81279 + Interview Questions in Mathematics QA in Mathematics

1.	Kanika had a piece of cloth 1 m long and 60 cm broad. She cut it into square shapedhandkerchiefs, each side measuring 20 cm and put a lace on the boundary. How much[HOTS]lace is needed for the handkerchiefs?
Answer» The perimeter of the cloth before cutting= 2(100+60) = 320 The perimeter of each square handkerchief= 4(20)=80 Total handkerchiefs = 320/80=4 Each hanky needs 80cm of lace according to the perimeter of the hanky Now for 4 hankys it'll be 4×80 = 320 cm = 3 m 20 cm

1.

Kanika had a piece of cloth 1 m long and 60 cm broad. She cut it into square shapedhandkerchiefs, each side measuring 20 cm and put a lace on the boundary. How much[HOTS]lace is needed for the handkerchiefs?

Answer»

The perimeter of the cloth before cutting= 2(100+60) = 320

The perimeter of each square handkerchief= 4(20)=80

Total handkerchiefs = 320/80=4

Each hanky needs 80cm of lace according to the perimeter of the hanky

Now for 4 hankys it'll be 4×80 = 320 cm = 3 m 20 cm

Discussion

2.	7x+6y=38003x+5y=1750
Answer»

Discussion

3.	\left. \begin{array} { l } { 5 a + 2 v = 32 } \\ { 6 a + 6 v = 42 } \end{array} \right.
Answer» 5a + 2v = 32..........(1)6a + 6v = 42..........(2)(1)×3;15a + 6v = 96.........(3)(3)-(2);9a=54a=6then v=1

Discussion

4.	\left. \begin{array} { l } { \text { If } \operatorname { sin } 3 \theta = \operatorname { cos } ( \theta - 6 ^ { \circ } ) , \text { where } 3 \theta \text { and } ( \theta - 6 ^ { \circ } ) \text { are acute ar } } \\ { ( 1 ) 42 ^ { \circ } } \end{array} \right.
Answer»

Discussion

5.	\begin{array}{l}{\text { Find } n \text { and } r, \text { if }} \\ {\text { (a) }^{n} P_{r}=720 \text { and }^{n} C_{r}=120} \\ {\text { (b) }^{n} C_{r-1} :^{n} C_{r} :^{n} C_{r+1}=20 : 35 : 42}\end{array}
Answer»

Discussion

6.	The mth term of an A. P. is n and the nh term is m. Show that its (m+ n,)th term is zero.
Answer» tysm

Discussion

7.	Example 17. A river 3 m deep and 40 m wide is flowing at the rate ofim per hour. How much water will fall into the sea in a minute?
Answer»

Discussion

8.	Afunctionf is defined on R by f(x)1,EQProve that f is continuous at no point cE R
Answer»

Discussion

9.	2. In a school function 360 remained after spending 82% of the moneyHow much money was there in the beginning? Verify your answer
Answer» After spending 82% of the money 18% remaining which is 360 so initial money = 360/0.18 = 2000 If you find this answer helpful then like it.

9.

2. In a school function 360 remained after spending 82% of the moneyHow much money was there in the beginning? Verify your answer

Answer»

After spending 82% of the money 18% remaining which is 360 so initial money = 360/0.18 = 2000

If you find this answer helpful then like it.

Discussion

10.	In a school function Rs. 360 remained after spending 80 % of the money. How much money was there in the beginning? Verify your answer.
Answer» let initial money be xsox - 82% of x = 360x - (82x)/100 = 36018x/100 = 360x = (360 × 100)18 = ₹2000Initially the money is ₹2000verification spend of 82% will 2000× 82/100 = 1640So, The money left is ₹2000-₹1640 = ₹360Verified

Discussion

11.	A two-digit number is such that theproduct of its digits 35. When 18 is addedto the number, the digits interchangetheir places. Find the number.
Answer»

Discussion

12.	i.e., π × d = 4 x 0.01. Shaila wants to put a lace on the edge of a circular table cover of diameter 1.4 m. Find the length f thelace required and also find its cošt, if one metre of lace cost22.
Answer»

