 20,34,7892)greatest number = 97,65,321smallest number = 12,35,679 greatest no - I) 9874320 ii) 9765321smallest no. I) 2034789 ii) 1235679

14.

2.Form the greatest and smallest numbers using thefollowing digits:(i) 3,7,0,2,8,9,4 (ii) 5,1,6,3,7,2,9

Answer»

que 1ans 9874320que 2ans 9765321

98743200234789

97653211235679

i) G -9874320 S-0234789ii) G-9765321 S-1235679

1.98743202.9765321.

1)greatest number = 98,74,320smallest number = 20,34,7892)greatest number = 97,65,321smallest number = 12,35,679

greatest no - I) 9874320 ii) 9765321smallest no. I) 2034789 ii) 1235679

Discussion

15.	-थर्ड नि T S g o Sदि 996 (9) द$५९ 0५६ (प) ki 2GE (B)दररीपरि छिरिटिClbi2 Lbeb] 12% हे— = ४It bk bjeiih % bk B8 D D6 Liphe Ll 16 oके.
Answer»

Discussion

16.	In the given V-T graph, calculate distancetravelled between 4S and 125.→(a) 80 m(b) 60εεεεvelocity(c) 40(0) 20 m24 6 8 10 12time (s)
Answer» distance = time x velocitya) 80m is the correct answer

Discussion

17.	Prove that the area of a trapezium is half the sum of the parallel sides multiplied bydistance between them.7.P. AB8. PORS and ABRS are parllelograms aany point on the side BR. Show that(G) ar(PQRS)- ar(ABRS)(i) ar(AAXS)-ar(PQRS)
Answer» 7. 8. Part 1 8. Part 2

17.

Prove that the area of a trapezium is half the sum of the parallel sides multiplied bydistance between them.7.P. AB8. PORS and ABRS are parllelograms aany point on the side BR. Show that(G) ar(PQRS)- ar(ABRS)(i) ar(AAXS)-ar(PQRS)

Answer»

7.

8. Part 1

8. Part 2

Discussion

18.	कक 20° + Cos” 70°50° — Cot* 4045° tan 53", का मान ज्ञात कीजिए ।A A __&. 4 आता 4 अली472 Cosec? 58° ~2 Cot 58° tan 32° ~ 4 tan 1% an 37° e
Answer»

Discussion

19.	\frac{\sin \alpha \sin 11 \alpha+\sin 3 \alpha \sin 7 \alpha}{\sin \alpha \cos 11 \alpha+\sin 3 \alpha \cos 7 \alpha}=\tan 8 \alpha
Answer» Sin11AsinA+sin7Asin3A/cos11AsinA+cos7Asin3A=2sin11AsinA+2sin7Asin3A/2cos11AsinA+2cos7Asin3A=[{cos(11A-A)-cos(11A+A)}+{cos(7A-3A)-cos(7A+3A)}]/[{sin(11A+A)-sin(11A-A)}+{sin(7A+3A)-sin(7A-3A)}]=(cos10A-cos12A+cos4A-cos10A)/(sin12A-sin10A+sin10A-sin4A)=(cos4A-cos12A)/(sin12A-sin4A)=[2sin(4A+12A)/2sin(12A-4A)/2]/[2cos(12A+4A)/2sin(12A-4A)/2]=sin8Asin4A/cos8Asin4A=sin8A/cos8A=tan8A (Proved)

Discussion

20.	18. The sum of five consecutive numbers is 190, What is thesum of the largest and the smallest numbers?(1) 75(4) 73(2) 77(5) of these(3) 76ito nositive integers is 462.
Answer» Let the five consecutive numbers are x-2,x-1,x,x+ 1,x+ 2. Sum of numbers = 190 Therefore, x - 2 + x - 1 + x + x + 1 + x + 2 = 190 = 5x = 190 Therefore, x = 38 Sum of largest and smallest numbers = 190 x+2+x-2= 2x= 2*38= 76Answer = 76Please like the solution 👍 ✔️

20.

