81279 + Interview Questions in Mathematics QA in Mathematics

1.	(81x^4 %2B 2)/(3x - 1)
Answer»

Discussion

2.	1+\frac{1}{(1+2)}+\frac{1}{(1+2+3)}+\ldots+\frac{1}{(1+2+3+\ldots+n)}=\frac{2 n}{(n+1)}
Answer»

Discussion

3.	1 + \frac { 1 } { ( 1 + 2 ) } + \frac { 1 } { ( 1 + 2 + 3 ) } + \ldots + \frac { 1 } { ( 1 + 2 + 3 + \ldots n ) } = \frac { 2 n } { ( n + 1 ) }
Answer»

Discussion

4.	If 36:81:: X:63, find the value of x.
Answer» 36 : 81 : : x : 63 ; 36 x 63 = 81 x X; =36 x 63 =81 x;, x= 2 2 6 8 / 81 = 2 8 x=18 is the correct answer 31×63=81X31×63/81=217/9so 217/9 is the answer

4.

If 36:81:: X:63, find the value of x.

Answer»

36 : 81 : : x : 63 ; 36 x 63 = 81 x X; =36 x 63 =81 x;, x= 2 2 6 8 / 81 = 2 8

x=18 is the correct answer

31×63=81X31×63/81=217/9so 217/9 is the answer

Discussion

5.	( 81 x ^ 4 %2B 2 ) \div ( 3 x - 1 )
Answer»

Discussion

6.	3 ^ 2 67 ^ \circ - \sin ^ 2 23 ^ \circ )
Answer» Cosθ=sin(90-θ)cos²θ=sin²(90-θ)cos²67=sin²(90-67)cos²67=sin²23cos²67-sin²23=0

Discussion

7.	^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?
Answer» Cos^267°- Sin^223°, So = Cos^267°- Sin^2( 90°- 67°) , = Cos^267°- Cos^267°, [ We know : Sin ( 90°- a ) = Cos a ] = 0

7.

^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?

Answer»

Cos^267°- Sin^223°, So

= Cos^267°- Sin^2( 90°- 67°) ,

= Cos^267°- Cos^267°, [ We know : Sin ( 90°- a ) = Cos a ]

= 0

Discussion

8.	SECTIONWhat is the value of cos 67Sin 2
Answer» cos^2 67 - sin^2 23 = cos^2 67 - (cos^2 (90-23)) = cos^2 67 - cos^2 67 = 0 cos² 67°-sin ²23°=cos² 67°-sin² (90°-67°)since cos(90°-A)=sin Acos² 67°-sin ²23°=cos ²67°-cos ²67°=0

8.

SECTIONWhat is the value of cos 67Sin 2

Answer»

cos^2 67 - sin^2 23

= cos^2 67 - (cos^2 (90-23))

= cos^2 67 - cos^2 67

= 0

cos² 67°-sin ²23°=cos² 67°-sin² (90°-67°)since cos(90°-A)=sin Acos² 67°-sin ²23°=cos ²67°-cos ²67°=0

Discussion

9.	\left(\cos ^{2} 67^{\circ}-\sin ^{2} 23^{\circ}\right) ?
Answer» Good

Discussion

10.	f ( \operatorname { cos } ^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?
Answer» thanks but how 63 came ohh...l understand

10.

f ( \operatorname { cos } ^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?

Answer»

thanks

but how 63 came

ohh...l understand

Discussion

11.	What is the value of (cos^2 67 - sin^2 23) ?
Answer» cos² (67°) - sin²(23°)cos²(90° - 23°) - sin²(23°)sin²(23°) - sin²(23°)0

Discussion

12.	23. sin 10째 sin 30째 sin 50째 sin 70째-16
Answer» We have sinxsin(60 – x)sin(60 + x) = 1/4* sin3x sin10sin30sin50sin70 =1/2sin10sin(60 – 10)sin(60 + 10) =1/21/4sin(310) =1/21/4*1/2 =1/16

12.