Discussion

13.	A two digit number is such that the product of itsdigits is 14. lf 45 is added to the number, the digitsinterchange their places. Find the number.
Answer»

Discussion

14.	5. A two-digit number is such that the product of its digits is 14. If45is added to the number, the digits interchange their places. Find theCBSE 2012number.
Answer» thanku.. bro

Discussion

15.	(a) A roll of lace contains 20 m of lace. From that roll, Asha used 14 tn 25 cm lace tostitch in her sari. Find the length of the remaining lace.
Answer» 20m lace =20100=2000cm14m 25cm=14100+25=1425cmHence length of remaining lace=2000-1425=575cm=5m 75cm

Discussion

16.	,Saimawants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs₹15. (Takeπ = 3.14)
Answer» Length of lace required would equal the circumference of table. Length of lace required = πd = 3.141.5 = 4.71 m. Cost of lace = 4.7 15 = 70.65 rupees.

16.

,Saimawants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs₹15. (Takeπ = 3.14)

Answer»

Length of lace required would equal the circumference of table.

Length of lace required = πd = 3.14*1.5 = 4.71 m.

Cost of lace = 4.7 * 15 = 70.65 rupees.

Discussion

17.	7. Show that the function defined as follows is continuous at x=1 x-2 but not differentiable at thesepoints< 15x-5if x > 2
Answer»

Discussion

18.	1. A function f(x) is defined as follows:= 3+2xfor 3/2<x<03-2x for 0<x<3/2=-3-2x for, x>3/2Show that fix) is continuous at x=0 and discontinuous at X=3/2
Answer» answer The question is to prove not an answer

18.

1. A function f(x) is defined as follows:= 3+2xfor 3/2<x<03-2x for 0<x<3/2=-3-2x for, x>3/2Show that fix) is continuous at x=0 and discontinuous at X=3/2

Answer»

answer

The question is to prove not an answer

Discussion

19.	EXERCISE 6.2in Fig. 6.17,() and (Gi), DE BC. Find EC in (i) and AD in (i).1.5 cm 1 cm7.2 cm3 c
Answer» i) As DE \|\| BC use basic proportionality theorem, AD/BD = AE/EC 1.5/3 = 1/EC EC = 3/1.5 = 30/15 = 2 cm EC = 2 cm

19.

EXERCISE 6.2in Fig. 6.17,() and (Gi), DE BC. Find EC in (i) and AD in (i).1.5 cm 1 cm7.2 cm3 c

Answer»

i) As DE || BC use basic proportionality theorem,

AD/BD = AE/EC

1.5/3 = 1/EC

EC = 3/1.5 = 30/15 = 2 cm

EC = 2 cm

Discussion

20.	7 the difon a Lertain um moneyears at st b.a. beĺ¤Š2s,then thećŁ2
Answer» full answer

Discussion

21.	(c) Show that the function f defined as follows, iscontinuous at x = 2, but not differentiable thereat :3x - 2,0<x51f (x) = 2x2 - x, 1<x<25x - 4, x>2. (C.B.S.E. 2010)
Answer»

Discussion

22.	Choose the eorrect answert is(a) an integer(b) a rational number(c) an irrational number(d) mone of these
Answer»

Discussion

23.	Eh a school function 360 sernita/- of then aftes sel. of the mone How muuhpendingeneep LW
Answer» let initial money be xsox - 82% of x = 360x - (82x)/100 = 36018x/100 = 360x = (360 × 100)18 = ₹2000Initially the money is ₹2000verification spend of 82% will 2000× 82/100 = 1640So, The money left is ₹2000-₹1640 = ₹360Verified

Discussion

24.	ABCD is a rectangle. The diagonals AC and BD intersect each other at O. Find the value of x ifOA = x + 2 and OC = 2x-1.
Answer» Digonal of rectangle bisect each other soOA = OCx+2 = 2x -1 3 = x

Discussion

25.	In the adjoining figure, ABCD is a trapeziumhich CD \|\| AB and its diagonals intersectin wat O. If AO= (5x-7) cm, OC = (2x+1) cm,DO = (7x-5) cmthe value of x.andOB = (7x + 1) cm, find
Answer»

Discussion

26.	In a two-digit number, the one's digit is 3 timesthe ten's digit. If 10 is added to the 2 times of thenumber, its digits interchange their places in thenew number. Find the number.
Answer» thanks thnx

26.

