81279 + Interview Questions in Mathematics QA in Mathematics

1.	4. From a window of a house in a street, h metres above the ground, the angles afelevation and depression of the top and the foot of another house on the opposite sideof the street are α and β respectively. Show that the height of the opposite hourh(1+ tan a.cot 8) metres.
Answer» you have to prove height h(1+tan A.cot B) m and what are u proving.....60(1+......)

Discussion

2.	1x Find the perimeter of a rectangle whose area is 600 cm and breadth is 25 cm
Answer»

Discussion

3.	Give possible expressions for the length and breadth of the rectangle whose area is25a2 - 35a +12.
Answer» So here

Discussion

4.	\|\| का अनुपात 1:46 है तथा इसका गणनफल 1944 है. इनमें सबसे बड़ी संख्या क्या है।(b) 12(c) 18(d) इनमें से कोई।।
Answer» option C is the correct answer 3x:4x:6x=194472x^3=1944x^3=1944/72x^3=27X=36x=3x6=18 answer 18 is the right answer for this question C) 18 is the right answer 18 ( option C) is the correct answer A/B/C/D is the following optionsoption C is the correct answer of the following question 18 is the correct answer of the given question (3x)×(4x)×(6x)=194472x^3=1944x^3=1944/72x^3=27 => x^3=(3)^3x=3बङी संख्या=6x=6×3=18. ans. 3x : 4x : 6x =1944, (3×4×6)x^3=1944, 72 x^3=1944; x^3=1944/72= 27; x^3=3^3; x=3 6x = 6 x 3 = 1 8 3:4:6=19443x × 4x × 6x = 1944 72x^3 = 1944x^3 = 1944/72x^3 = 27x = 33x=3×3=94x=4×3=126x=6×3=18option (c) 18 is the correct answer. 18 is the best answer c) 18 is the right answer.

4.

|| का अनुपात 1:46 है तथा इसका गणनफल 1944 है. इनमें सबसे बड़ी संख्या क्या है।(b) 12(c) 18(d) इनमें से कोई।।

Answer»

option C is the correct answer

3x:4x:6x=194472x^3=1944x^3=1944/72x^3=27X=36x=3x6=18 answer

18 is the right answer for this question

C) 18 is the right answer

18 ( option C) is the correct answer

A/B/C/D is the following optionsoption C is the correct answer of the following question

18 is the correct answer of the given question

(3x)×(4x)×(6x)=194472x^3=1944x^3=1944/72x^3=27 => x^3=(3)^3x=3बङी संख्या=6x=6×3=18. ans.

3x : 4x : 6x =1944, (3×4×6)x^3=1944, 72 x^3=1944; x^3=1944/72= 27; x^3=3^3; x=3

6x = 6 x 3 = 1 8

3:4:6=19443x × 4x × 6x = 1944 72x^3 = 1944x^3 = 1944/72x^3 = 27x = 33x=3×3=94x=4×3=126x=6×3=18option (c) 18 is the correct answer.

18 is the best answer

c) 18 is the right answer.

Discussion

5.	Identify the following in the given figure.KUA. Vertically opposite anglesB. Corresponding angles
Answer» vertically opposite= 1 and 3 , 2 and 4 , 5 and 7 , 6 and 8 corresponding angles= 2 and 3, 1 and 4, 6 and 7, 5 and 8

5.

Identify the following in the given figure.KUA. Vertically opposite anglesB. Corresponding angles

Answer»

vertically opposite= 1 and 3 , 2 and 4 , 5 and 7 , 6 and 8

corresponding angles= 2 and 3, 1 and 4, 6 and 7, 5 and 8

Discussion

6.	If α β are the roots of the equation 8x2-3x+27 =0,32then the value ofis3 1tb72(d) 44
Answer»

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7.	10 = {B + (4% 208
Answer» 10-{8+(4÷2)}=10-{8+2}=10-10 =0

Discussion

8.	24From the given figure, Identify?a) Diagonalsb) Opposite sidesC) Adjacent angles
Answer» a) AC and BD b) AB and DC also AD and BCc) A and D, A and B , B and C, C and D

Discussion

9.	4 From the given figure, Identify?a) Diagonalsb) Opposite sidesc) Adjacent angles
Answer» a) AC and BD b) AB and DC also AD and BCc) A and D, A and B , B and C, C and D

Discussion

10.	8. In the given figure, name the pairs ofvertically opposite angles.s/e9. In the following figure, find the measure of other angles, if 41-50
Answer» 8. Pairs of vertically opposite angles: (1 and 3), (2 and 4), (6and 8) and (5and7) 9. angle 2 = angle 1 =50 degrees (vertically opposite angles). angle 1 +angle 3 =180 (linear pair of angles)angle 3 =130 angle 4 = angle 3 =130 degrees (vertically opposite angles)

10.