23. sin 10째 sin 30째 sin 50째 sin 70째-16

Answer»

We have sinx*sin(60 – x)*sin(60 + x) = 1/4* sin3x

sin10*sin30*sin50*sin70

=1/2*sin10*sin(60 – 10)*sin(60 + 10)

=1/2*1/4*sin(3*10)

=1/2*1/4*1/2

=1/16

Discussion

13.	If A is a set with n(A) = m then write the number of elements of P(A).
Answer» tq bro

Discussion

14.	The value of log /3) 81 is equal to:
Answer» compare with log of a with the base b.a=81b=-1/3a=b^y81=-1/3^yy=-4 answer is 4

14.

The value of log /3) 81 is equal to:

Answer»

compare with log of a with the base b.a=81b=-1/3a=b^y81=-1/3^yy=-4

answer is 4

Discussion

15.	The linear equation y = 2x + 3 cuts the y-axis at the point0(D) 202
Answer» it is (0,3) cuts y axis means it's x coordinate =0substitute in equation

Discussion

16.	5 Slope of a line which cuts intercepts of equal lengths on the axes is4)1)-12) 03) 2
Answer»

Discussion

17.	(11) Find the equation of the circle whose centre is(3,-2) and which cuts off an intercept of length6on the line 4x-3y + 2 0.
Answer» tnx oc 29 kese aaya kuch bhi question dusra pucha or answer kuch aur, nhi aata toh nhi dene ga

17.

(11) Find the equation of the circle whose centre is(3,-2) and which cuts off an intercept of length6on the line 4x-3y + 2 0.

Answer»

tnx

oc 29 kese aaya

kuch bhi question dusra pucha or answer kuch aur, nhi aata toh nhi dene ga

Discussion

18.	(c (1o)316 4817.is equal to(b)äş2727
Answer» Answer:d)27/8Explanation:

Discussion

19.	5 Slope of a line which cuts intercepts of equal lengths on the axes is1)-12) 03) 2
Answer» Equation of a straight line in intercept form isx/a +y/b =1whereaandbarex- interceptandy-interceptrespectively. Now intercepts are of equal length. Soa=b Putting these values in equation we getx/a +y/a =1 =>x + y = a Comparing it with general equation of liney = mx + c(where m is slope of line ), We getm=-1 Thus slope of line cutting intercepts of equal length on axis is-1. Hence, option (1) is correct.

19.

5 Slope of a line which cuts intercepts of equal lengths on the axes is1)-12) 03) 2

Answer»

Equation of a straight line in intercept form isx/a +y/b =1whereaandbarex- interceptandy-interceptrespectively.

Now intercepts are of equal length. Soa=b

Putting these values in equation we getx/a +y/a =1

=>x + y = a

Comparing it with general equation of liney = mx + c(where m is slope of line ),

We getm=-1

Thus slope of line cutting intercepts of equal length on axis is-1.

Hence, option (1) is correct.

Discussion

20.	a23. (81)*** x(9)" * (27) + (243)") is equal toP 9()
Answer» the correct answer is81

Discussion

21.	(D) of theseπ and2If 081 sm2 x + 81 cos,30, then x is equal to :x(A) π or--(B) or 04(B) 플 or 0(C)ππ-or-(D) of these
Answer»

Discussion

22.	Using Venn diagrams, representi) (AUB), İİ) A'UB' İİİ) A''-)B iv) AaB.1V
Answer» X={5,6,7,}and Y={5,7,9,10}

Discussion

23.	5.What is the value of (cos 67 -sin 23°)?
Answer» Value of (cos^2 67 - sin^2 23) We knowsin x = cos(90 - x) Then we get, (cos^2 67 - sin^2 23)= (cos^2 67 - cos^2 (90 - 23)= (cos^2 67 - cos^2 67)= 0

23.

5.What is the value of (cos 67 -sin 23°)?