18. The sum of five consecutive numbers is 190, What is thesum of the largest and the smallest numbers?(1) 75(4) 73(2) 77(5) of these(3) 76ito nositive integers is 462.

Answer»

Let the five consecutive numbers are x-2,x-1,x,x+ 1,x+ 2.

Sum of numbers = 190

Therefore, x - 2 + x - 1 + x + x + 1 + x + 2 = 190

= 5x = 190

Therefore, x = 38

Sum of largest and smallest numbers = 190

x+2+x-2= 2x= 2*38= 76Answer = 76Please like the solution 👍 ✔️

Discussion

21.	) छा 25०: :68 65० + ge 280 Sin 65 T elकीफिए \|
Answer» Sin( a+b)= sinacosb+cosa-sinaa= 25b= 65sin(65+25)= sin90° = 1

Discussion

22.	\frac { \tan ^ { 3 } \alpha } { 1 + \tan ^ { 2 } \alpha } + \frac { \cot ^ { 3 } \alpha } { 1 + \cot ^ { 2 } \alpha } = \sec \alpha \csc ( \alpha - 2 \sin \alpha \cos a
Answer» 1

Discussion

23.	(2/3)(58^circcosec^2) - 2tan(32^circ)cot(58^circ)/3 - 5tan(13^circ)tan(37^circ)/3
Answer» {2/3 cosec^2 (58)} - {2/3 (cot 58)( tan 32)} - {5/3 (tan 13)( tan 37 )( tan 45 )( tan 53 )( tan 77)}] Using: tan x = cot (90 - x) ={[2/3 cosec^2 58} -{2/3 cot^2 58} - {5/3 (tan 13 tan 37 tan 45 cot 37 cot 13}] =2/3(cosec^2 58 - cot^2 58) - 5/3 [since, tan 45 = 1] =2/3 -5/3 [Using cosec^2 x - cot^2 x = 1] = -1

23.

(2/3)(58^circcosec^2) - 2tan(32^circ)cot(58^circ)/3 - 5tan(13^circ)tan(37^circ)/3

Answer»

{2/3 cosec^2 (58)} - {2/3 (cot 58)( tan 32)} - {5/3 (tan 13)( tan 37 )( tan 45 )( tan 53 )( tan 77)}] Using: tan x = cot (90 - x)

={[2/3 cosec^2 58} -{2/3 cot^2 58} - {5/3 (tan 13 tan 37 tan 45 cot 37 cot 13}] =2/3(cosec^2 58 - cot^2 58) - 5/3 [since, tan 45 = 1] =2/3 -5/3 [Using cosec^2 x - cot^2 x = 1] = -1

Discussion

24.	\left[\frac{1-\sin \alpha}{\cos \alpha}+\frac{\cos \alpha}{1+\sin \alpha}\right]\left[\sec \alpha+\frac{1}{\cot \alpha}\right] is
Answer»

Discussion

25.	2. Find five rational numbers between 1 and 2.
Answer» =1/1×6/6=6/6and=2/1×6/6=12/6five rational numbers 7/6 8/6 9/6 10/6 11/6 1×6/6=6,2*6/6=12,,6/6and12/6,6/6,6/7,6/8,6/9,6/10,6/11,6/12

25.

2. Find five rational numbers between 1 and 2.

Answer»

=1/1×6/6=6/6and=2/1×6/6=12/6five rational numbers 7/6 8/6 9/6 10/6 11/6

1×6/6=6,2*6/6=12,,6/6and12/6,6/6,6/7,6/8,6/9,6/10,6/11,6/12

Discussion

26.	2. Find five rational numbers between 1 and 2
Answer»

Discussion

27.	Find five rational numbers between and 2.
Answer» L.C.M of 3/5and 2/3 is 15 3/5=3×3/5×3=9/15 ,2/3=2×5/3×5=10/15 so we will multiple ×6 of both 9/15 and 10/15 =54/90 and 60/90 so the five rational number is55/90,56/90,57/90,58/90 and 59/90