8. In the given figure, name the pairs ofvertically opposite angles.s/e9. In the following figure, find the measure of other angles, if 41-50

Answer»

8. Pairs of vertically opposite angles:

(1 and 3), (2 and 4), (6and 8) and (5and7)

9. angle 2 = angle 1 =50 degrees (vertically opposite angles). angle 1 +angle 3 =180 (linear pair of angles)angle 3 =130

angle 4 = angle 3 =130 degrees (vertically opposite angles)

Discussion

11.	2 Angles opposite to equal sides of an isosceles triangle are equat.17.2orts result can be praved in many ways. One ofthe proofs is given here.We are given an isosceles triangle ABCin which AB = AC. We need to prove that
Answer»

Discussion

12.	Let us consider Sohle exampies.Example 2 : Find the zeroes of the quadratic polynomialrelationship between the zeroes and the coefficients.+7x + 10, and verify
Answer» X²+7x+10=0 x²+2x+5x+10=0 x(x+2)+5(x+2)=0 (x+2)(x+5) = 0 x+2 = 0 ; x = -2 x+5 = 0 ; x = -5 Relationship between the zeroes and coefficients :- Sum of zeroes = -2+(-5) = -2-5 = -7/1 = -x coefficient /x² coefficient Product of zeroes = (-2)(-5) = 10/1 = constant/x² coefficient

12.

Let us consider Sohle exampies.Example 2 : Find the zeroes of the quadratic polynomialrelationship between the zeroes and the coefficients.+7x + 10, and verify

Answer»

X²+7x+10=0

x²+2x+5x+10=0

x(x+2)+5(x+2)=0

(x+2)(x+5) = 0

x+2 = 0 ; x = -2

x+5 = 0 ; x = -5

Relationship between the zeroes and coefficients :-

Sum of zeroes = -2+(-5) = -2-5 = -7/1 = -x coefficient /x² coefficient

Product of zeroes = (-2)(-5) = 10/1 = constant/x² coefficient

Discussion

13.	The sum of two natural numbers is 117. If one number is twelve times the other ,findthe two numbers.
Answer»

Discussion

14.	TherefcrossVerify this answer by checking if it asExample 9 Let us consider Example 2 in Section 3.3. i.e., the cost of 2 pencils and18. Find the cost of each3 erasers is? 9 and the cost of 4 pencils and 6 erasers ispencil and each eraser.Sointion The pair of linear equations formed were:
Answer»

Discussion

15.	8. Two natural numbers differ by 3 and their product is 504. Find thenumbers.
Answer» thanks

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16.	2If2 , let us show thaty a+4
Answer»

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17.	The sum of two natural numbers is 20 while their difference is 4. Findthe numbers.
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18.	If the roots of the equation ax2 + bx + c = 0 are \| 2α and β, then the quadratic equation whoseroots are -a and -p is2,(A) ax2-bx-c=0(C) ax2 + bx-c=0(B) ax2-bx + c 0(D) ax2-bx + 2c = 0
Answer»

Discussion

19.	The difference of two natural numbers is 5 and the difference of their reciprocats is. Find the numbers.410
Answer»

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20.	5. Sum of two natural numbers is 8 and thedifference of their reciprocals = 2Find thenumbers.[ICSE 2015]
Answer»

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21.	The sum of two natural numbers is 15 and the sum of their reciprocais Find the numbers.CBSE 20810
Answer»

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22.	OrWhat happened on 22 february 1944
Answer» Tuesday 22 February 1944. It was Tuesday, under the sign of Pisces (see planets position on February 22, 1944). The US president was Franklin D. Roosevelt (Democratic). Famous people born on this day include Robert Kardashian and Jonathan Demme

Discussion

23.	Solve the following quadratic equation for x :la a+bx+1=02 +(a+baOR
Answer» x. x+2a.a+xb.b+2abx+1=0 is the best answer x.x+2a.a+xb.b+2abx+1=0 is the best answer

23.