Answer»

Value of (cos^2 67 - sin^2 23)

We knowsin x = cos(90 - x)

Then we get, (cos^2 67 - sin^2 23)= (cos^2 67 - cos^2 (90 - 23)= (cos^2 67 - cos^2 67)= 0

Discussion

24.	Represent the following with Venndiagrams:2+2(i) Bc A and An B -B(i) An (BU C)
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Discussion

25.	Find the value of cos²67- sin²23
Answer»

Discussion

26.	What is the value of (cos 67-sin 23
Answer» cos^2 67° - sin^2 23°= cos^2 67° - cos^2 (90-23)= cos^2 67° - cos^2 67°= 0

Discussion

27.	What is the value of (cos²67°-sin²23°)?
Answer» GIVEN : cos²67° - sin²23°cos²(90° - 23°) - sin²23°sin²23° - sin²23° = 0[cos(90 - A) = sinA]Hence, the value of cos²67° - sin²23° is 0 (zero).

Discussion

28.	5. What is the value of (cos 67 -sin 23)?
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Discussion

29.	What is the value of (cos 67-sin2 23)
Answer»

Discussion

30.	2) Study the sets P, Q & Rgiven by Venn diagrams.() Write P n(ii) write Q u Ra b
Answer» intersection of P Q R=kQ U R=f,g,h,j,k

Discussion

31.	8. Suppose we randomly select two workers from a company and observe whetherthe worker selected each time is a man or a woman. Write all the outcomes forthis experiment. Draw the Venn and tree diagrams for this experiment.
Answer»

Discussion

32.	osthe difference of an integer a and C-W.Lind the traliee of a
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Discussion

33.	A tangent to the parabola x2 +4ay= 0 cuts the parabola x2= 4by at A and B the locus of the mid point of AB is:(a)(a+2 b) x^{2}=4 b^{2} y \quad(b)(b+2 a) x^{2}=4 b^{2} y$(\mathrm{c})(\mathrm{a}+2 \mathrm{b}) \mathrm{y}^{2}=4 \mathrm{b}^{2} \mathrm{x} \quad$ (d) $(\mathrm{b}+2 \mathrm{x}) \mathrm{x}^{2}=4 \mathrm{a}^{2} \mathrm{y}$
Answer»

Discussion

34.	\frac { \operatorname { sin } ( 4 A - 2 B ) + \operatorname { sin } ( 4 B - 2 A ) } { \operatorname { cos } ( 4 A - 2 B ) + \operatorname { cos } ( 4 B - 2 A ) } = \operatorname { tan } ( A + B )
Answer» L.H.S.=(2sin(A+B)cos(3A-3B))/(2cos(A+B)cos(3A-3B)) =sin(A+B)/cos(A+B) =tan(A+B) =R.H.S.Hence Proved

Discussion

35.	-12a^2b^2 %2B a^2(b^2x^2) - x(-3a^4 %2B 4*b^2)=0
Answer» a^2b^2x^2-4xb^2+3xa^2-12a^2b^2

Discussion

36.	B 9. In parallelogram ABCD, two points Pand Q areBQtaken on diagonal BD such that DP(see Fig. 8.20). Show that:(i) AP CQ(iii) Δ AQBe ΔCPD(iv) AQ-CP(v) APCQ is a parallelogramFig. 8.20
Answer»

Discussion

37.	2 a ^ 2 b ^ 2 %2B 2 b ^ 2 c ^ 2 \pm 2 c ^ 2 a ^ 2 - a ^ 4 - b ^ 4 - c ^ 4
Answer»

Discussion

38.	\begin{array}{c}{\text { 13. Factorise the following using suitable identity: }} \\ {\text { (i) } \quad a^{4}+a b^{3}} \\ {\text { (ii) } a^{4}+b^{4}+c^{4}+2 a^{2} b^{2}+2 b^{2} c^{2}+2 c^{2} a^{2}}\end{array}
Answer»

Discussion

39.	3. Draw a circle of radius 3 cm. Take two points Pand Q on one of its extended diametereach at a distance of 7 cm from its centre. Draw tangents to the circle from these twopoints P and Q
Answer» thankyou

Discussion

40.	9.n paratlelogram AcD, two points Pand Q avetaken en disgonai DD sueh that De- nooe Pig 820) Show that()AP-CO(Gi) A AQB CrDv) AQ CP1) APCOIs a parallelogram
Answer» Kindly post a clear picture.