In a two-digit number, the one's digit is 3 timesthe ten's digit. If 10 is added to the 2 times of thenumber, its digits interchange their places in thenew number. Find the number.

Answer»

thanks

thnx

Discussion

27.	7. In the given figure, AOB is a straight line and the ray OC stands onit.If LAOC (2x-10)° and 4BOCAlso, find ZAOC and ZBOC(3x +20)°, find the value of x.(2x 10(3x+ 20)
Answer»

Discussion

28.	Is the number increasedWrite all newThe digits of thousand's and ten's places in 6542 are interchanged. Is the numberdecreased, by how much?
Answer»

Discussion

29.	Ingiven figure DEÄ°l BC. IfAD-3an, DB4cm and AE_6cr, then find EC
Answer» Please hit the like button if this helped you

Discussion

30.	1. Ina two-digit number, the one's digit is 3 times the ten's digit. If 10 is added to the 2times of the number, its digits interchange their places in the new number. Find theCnumber.
Answer»

Discussion

31.	7. In the adjoining figure, ABCD is a trapeziumin which CD'Il AB and its diagonals intersectat O. If AO-6x-7)cm, oC-(2x + 1)cm,DO (7x-5) cm and OB (7x+1) cm, findthe value of x.noints on the sides AB and AC respectively
Answer» tqq

Discussion

32.	1. (a) Find EC.
Answer»

Discussion

33.	1.5cm cm2. In figure, DElIBC, the find EC3 c
Answer» In ∆ ABC, given that DE\|\|BC So, apply Basic Proportionality Theorem, AD/BD = AE/EC 1.5/3 = 1/EC EC = 3/1.5 = 2 cm EC = 2 cm

33.

1.5cm cm2. In figure, DElIBC, the find EC3 c

Answer»

In ∆ ABC, given that DE||BC

So, apply Basic Proportionality Theorem,

AD/BD = AE/EC

1.5/3 = 1/EC

EC = 3/1.5 = 2 cm

EC = 2 cm

Discussion

34.	In the given fig. If DE \|\| BC Find EC.15 cmlem3 cm
Answer» ec=xcm. ad_dn=ae_ec1.5_3=1_x1.5x=3x=3_1.5x=3_15=3(10)_15=2cm. Here ,EC = 3/1.5×1 = 2 cm

34.

In the given fig. If DE || BC Find EC.15 cmlem3 cm

Answer»

ec=xcm. ad_dn=ae_ec1.5_3=1_x1.5x=3x=3_1.5x=3_15=3(10)_15=2cm.

Here ,EC = 3/1.5×1 = 2 cm

Discussion

35.	In Fig. 6.17, ) and (ii), DE I BC. Find EC in (i) and AD in (Gi).
Answer»

Discussion

36.	l In the adjoining figure PQRS is a kite.Find the values of x and y.Q120Â°50Â°
Answer» But in the book it is written that y is 70 degree?

Discussion

37.	Iftwo cubes of edges 6cm are joined face to face it will take the shape of a cuboid whose lah!breadth and height are (6+6) cm, 6cm and 6cm i.e. 12 cm, 6cm and 6cm respectively. Theretotal surface area of the cuboid
Answer»

Discussion

38.	7. Radius of base and height of right circular cone are 6cm and 8cm respectively. Findits volume.
Answer»

Discussion

39.	IS 60°. Find the length of the string, assug. The angle ofAl boy is standing at some distance from a 30 m tall building. Thealelevationfrom his eyes to the top of the building increases from 30° to 60° as hed the distance he walked towards the building
Answer» Let AB=CD= EQ = 1.5 mLet dist. covered by boy is BD=xLet BD=AC=xLet DQ=CE=yIn fig. PE=30-1.5=28.5mAngles are 30° and 60°In ∆ PAE tan 30 = PE/AE1/√3=28.5/x+y 28.5√3=x+y –(1) In ∆PCEtan60=PE/CE√3=28.5/yy=28.5/√3 Put in (1)x+28.5/√3=28.5√4x=(28.5×3-28.5)/√3= (85.5-28.5)/√3=57/√3 Rationalize=57/√3×√3/√3=57√3/3=19√3

39.