Discussion

28.	2. Find five rational numbers betweenand
Answer» -25/35 and 13/53-10/15 and ,3/15-9/15,-8/15,-7/15,-6/15,-5/15

Discussion

29.	If $\tan \theta=\frac{\cos \alpha-\sin \alpha}{\cos \alpha+\sin \alpha}$ and $\theta^{\prime}$ is acute then $\theta+\alpha=$
Answer»

Discussion

30.	\frac { \operatorname { cos } ^ { 3 } \alpha - \operatorname { cos } 3 \alpha } { \operatorname { cos } \alpha } + \frac { \operatorname { sin } ^ { 3 } \alpha + \operatorname { sin } 3 \alpha } { \operatorname { sin } \alpha } = 3
Answer»

Discussion

31.	\| e :S= (Jâ58)x2(l6) #
Answer» [(8)^1/5]^5/2 * (16)^-3/2= (8)^[1/2](4)[2 -3/2]= (2)^3/2*(4)^-3= (2)^[3/2 + 6]= (2)^[15/2]

Discussion

32.	Express each of the following as a Roman numeral : a2 b8 c14 d29 e36 f43 g54 h61 i99 j105 k114
Answer» a ll ,b viii,c xiv ,d xxix, e xxxvi, f XLlll ,g LlV ,h LXl, i XClX ,j CV,k CXIV

Discussion

33.	IVa)b)c)d)Who am I? Write in Roman numeralI am 5 more than 5I am 7 less than 9I am thrice of 3I am half of 6
Answer» 52153is the answer of the following 52153these are the answers a) 5b) 2c) 15d) 3 is the answer of the following 52153Are correct answer to that question. a)x b)ii c)ix d)iii. 10=x2= II15=xIV3= IIIthese are the answer 10=x2=ii15=xv3 = ¡¡¡ ,these are the ans 10=x2=ii15=xv3=iiiis the correct answer

33.

IVa)b)c)d)Who am I? Write in Roman numeralI am 5 more than 5I am 7 less than 9I am thrice of 3I am half of 6

Answer»

52153is the answer of the following

52153these are the answers

a) 5b) 2c) 15d) 3 is the answer of the following

52153Are correct answer to that question.

a)x b)ii c)ix d)iii.

10=x2= II15=xIV3= IIIthese are the answer

10=x2=ii15=xv3 = ¡¡¡ ,these are the ans

10=x2=ii15=xv3=iiiis the correct answer

Discussion

34.	\frac{\sin ^{2} 20+\sin ^{2} 70}{\sec ^{2} 50-\cot ^{2} 40}+2 \csc ^{2} 58-2 \cot 58 \tan 32-4 \tan 13 \tan 37 \tan 45 \tan 53 \tan 77
Answer» page 1. page 2.

34.

\frac{\sin ^{2} 20+\sin ^{2} 70}{\sec ^{2} 50-\cot ^{2} 40}+2 \csc ^{2} 58-2 \cot 58 \tan 32-4 \tan 13 \tan 37 \tan 45 \tan 53 \tan 77

Answer»

page 1.

page 2.

Discussion

35.	e tan A tan B+ cot BA - cot Be the follotwnte2001111 58
Answer»

Discussion

36.	13, 14, 18, 27, 43,(e) 4s(m) 58(E) 65() 68
Answer» 13+1² = 14 14+2² = 18 18+3² = 27 27+4² = 43 43+5² = 68

36.

13, 14, 18, 27, 43,(e) 4s(m) 58(E) 65() 68

Answer»

13+1² = 14

14+2² = 18

18+3² = 27

27+4² = 43

43+5² = 68

Discussion

37.	1(A)xerciseWrite the numeral for each of the following numbers:(a) Five thousand six hundred two.
Answer» a) five thousand six hundred two-----5602

37.

1(A)xerciseWrite the numeral for each of the following numbers:(a) Five thousand six hundred two.