Solve the following quadratic equation for x :la a+bx+1=02 +(a+baOR

Answer»

x. x+2a.a+xb.b+2abx+1=0 is the best answer

x.x+2a.a+xb.b+2abx+1=0 is the best answer

Discussion

24.	If the discriminant of the quadratic equation 8x2 -bx +2 0 is 1, find the value ofb'
Answer» Discrimanat is(-b)² - 4 × 8 × 2 = 1b² - 64 = 1b² = 65 b = + or - √(65)

Discussion

25.	12. In the Quadratic equation ax2+bx+c=0 if b2-4ac>0 then write its Natureof Roots.
Answer»

Discussion

26.	819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .
Answer» secθ - tanθ = 4 -----> (1) Multiplying and dividing bysecθ +tanθ =secθ - tanθ×secθ +tanθ/secθ +tanθ = sec²θ - tan²θ/secθ + tanθ = 4 we know that --> sec²θ - tan²θ = 1 1/secθ + tanθ = 4 therefore , secθ + tanθ = 1/4----> (2) Adding equations (1) and (2) :- secθ - tanθ = 4 secθ + tanθ = 1/4 --------------------------2secθ = 4 + 1/42secθ = 17/4 secθ = 17/4*2 = 17/8 we know that cosθ = 1/secθ = 1/(17/8) = 8/17

26.

819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .

Answer»

secθ - tanθ = 4 -----> (1)

Multiplying and dividing bysecθ +tanθ

=secθ - tanθ×secθ +tanθ/secθ +tanθ

= sec²θ - tan²θ/secθ + tanθ = 4

we know that --> sec²θ - tan²θ = 1

1/secθ + tanθ = 4

therefore ,

secθ + tanθ = 1/4----> (2)

Adding equations (1) and (2) :-

secθ - tanθ = 4

secθ + tanθ = 1/4 --------------------------2secθ = 4 + 1/42secθ = 17/4

secθ = 17/4*2 = 17/8

we know that

cosθ = 1/secθ = 1/(17/8) = 8/17

Discussion

27.	___limx â 0
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28.	st' â] 0)
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29.	Find x â 0
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30.	sin B âcos 0 +11 "=, using the identitâano " o Exsmp F % sin 0+ cos Osect =1+t 0, O
Answer» LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved

Discussion

31.	which of the following equationshave the ones that are exact:e^{y} d x+\left(x e^{y}+2 y\right) d y=0
Answer»

Discussion

32.	o xl0 â \|0 =8
Answer» 10010-10÷10010010-1/101000-1/109999/10999.9

Discussion

33.	Q. Ifa andſ are the zeroes of f(x) = 4x2- 5x-1, then evaluate:Ha? + B² (ija? +B3 Eini) at +84 (iv) a ?-B?C
Answer» usea+b=5/4ab=1/4and now solve each term

Discussion

34.	31/01रामकल्याण जीत्रा--2-__५-+___aludu+५dy५dz-
Answer»

Discussion

35.	eV Sg———के... .e (SOd 7 - 500 7 Tz =909 >ही RRYS DY 1 e b के¥ SO b Bk % YO N dO fudey 13wk 20 Dy1B 3O Loy 13 B} 22 OO 5119 ydae ®
Answer»

Discussion

36.	Dy e फिट है!)
Answer»

Discussion

37.	The differential equation of the family of curvesy e (Acos.x + Bsin x), where A and B arearbitrary constants, is :69.dy dydx dxdy dy
Answer»

Discussion

38.	The solution of D. Edy- secx -y tan x is
Answer»

Discussion

39.	7. Find , when x-e cot, y- e sint.dy
Answer» please like my answer if you find it useful

Discussion

40.	e following equations and verify the solutions1. Solve the following equations a(a) 5(x + 3) = 20
Answer» X= 1 is the correct answer of the given question 5( x + 3) = 20; 5x + 15 = 20;; 5x = 20 - 15; x = 5/5 =1 x=1 is right answer.

40.

e following equations and verify the solutions1. Solve the following equations a(a) 5(x + 3) = 20

Answer»

X= 1 is the correct answer of the given question

5( x + 3) = 20; 5x + 15 = 20;; 5x = 20 - 15; x = 5/5 =1

x=1 is right answer.

Discussion

41.	Find the value of x and y in the following equations the following equations:2xy/x+y = 3/2 ; xy/2x-y = -3/10Where x + y ≠ 0 and 2x - y ≠ 0
Answer»

Discussion

42.	following equations
Answer» 3x-7/5 = 1-x/-3= -3(3x-7) = 5(1-x) [cross multiply]= -9x+21 = 5-5x= -9x+5x = 5-21= -4x = -16= x = 16/4= x = 4

Discussion

43.	है 1 P) (l+x—}<2—[l—x—}<4
Answer» (x+1)2/x = (x-1)4/x2x+2/x = 4x-4/x 4x-4 = 2x+24x-2x = 4+22x = 6x = 6/2x = 3

Discussion

44.	Solve the following equations.
Answer» = n / 5 - 5 / 7 = 2 / 3 = n / 5 = 2 / 3 + 5 / 7 = n / 5 = (2 * 7 + 5 * 3 ) / 21 = n / 5 = (14 + 15 ) / 21 = n = 29 / 21 * 5 = n = 145 / 21.