IS 60°. Find the length of the string, assug. The angle ofAl boy is standing at some distance from a 30 m tall building. Thealelevationfrom his eyes to the top of the building increases from 30° to 60° as hed the distance he walked towards the building

Answer»

Let AB=CD= EQ = 1.5 mLet dist. covered by boy is BD=xLet BD=AC=xLet DQ=CE=yIn fig. PE=30-1.5=28.5mAngles are 30° and 60°In ∆ PAE tan 30 = PE/AE1/√3=28.5/x+y 28.5√3=x+y –(1)

In ∆PCEtan60=PE/CE√3=28.5/yy=28.5/√3

Put in (1)x+28.5/√3=28.5√4x=(28.5×3-28.5)/√3= (85.5-28.5)/√3=57/√3

Rationalize=57/√3×√3/√3=57√3/3=19√3

Discussion

40.	A 1.5 m tall boy is standing at some distance from a 30 m tail building. Theelevation from his eyes to the top of the building increases from 30 to 6onwards the building. Find the distance he walked towards the building
Answer»

Discussion

41.	Factorise the following:(i) (p-q)2-6(p-q) _ 16
Answer»

Discussion

42.	3. Factorise the following:(i)(p-q)2 - 6 (p-q)- 16
Answer»

Discussion

43.	12.lnthe adjoning figure, ABC is a trine สwhich AB AC D and E are nton Aand AC respectively such that AD Athat the points B C. E and D ane concyc
Answer»

Discussion

44.	3) The diagonals of parallelogram, intersect each other at rightangles. The parallelogram is:a) a rectangle b) rhombus c) parallelogram d) trapezium
Answer» b) rhombus Diagonal of parallelogram intersects gives us rhombus

44.

3) The diagonals of parallelogram, intersect each other at rightangles. The parallelogram is:a) a rectangle b) rhombus c) parallelogram d) trapezium

Answer»

b) rhombus

Diagonal of parallelogram intersects gives us rhombus

Discussion

45.	(G) If AD 3.6 cm, AB-10 cm and AE 4.5 cm,find EC and AC.
Answer»

Discussion

46.	This question is based on letter series in which some of the letters are missing. The missing letters are given in the proper sequence in one of the alternatives among the four given under each question. Find out the correct alternatives.__ __a bb __bba __bab __a __(a)abaaba(b)aabbaa(c)bbabbb(d)bbaabb
Answer» (c) bba bba bba bba bba b

Discussion

47.	13]ints (-2, -2) and (2, -4) respectively find the coordinates of P on21. If A and B are the poAB,12]the line segment AB such that AP
Answer» Let P(x,y)7AP=3ABPoint P is dividing the AB in 3:7Use section formula,x=(3(2)+7(-2))/10x=6-14/10x=-8/10y=(3(-4)+7(-2))/10y=-12-14/10y=-26/10P=(-8/10,-26/10)

Discussion

48.	41. What is the missing letter in this series:IMOL, STPA, BZQD, .............., CYSUA) HGFDB) CABCC) JKLID) LIRX
Answer» lirx is the missing letter in this series lirx is the missing letter in this series

48.