Answer»

a) five thousand six hundred two-----5602

Discussion

38.	थम sin6- olv ] ७2: 8 + (जाति S0l
Answer» Given Exp. = √(1+sin x)/√(1-sin x) × √(1+sin x) /√(1+sin x) = (1+ sin x )/√(1-sin²x) = (1+ sin x )/cos x = ( 1/cos x +sin x/cos x ) = ( sec x + tan x ) Like my answer if you find it useful!

38.

थम sin6- olv ] ७2: 8 + (जाति S0l

Answer»

Given Exp.

= √(1+sin x)/√(1-sin x) × √(1+sin x) /√(1+sin x)

= (1+ sin x )/√(1-sin²x) = (1+ sin x )/cos x

= ( 1/cos x +sin x/cos x ) = ( sec x + tan x )

Like my answer if you find it useful!

Discussion

39.	Find five rational numbers betweenalwandin
Answer» 19/30,20/30,21/30,22/30,23/30,24/30 five rational in between 3/5 and 4/53/5=3×10/5×104/5=4×10/5×1030/50and40/50 five rational number are30/50,31/50,32,50,33/50,34/50,35/50

39.

Find five rational numbers betweenalwandin

Answer»

19/30,20/30,21/30,22/30,23/30,24/30

five rational in between 3/5 and 4/53/5=3×10/5×104/5=4×10/5×1030/50and40/50 five rational number are30/50,31/50,32,50,33/50,34/50,35/50

Discussion

40.	2PINU SI TULUM36 Find five rational numbers betweenalwand
Answer»

Discussion

41.	Define Alpha Numeral
Answer» Alphanumeric is a term encompassing all the letters in a given language set as well as the numerals. Alphanumericis a combination of alphabetic and numeric characters, and is used to describe the collection of Latin letters and Arabic digits or a text constructed from the collection.

41.

Define Alpha Numeral

Answer»

Alphanumeric is a term encompassing all the letters in a given language set as well as the numerals.

Alphanumericis a combination of alphabetic and numeric characters, and is used to describe the collection of Latin letters and Arabic digits or a text constructed from the collection.

Discussion

42.	01. Write each of the following in numeral form:a) Seven million, four thousand, eighty nine.
Answer» 704089 is the right answer 7004089 is the best answer 7004089 is the right answer. 7004089 is the right answer... 7004089isthe right answer 7004089 is the right answer 70,04089 is the right answer 7004089is the correct answer 7004089 is the answer.... 7,004,089is your answer 7004089 is the correct answer 7004089 is the correct answer of the given question 704089 is the best answer for me 7004089 is the correct answer

42.

01. Write each of the following in numeral form:a) Seven million, four thousand, eighty nine.

Answer»

704089 is the right answer

7004089 is the best answer

7004089 is the right answer.

7004089 is the right answer...

7004089isthe right answer

7004089 is the right answer

70,04089 is the right answer

7004089is the correct answer

7004089 is the answer....

7,004,089is your answer

7004089 is the correct answer

7004089 is the correct answer of the given question

704089 is the best answer for me

7004089 is the correct answer

Discussion

43.	The Ganga is two thousand fivehundred ten km long. Write thenumeral.
Answer» In numerals, it is 2510 km.

Discussion

44.	A dealer lists his goods at 20% above cost price and allows a discount of 10%. His gainper cent is1.(a)10%(b) 9%(c) 8%(d) 12%
Answer»

Discussion

45.	12. A vendor bought a toffee at 6 for a rupee. How many for a rupee must he sell to gain 20%
Answer»

Discussion

46.	On which Roman numeral will the minute hand be at quarter totwelve?(2) XI(4) IX
Answer» thnx

Discussion

47.	4. 100 families with 2 children the following data were recorded:Number of girls in family 2Number of familiesCompute the probability of a family, having (1) two girls(2)one girl (3) No girl.012 808
Answer» total families=12+80+8=100probability of 2 girls=12/100=0.12probability of 1 girl=80/100=0.8probability of no girl=8/100=0.08

Discussion

48.	Retewas born in August.lil8 the probability that a student of thessed simultaneously 200 times with the following frequencies ofThree coins aredifferent outcomes:simultaneoOutcome3 heads 2 heads 1 head No headFrequency237228e coins are simultaneously tossed again, compute the probability of 2 headsIf the threecoming up.lected 2400 families at random and surveved them to determine a
Answer»

Discussion

49.	1-Write decimal numeral for each of the following.A-Five hundred two and thirty eight hundredths
Answer» 1.502 is for five hundred two 2.3800 is for thirty eight hundred

49.