Discussion

41.	parallelagrans ABCD, two points Pand Q amtaken on diagonal BD sach that DP . B0
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Discussion

42.	Pand Q are any two points lying on the sides DC andAD respectively of a parallelogramABCD. Show that ar (APB) ar (BQC)..
Answer»

Discussion

43.	3.Pand Q are any two points lying on the sides DC and AD respectively of a parallelograrABCD. Show that ar (APB)-ar (BQC).
Answer»

Discussion

44.	3. Pand Q are any two points lying on the sides DC and AD respectively of a parallelogramABCD. Show that ar (APB) = ar (BOC).
Answer»

Discussion

45.	tle of (os 67 -sin2 23)7de value of (cos 67 sin 23
Answer» cos²67-sin²23sin²23-sin²230

Discussion

46.	locusExamine the continuty of Po) - Yaexempor 240o por 2-o, at) Discuss continuity ofPa) = sing ip atode Os tenie doIP FO) - g2-2012 when 2+2Kt2when 12
Answer» questions are not seen properly please ask questions proper ask only one question on 1

46.

locusExamine the continuty of Po) - Yaexempor 240o por 2-o, at) Discuss continuity ofPa) = sing ip atode Os tenie doIP FO) - g2-2012 when 2+2Kt2when 12

Answer»

questions are not seen properly

please ask questions proper

ask only one question on 1

Discussion

47.	Os) Find brasil de loss percent it cost price isR8 400 and selling price is R8520
Answer»

Discussion

48.	in years was 48.Ts it possible to design a rectangular park of perimeter 80 m and areaits length and breadth.
Answer»

Discussion

49.	6. If cOS A, find the value of 4+4 tan A.
Answer» Like if you find it useful

Discussion

50.	A wall of length 20 m was to be built across an open ground. The height of the9 m and the thickness of the wall is 24 cm. If this wall is to be built up withwhose dimensions are 18 cm x 10 cm x 6 cm, how many bricks would be remd. The height of the wall isbuilt up with brickscks would be required?
Answer» Answer hai Bhai eska 40,000

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

(81*x^4 %2B 2)/(3*x - 1)

1+\frac{1}{(1+2)}+\frac{1}{(1+2+3)}+\ldots+\frac{1}{(1+2+3+\ldots+n)}=\frac{2 n}{(n+1)}

1 + \frac { 1 } { ( 1 + 2 ) } + \frac { 1 } { ( 1 + 2 + 3 ) } + \ldots + \frac { 1 } { ( 1 + 2 + 3 + \ldots n ) } = \frac { 2 n } { ( n + 1 ) }

If 36:81:: X:63, find the value of x.

( 81 x ^ 4 %2B 2 ) \div ( 3 x - 1 )

3 ^ 2 67 ^ \circ - \sin ^ 2 23 ^ \circ )

^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?

SECTIONWhat is the value of cos 67Sin 2

\left(\cos ^{2} 67^{\circ}-\sin ^{2} 23^{\circ}\right) ?

f ( \operatorname { cos } ^ { 2 } 67 ^ { \circ } - \operatorname { sin } ^ { 2 } 23 ^ { \circ } ) ?

What is the value of (cos^2 67 - sin^2 23) ?

23. sin 10째 sin 30째 sin 50째 sin 70째-16

If A is a set with n(A) = m then write the number of elements of P(A).

The value of log /3) 81 is equal to:

The linear equation y = 2x + 3 cuts the y-axis at the point0(D) 202

5 Slope of a line which cuts intercepts of equal lengths on the axes is4)1)-12) 03) 2

(11) Find the equation of the circle whose centre is(3,-2) and which cuts off an intercept of length6on the line 4x-3y + 2 0.

(c (1o)316 4817.is equal to(b)äş2727

5 Slope of a line which cuts intercepts of equal lengths on the axes is1)-12) 03) 2

a23. (81)*** x(9)" * (27) + (243)") is equal toP 9()

(D) of theseπ and2If 081 sm2 x + 81 cos,30, then x is equal to :x(A) π or--(B) or 04(B) 플 or 0(C)ππ-or-(D) of these

Using Venn diagrams, representi) (AUB), İİ) A'UB' İİİ) A''-)B iv) AaB.1V

5.What is the value of (cos 67 -sin 23°)?