44.

Solve the following equations.

Answer»

= n / 5 - 5 / 7 = 2 / 3

= n / 5 = 2 / 3 + 5 / 7

= n / 5 = (2 * 7 + 5 * 3 ) / 21

= n / 5 = (14 + 15 ) / 21

= n = 29 / 21 * 5

= n = 145 / 21.

Discussion

45.	L kb p R'BIIRLOLE L +x= x 2y
Answer»

Discussion

46.	\left. \begin array l l ( x %2B 2 ) ^ 3 = x ( x ^ 2 - 1 ) & ( B ) \\ ( x - 2 ) ( x %2B 2 ) = 5 & \text (D) x ^ 2 %2B \frac 1 x ^ 2 = 2 \end array \right.
Answer» Option Dx²+1/x² = 2As, x² comes in denominator.

Discussion

47.	7 kg \text { to } 140 g
Answer» thanks didi

Discussion

48.	Solve the following equations:
Answer»

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49.	EXERCISolve the following equations.
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50.	1+/x+1 Gy‘_+.‘l‘-\/—-x+l &
Answer» sqrt(3x +1) + sqrt(x+1)/sqrt(3x+1) - sqrt(x+1) = 4 [sqrt(3x +1) + sqrt(x+1)] ^2/[(3x+1) - (x+1)] = 4 (3x+1 + x + 1) + 2sqrt[(3x+1)(x+1)] = 2x4 2sqrt[(3x+1)(x+1)] = 4x - 2 sqrt[(3x+1)(x+1)] = 2x - 1 Squaring both sides, we get(3x+ 1)(x +1) = 4x^2 + 1 - 4x3x^2 + 4x + 1 = 4x^2 - 4x + 1x^2 - 8x = 0x(x - 8) = 0x = 0, 8

50.

1+/x+1 Gy‘_+.‘l‘-\/—-x+l &

Answer»

sqrt(3x +1) + sqrt(x+1)/sqrt(3x+1) - sqrt(x+1) = 4

[sqrt(3x +1) + sqrt(x+1)] ^2/[(3x+1) - (x+1)] = 4

(3x+1 + x + 1) + 2sqrt[(3x+1)*(x+1)] = 2x*4

2sqrt[(3x+1)*(x+1)] = 4x - 2

sqrt[(3x+1)*(x+1)] = 2x - 1

Squaring both sides, we get(3x+ 1)(x +1) = 4x^2 + 1 - 4x3x^2 + 4x + 1 = 4x^2 - 4x + 1x^2 - 8x = 0x(x - 8) = 0x = 0, 8

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

4. From a window of a house in a street, h metres above the ground, the angles afelevation and depression of the top and the foot of another house on the opposite sideof the street are α and β respectively. Show that the height of the opposite hourh(1+ tan a.cot 8) metres.

1x Find the perimeter of a rectangle whose area is 600 cm and breadth is 25 cm

Give possible expressions for the length and breadth of the rectangle whose area is25a2 - 35a +12.

|| का अनुपात 1:46 है तथा इसका गणनफल 1944 है. इनमें सबसे बड़ी संख्या क्या है।(b) 12(c) 18(d) इनमें से कोई।।

Identify the following in the given figure.KUA. Vertically opposite anglesB. Corresponding angles

If α β are the roots of the equation 8x2-3x+27 =0,32then the value ofis3 1tb72(d) 44

10 = {B + (4% 208

24From the given figure, Identify?a) Diagonalsb) Opposite sidesC) Adjacent angles

4 From the given figure, Identify?a) Diagonalsb) Opposite sidesc) Adjacent angles

8. In the given figure, name the pairs ofvertically opposite angles.s/e9. In the following figure, find the measure of other angles, if 41-50

2 Angles opposite to equal sides of an isosceles triangle are equat.17.2orts result can be praved in many ways. One ofthe proofs is given here.We are given an isosceles triangle ABCin which AB = AC. We need to prove that

Let us consider Sohle exampies.Example 2 : Find the zeroes of the quadratic polynomialrelationship between the zeroes and the coefficients.+7x + 10, and verify

The sum of two natural numbers is 117. If one number is twelve times the other ,findthe two numbers.