1-Write decimal numeral for each of the following.A-Five hundred two and thirty eight hundredths

Answer»

1.502 is for five hundred two

2.3800 is for thirty eight hundred

Discussion

50.	Write the Roman numeral for each of the following(a) 16(b) 20e 58(1) 95
Answer» 16=X+VI=XVI20=X+X=XX58=L+VIII=LVIII95=XC+V=XCV

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

95. Prove that : ०० 6+0००5९८6-1 _ l+cosA" cotA—cosecA+l sinA

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.7.

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.1

7. Prove that the area of a trapezium is halfthe sum of the parallel sides multiplied by thedistance between them.

Jлитипотрессгосту. І пти Чл.12. Find the zeroes of the quadratic polynomial 6x2 – 7 – 11x.13 Show that the saare of any nositive integer is either of the form 22

\frac{4}{3} \tan ^{2} 60^{\circ}+3 \cos ^{2} 30^{\circ}-2 \csc ^{2} 60^{\circ}-\frac{3}{4} \cot ^{2} 45^{\circ}

Be sin A = L then what is the valueof cosa?

हि रह आकर:cosa 5100.यदि वसा = हो, तो सिंद्ध कीजिए किcosfsin®B = l+p? g pi ot

-2*60^circ*cosec^2 %2B 3*cos(30^circ)^2 %2B (4/3)*tan(60^circ)^2 - 3*cot(45^circ)^2/4

(2/3)*(-sin(45^circ)^4 %2B cos(30^circ)^4) - 3*(sin(60^circ)^2 - sec(45^circ)^2) %2B cot(30^circ)^2/4

&amp; Find two numbers such that one of them exceeds the other by 8 and their sum is 0

892 1७98 छेछा2859छु8 ७6 डी -€पक...: छछल9 3७9७७॥28 'छात्छाठ9छ5 कि : BIRILD| B8 BBS 1098 © 7 +X¢ = (Vd: pI - DBBI

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2.Form the greatest and smallest numbers using thefollowing digits:(i) 3,7,0,2,8,9,4 (ii) 5,1,6,3,7,2,9

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In the given V-T graph, calculate distancetravelled between 4S and 125.→(a) 80 m(b) 60εεεεvelocity(c) 40(0) 20 m24 6 8 10 12time (s)

Prove that the area of a trapezium is half the sum of the parallel sides multiplied bydistance between them.7.P. AB8. PORS and ABRS are parllelograms aany point on the side BR. Show that(G) ar(PQRS)- ar(ABRS)(i) ar(AAXS)-ar(PQRS)

कक 20° + Cos” 70°50° — Cot* 4045° tan 53", का मान ज्ञात कीजिए ।A A __&amp;. 4 आता 4 अली472 Cosec? 58° ~2 Cot 58° tan 32° ~ 4 tan 1% an 37° e

\frac{\sin \alpha \sin 11 \alpha+\sin 3 \alpha \sin 7 \alpha}{\sin \alpha \cos 11 \alpha+\sin 3 \alpha \cos 7 \alpha}=\tan 8 \alpha

18. The sum of five consecutive numbers is 190, What is thesum of the largest and the smallest numbers?(1) 75(4) 73(2) 77(5) of these(3) 76ito nositive integers is 462.