41. What is the missing letter in this series:IMOL, STPA, BZQD, .............., CYSUA) HGFDB) CABCC) JKLID) LIRX

Answer»

lirx is the missing letter in this series

Discussion

49.	2. In the adjoining figure, show that ABCD isa parallelogram.Calculate the area of lIgm ABCD.D 5 cm C卜A 5 cm B
Answer»

Discussion

50.	26. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle ofelevation from his eyes to the top of the building increases from 30 to 60° as he walkstowards the building. Find the distance he walked towards the building.
Answer» The answer is 43.89m

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Kanika had a piece of cloth 1 m long and 60 cm broad. She cut it into square shapedhandkerchiefs, each side measuring 20 cm and put a lace on the boundary. How much[HOTS]lace is needed for the handkerchiefs?

7x+6y=38003x+5y=1750

\left. \begin{array} { l } { 5 a + 2 v = 32 } \\ { 6 a + 6 v = 42 } \end{array} \right.

\left. \begin{array} { l } { \text { If } \operatorname { sin } 3 \theta = \operatorname { cos } ( \theta - 6 ^ { \circ } ) , \text { where } 3 \theta \text { and } ( \theta - 6 ^ { \circ } ) \text { are acute ar } } \\ { ( 1 ) 42 ^ { \circ } } \end{array} \right.

\begin{array}{l}{\text { Find } n \text { and } r, \text { if }} \\ {\text { (a) }^{n} P_{r}=720 \text { and }^{n} C_{r}=120} \\ {\text { (b) }^{n} C_{r-1} :^{n} C_{r} :^{n} C_{r+1}=20 : 35 : 42}\end{array}

The mth term of an A. P. is n and the nh term is m. Show that its (m+ n,)th term is zero.

Example 17. A river 3 m deep and 40 m wide is flowing at the rate ofim per hour. How much water will fall into the sea in a minute?

Afunctionf is defined on R by f(x)1,EQProve that f is continuous at no point cE R

2. In a school function 360 remained after spending 82% of the moneyHow much money was there in the beginning? Verify your answer

In a school function Rs. 360 remained after spending 80 % of the money. How much money was there in the beginning? Verify your answer.

A two-digit number is such that theproduct of its digits 35. When 18 is addedto the number, the digits interchangetheir places. Find the number.

i.e., π × d = 4 x 0.01. Shaila wants to put a lace on the edge of a circular table cover of diameter 1.4 m. Find the length f thelace required and also find its cošt, if one metre of lace cost22.

A two digit number is such that the product of itsdigits is 14. lf 45 is added to the number, the digitsinterchange their places. Find the number.

5. A two-digit number is such that the product of its digits is 14. If45is added to the number, the digits interchange their places. Find theCBSE 2012number.

(a) A roll of lace contains 20 m of lace. From that roll, Asha used 14 tn 25 cm lace tostitch in her sari. Find the length of the remaining lace.

,Saimawants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs₹15. (Takeπ = 3.14)

7. Show that the function defined as follows is continuous at x=1 x-2 but not differentiable at thesepoints&lt; 15x-5if x &gt; 2

1. A function f(x) is defined as follows:= 3+2xfor 3/2&lt;x&lt;03-2x for 0&lt;x&lt;3/2=-3-2x for, x&gt;3/2Show that fix) is continuous at x=0 and discontinuous at X=3/2

EXERCISE 6.2in Fig. 6.17,() and (Gi), DE BC. Find EC in (i) and AD in (i).1.5 cm 1 cm7.2 cm3 c

7 the difon a Lertain um moneyears at st b.a. beĺ¤Š2s,then thećŁ2

(c) Show that the function f defined as follows, iscontinuous at x = 2, but not differentiable thereat :3x - 2,0&lt;x51f (x) = 2x2 - x, 1&lt;x&lt;25x - 4, x&gt;2. (C.B.S.E. 2010)

Choose the eorrect answert is(a) an integer(b) a rational number(c) an irrational number(d) mone of these

Eh a school function 360 sernita/- of then aftes sel. of the mone How muuhpendingeneep LW

ABCD is a rectangle. The diagonals AC and BD intersect each other at O. Find the value of x ifOA = x + 2 and OC = 2x-1.