TherefcrossVerify this answer by checking if it asExample 9 Let us consider Example 2 in Section 3.3. i.e., the cost of 2 pencils and18. Find the cost of each3 erasers is? 9 and the cost of 4 pencils and 6 erasers ispencil and each eraser.Sointion The pair of linear equations formed were:

8. Two natural numbers differ by 3 and their product is 504. Find thenumbers.

2If2 , let us show thaty a+4

The sum of two natural numbers is 20 while their difference is 4. Findthe numbers.

If the roots of the equation ax2 + bx + c = 0 are | 2α and β, then the quadratic equation whoseroots are -a and -p is2,(A) ax2-bx-c=0(C) ax2 + bx-c=0(B) ax2-bx + c 0(D) ax2-bx + 2c = 0

The difference of two natural numbers is 5 and the difference of their reciprocats is. Find the numbers.410

5. Sum of two natural numbers is 8 and thedifference of their reciprocals = 2Find thenumbers.[ICSE 2015]

The sum of two natural numbers is 15 and the sum of their reciprocais Find the numbers.CBSE 20810

OrWhat happened on 22 february 1944

Solve the following quadratic equation for x :la a+bx+1=02 +(a+baOR

If the discriminant of the quadratic equation 8x2 -bx +2 0 is 1, find the value ofb'

12. In the Quadratic equation ax2+bx+c=0 if b2-4ac&gt;0 then write its Natureof Roots.

819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .

___limx â 0

st' â] 0)

Find x â 0

sin B âcos 0 +11 "=, using the identitâano " o Exsmp F % sin 0+ cos Osect =1+t 0, O

which of the following equationshave the ones that are exact:e^{y} d x+\left(x e^{y}+2 y\right) d y=0

o xl0 â |0 =8

Q. Ifa andſ are the zeroes of f(x) = 4x2- 5x-1, then evaluate:Ha? + B² (ija? +B3 Eini) at +84 (iv) a ?-B?C

31/01रामकल्याण जीत्रा--2-__५-+___aludu+५dy५dz-

eV Sg———के... .e (SOd 7 - 500 7 Tz =909 &gt;ही RRYS DY 1 e b के¥ SO b Bk % YO N dO fudey 13wk 20 Dy1B 3O Loy 13 B} 22 OO 5119 ydae ®

Dy e फिट है!)

The differential equation of the family of curvesy e (Acos.x + Bsin x), where A and B arearbitrary constants, is :69.dy dydx dxdy dy

The solution of D. Edy- secx -y tan x is

7. Find , when x-e cot, y- e sint.dy

e following equations and verify the solutions1. Solve the following equations a(a) 5(x + 3) = 20

Find the value of x and y in the following equations the following equations:2xy/x+y = 3/2 ; xy/2x-y = -3/10Where x + y ≠ 0 and 2x - y ≠ 0

following equations

है 1 P) (l+x—}&lt;2—[l—x—}&lt;4

Solve the following equations.

L kb p R'BIIRLOLE L +x= x 2y

\left. \begin array l l ( x %2B 2 ) ^ 3 = x ( x ^ 2 - 1 ) &amp; ( B ) \\ ( x - 2 ) ( x %2B 2 ) = 5 &amp; \text (D) x ^ 2 %2B \frac 1 x ^ 2 = 2 \end array \right.

7 kg \text { to } 140 g

Solve the following equations:

EXERCISolve the following equations.

1+/x+1 Gy‘_+.‘l‘-\/—-x+l &amp;

12. In the Quadratic equation ax2+bx+c=0 if b2-4ac>0 then write its Natureof Roots.

819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .

___limx â 0

st' â] 0)

Find x â 0

sin B âcos 0 +11 "=, using the identitâano " o Exsmp F % sin 0+ cos Osect =1+t 0, O

o xl0 â |0 =8

31/01रामकल्याण जीत्रा--2-५-+_aludu+५dy५dz-

eV Sg———के... .e (SOd 7 - 500 7 Tz =909 >ही RRYS DY 1 e b के¥ SO b Bk % YO N dO fudey 13wk 20 Dy1B 3O Loy 13 B} 22 OO 5119 ydae ®

है 1 P) (l+x—}<2—[l—x—}<4

\left. \begin array l l ( x %2B 2 ) ^ 3 = x ( x ^ 2 - 1 ) & ( B ) \\ ( x - 2 ) ( x %2B 2 ) = 5 & \text (D) x ^ 2 %2B \frac 1 x ^ 2 = 2 \end array \right.

1+/x+1 Gy‘_+.‘l‘-\/—-x+l &