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\frac { \tan ^ { 3 } \alpha } { 1 + \tan ^ { 2 } \alpha } + \frac { \cot ^ { 3 } \alpha } { 1 + \cot ^ { 2 } \alpha } = \sec \alpha \csc ( \alpha - 2 \sin \alpha \cos a

(2/3)*(58^circ*cosec^2) - 2*tan(32^circ)*cot(58^circ)/3 - 5*tan(13^circ)*tan(37^circ)/3

\left[\frac{1-\sin \alpha}{\cos \alpha}+\frac{\cos \alpha}{1+\sin \alpha}\right]\left[\sec \alpha+\frac{1}{\cot \alpha}\right] is

2. Find five rational numbers between 1 and 2.

2. Find five rational numbers between 1 and 2

Find five rational numbers between and 2.

2. Find five rational numbers betweenand

If $\tan \theta=\frac{\cos \alpha-\sin \alpha}{\cos \alpha+\sin \alpha}$ and $\theta^{\prime}$ is acute then $\theta+\alpha=$

\frac { \operatorname { cos } ^ { 3 } \alpha - \operatorname { cos } 3 \alpha } { \operatorname { cos } \alpha } + \frac { \operatorname { sin } ^ { 3 } \alpha + \operatorname { sin } 3 \alpha } { \operatorname { sin } \alpha } = 3

| e :S= (Jâ58)x2(l6) #

Express each of the following as a Roman numeral : a2 b8 c14 d29 e36 f43 g54 h61 i99 j105 k114

IVa)b)c)d)Who am I? Write in Roman numeralI am 5 more than 5I am 7 less than 9I am thrice of 3I am half of 6

\frac{\sin ^{2} 20+\sin ^{2} 70}{\sec ^{2} 50-\cot ^{2} 40}+2 \csc ^{2} 58-2 \cot 58 \tan 32-4 \tan 13 \tan 37 \tan 45 \tan 53 \tan 77

e tan A tan B+ cot BA - cot Be the follotwnte2001111 58

13, 14, 18, 27, 43,(e) 4s(m) 58(E) 65() 68

1(A)xerciseWrite the numeral for each of the following numbers:(a) Five thousand six hundred two.

थम sin6- olv ] ७2: 8 + (जाति S0l

Find five rational numbers betweenalwandin

2PINU SI TULUM36 Find five rational numbers betweenalwand

Define Alpha Numeral

01. Write each of the following in numeral form:a) Seven million, four thousand, eighty nine.

The Ganga is two thousand fivehundred ten km long. Write thenumeral.

A dealer lists his goods at 20% above cost price and allows a discount of 10%. His gainper cent is1.(a)10%(b) 9%(c) 8%(d) 12%

12. A vendor bought a toffee at 6 for a rupee. How many for a rupee must he sell to gain 20%

On which Roman numeral will the minute hand be at quarter totwelve?(2) XI(4) IX

4. 100 families with 2 children the following data were recorded:Number of girls in family 2Number of familiesCompute the probability of a family, having (1) two girls(2)one girl (3) No girl.012 808

1-Write decimal numeral for each of the following.A-Five hundred two and thirty eight hundredths

Write the Roman numeral for each of the following(a) 16(b) 20e 58(1) 95

-260^circcosec^2 %2B 3cos(30^circ)^2 %2B (4/3)tan(60^circ)^2 - 3*cot(45^circ)^2/4

(2/3)(-sin(45^circ)^4 %2B cos(30^circ)^4) - 3(sin(60^circ)^2 - sec(45^circ)^2) %2B cot(30^circ)^2/4

& Find two numbers such that one of them exceeds the other by 8 and their sum is 0

कक 20° + Cos” 70°50° — Cot* 4045° tan 53", का मान ज्ञात कीजिए ।A A __&. 4 आता 4 अली472 Cosec? 58° ~2 Cot 58° tan 32° ~ 4 tan 1% an 37° e

(2/3)(58^circcosec^2) - 2tan(32^circ)cot(58^circ)/3 - 5tan(13^circ)tan(37^circ)/3

| e :S= (Jâ58)x2(l6) #