In the adjoining figure, ABCD is a trapeziumhich CD || AB and its diagonals intersectin wat O. If AO= (5x-7) cm, OC = (2x+1) cm,DO = (7x-5) cmthe value of x.andOB = (7x + 1) cm, find

In a two-digit number, the one's digit is 3 timesthe ten's digit. If 10 is added to the 2 times of thenumber, its digits interchange their places in thenew number. Find the number.

7. In the given figure, AOB is a straight line and the ray OC stands onit.If LAOC (2x-10)° and 4BOCAlso, find ZAOC and ZBOC(3x +20)°, find the value of x.(2x 10(3x+ 20)

Is the number increasedWrite all newThe digits of thousand's and ten's places in 6542 are interchanged. Is the numberdecreased, by how much?

Ingiven figure DEÄ°l BC. IfAD-3an, DB4cm and AE_6cr, then find EC

1. Ina two-digit number, the one's digit is 3 times the ten's digit. If 10 is added to the 2times of the number, its digits interchange their places in the new number. Find theCnumber.

7. In the adjoining figure, ABCD is a trapeziumin which CD'Il AB and its diagonals intersectat O. If AO-6x-7)cm, oC-(2x + 1)cm,DO (7x-5) cm and OB (7x+1) cm, findthe value of x.noints on the sides AB and AC respectively

1. (a) Find EC.

1.5cm cm2. In figure, DElIBC, the find EC3 c

In the given fig. If DE || BC Find EC.15 cmlem3 cm

In Fig. 6.17, ) and (ii), DE I BC. Find EC in (i) and AD in (Gi).

l In the adjoining figure PQRS is a kite.Find the values of x and y.Q120Â°50Â°

Iftwo cubes of edges 6cm are joined face to face it will take the shape of a cuboid whose lah!breadth and height are (6+6) cm, 6cm and 6cm i.e. 12 cm, 6cm and 6cm respectively. Theretotal surface area of the cuboid

7. Radius of base and height of right circular cone are 6cm and 8cm respectively. Findits volume.

IS 60°. Find the length of the string, assug. The angle ofAl boy is standing at some distance from a 30 m tall building. Thealelevationfrom his eyes to the top of the building increases from 30° to 60° as hed the distance he walked towards the building

A 1.5 m tall boy is standing at some distance from a 30 m tail building. Theelevation from his eyes to the top of the building increases from 30 to 6onwards the building. Find the distance he walked towards the building

Factorise the following:(i) (p-q)2-6(p-q) _ 16

3. Factorise the following:(i)(p-q)2 - 6 (p-q)- 16

12.lnthe adjoning figure, ABC is a trine สwhich AB AC D and E are nton Aand AC respectively such that AD Athat the points B C. E and D ane concyc

3) The diagonals of parallelogram, intersect each other at rightangles. The parallelogram is:a) a rectangle b) rhombus c) parallelogram d) trapezium

(G) If AD 3.6 cm, AB-10 cm and AE 4.5 cm,find EC and AC.

13]ints (-2, -2) and (2, -4) respectively find the coordinates of P on21. If A and B are the poAB,12]the line segment AB such that AP

41. What is the missing letter in this series:IMOL, STPA, BZQD, .............., CYSUA) HGFDB) CABCC) JKLID) LIRX

2. In the adjoining figure, show that ABCD isa parallelogram.Calculate the area of lIgm ABCD.D 5 cm C卜A 5 cm B

26. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle ofelevation from his eyes to the top of the building increases from 30 to 60° as he walkstowards the building. Find the distance he walked towards the building.

7. Show that the function defined as follows is continuous at x=1 x-2 but not differentiable at thesepoints< 15x-5if x > 2

1. A function f(x) is defined as follows:= 3+2xfor 3/2<x<03-2x for 0<x<3/2=-3-2x for, x>3/2Show that fix) is continuous at x=0 and discontinuous at X=3/2

7 the difon a Lertain um moneyears at st b.a. beĺ¤Š2s,then thećŁ2

(c) Show that the function f defined as follows, iscontinuous at x = 2, but not differentiable thereat :3x - 2,0<x51f (x) = 2x2 - x, 1<x<25x - 4, x>2. (C.B.S.E. 2010)