Represent the following with Venndiagrams:2+2(i) Bc A and An B -B(i) An (BU C)

Find the value of cos²67- sin²23

What is the value of (cos 67-sin 23

What is the value of (cos²67°-sin²23°)?

5. What is the value of (cos 67 -sin 23)?

What is the value of (cos 67-sin2 23)

2) Study the sets P, Q &amp; Rgiven by Venn diagrams.() Write P n(ii) write Q u Ra b

8. Suppose we randomly select two workers from a company and observe whetherthe worker selected each time is a man or a woman. Write all the outcomes forthis experiment. Draw the Venn and tree diagrams for this experiment.

osthe difference of an integer a and C-W.Lind the traliee of a

\frac { \operatorname { sin } ( 4 A - 2 B ) + \operatorname { sin } ( 4 B - 2 A ) } { \operatorname { cos } ( 4 A - 2 B ) + \operatorname { cos } ( 4 B - 2 A ) } = \operatorname { tan } ( A + B )

-12*a^2*b^2 %2B a^2*(b^2*x^2) - x*(-3*a^4 %2B 4*b^2)=0

B 9. In parallelogram ABCD, two points Pand Q areBQtaken on diagonal BD such that DP(see Fig. 8.20). Show that:(i) AP CQ(iii) Δ AQBe ΔCPD(iv) AQ-CP(v) APCQ is a parallelogramFig. 8.20

2 a ^ 2 b ^ 2 %2B 2 b ^ 2 c ^ 2 \pm 2 c ^ 2 a ^ 2 - a ^ 4 - b ^ 4 - c ^ 4

\begin{array}{c}{\text { 13. Factorise the following using suitable identity: }} \\ {\text { (i) } \quad a^{4}+a b^{3}} \\ {\text { (ii) } a^{4}+b^{4}+c^{4}+2 a^{2} b^{2}+2 b^{2} c^{2}+2 c^{2} a^{2}}\end{array}

3. Draw a circle of radius 3 cm. Take two points Pand Q on one of its extended diametereach at a distance of 7 cm from its centre. Draw tangents to the circle from these twopoints P and Q

9.n paratlelogram AcD, two points Pand Q avetaken en disgonai DD sueh that De- nooe Pig 820) Show that()AP-CO(Gi) A AQB CrDv) AQ CP1) APCOIs a parallelogram

parallelagrans ABCD, two points Pand Q amtaken on diagonal BD sach that DP . B0

Pand Q are any two points lying on the sides DC andAD respectively of a parallelogramABCD. Show that ar (APB) ar (BQC)..

3.Pand Q are any two points lying on the sides DC and AD respectively of a parallelograrABCD. Show that ar (APB)-ar (BQC).

3. Pand Q are any two points lying on the sides DC and AD respectively of a parallelogramABCD. Show that ar (APB) = ar (BOC).

tle of (os 67 -sin2 23)7de value of (cos 67 sin 23

locusExamine the continuty of Po) - Yaexempor 240o por 2-o, at) Discuss continuity ofPa) = sing ip atode Os tenie doIP FO) - g2-2012 when 2+2Kt2when 12

Os) Find brasil de loss percent it cost price isR8 400 and selling price is R8520

in years was 48.Ts it possible to design a rectangular park of perimeter 80 m and areaits length and breadth.

6. If cOS A, find the value of 4+4 tan A.

A wall of length 20 m was to be built across an open ground. The height of the9 m and the thickness of the wall is 24 cm. If this wall is to be built up withwhose dimensions are 18 cm x 10 cm x 6 cm, how many bricks would be remd. The height of the wall isbuilt up with brickscks would be required?

(81x^4 %2B 2)/(3x - 1)

(c (1o)316 4817.is equal to(b)äş2727

2) Study the sets P, Q & Rgiven by Venn diagrams.() Write P n(ii) write Q u Ra b

-12a^2b^2 %2B a^2(b^2x^2) - x(-3a^4 %2B 4*b^2)=0