3694 + Interview Questions in Maths in Class 10 Page 2 InterviewSolution

51.	In the following frequency distribution, find the median class. What is the value of median height ?
Answer» 145.67 157.67 155.83 159.67 Solution :Median, `""M_(d)=L+(((N)/(2)-F)/(f))h=155+(50-54)/(30)xx5=155+(5)/(6)=(935)/(6)=155.83` THUS ( c ) is CORRECT option.

Discussion

52.	Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]
Answer» ANSWER :`(i) [{:(,0,0),(,4,-3):}]` (II) `[{:(,2,1,1),(,-1,7,7):}]`

Discussion

53.	For what values of a and b the following pair of linear equations have infinite number of solutions? 2x+3y=7 a(x+y)-b(x-y)=3a+b-2
Answer» ANSWER :`a=5, b=1`

Discussion

54.	Prove that: (a)(1+sintheta)/(1-sintheta)=(sectheta+tantheta)^(2) (b)(cosA)/(1-tanA)+(sinA)/(1-cotA)=sinA+cosA.
Answer» ANSWER :RHS

Discussion

55.	Write the reciprocals of the above numbers and add them. You will get a number of the form (p)/(q).
Answer» Answer :`=(1)/(5)+(1)/(7)=(12)/(35)`

Discussion

56.	Determine graphically whether the following pair of linear equations :3x-y=72x+5y+1=0 has :(i) a unique solution(ii) infinitely many solutions or(iii) no solution.
Answer» ANSWER :X = 2 and `y =-1`

Discussion

57.	If the points A (k +1, 2k), B (3k, 2k + 3) and C (5k-1, 5k) are collinear, then find the value of k.
Answer» ANSWER :K = 2

Discussion

58.	How many multiple of 4 lie between 10 and 250 ?
Answer» ANSWER :`60`

Discussion

59.	Using the factor theorem, show that (x-2) is a factor of 3x^(2)-5x-2. Hence factorise the given expression.
Answer» ANSWER :`(x-2) (3x+1)`

Discussion

60.	A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3……., 12 as shown in the Fig. What is the probability that it will point to: (i) 6? (ii) an even number? (iii) a prime number? (iv) a multiple of 4?
Answer» Answer :`(i) (1)/(12) (ii) (1)/(2) (III) (5)/(12) (iv) (1)/(4)`

Discussion

61.	If A={2,4,6,8,10} and B={3,6,9,12,15}. Find A-B and B-A.
Answer» ANSWER :A-B={2,4,8,10} B-A={3,9,12,15}

Discussion

62.	If (a, b) is a point in the solution region for the system of inequalities shown above and a=6, what is the minimu possible value of b? (sqrt(2)x^((5)/(6))x)/(root(3)(x))
Answer» ANSWER :A

Discussion

63.	If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x,y) and Plies on the line x + y -10 = 0, find the value of k.
Answer» ANSWER :k=7

Discussion

64.	Water flows at the rate of 10 m/min through a cylinderical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?
Answer» ANSWER :51.3 MIN (APPROX)

Discussion

65.	The mode of the following series is 36. Find the missing frequency in it :
Answer» ANSWER :10

Discussion

66.	If P is brother of Q, R is father of P, S is brother of T, T is daughter of Q, then uncle of S is
Answer» P Q R S Answer :A

Discussion

67.	In triangle ABC, right angled at B, if tanA=1/sqrt(3) find the value ofSin Acos C + cos A sin C OR Prove the identity tan^(2)theta-sin^(2)theta=tan^(2)theta-sin^(2)theta
Answer» ANSWER :1

Discussion

68.	Find the mean percentage of the work completedfor a presect in a country from the following frequency idstribution by step deviation method. :
Answer» ANSWER :`41.6%`

Discussion

69.	What is the perimeter of the triangle formed by the points (0, 0), (1, 0) and (0, 1) ?
Answer» `SQRT(2)` 2 `2-sqrt(2)` `2+sqrt(2)` ANSWER :D

Discussion

70.	In what ratio does the line x - y - 2 = 0 divide the line segment joining the points (3.-1) and (8,9) ? Also, find the co-ordinates of the point of intersection.
Answer» ANSWER :2: 3 (5,3)

Discussion

71.	The volume of a cube is 64 cm^(3). Find the total sufrace area of the cube.
Answer» ANSWER :Surface AREA of CUBE `=96cm^(2)`

Discussion

72.	triangle PQR~ triangle LTR. In triangle PQR,PQ=4.2 cm, QR=5.4 cm, PR=4.8 cm. Construct triangle PQR " and " triangle LTR, such that (PQ)/(LT)=(3)/(4).
Answer» Answer :If seg QR is divided into 3 equal parts, then TR will be 4 times each part of seg QR. So, if we construct `triangle PQR`, point T will be on side RQ, at a distance equal to 4 parts from R. Now, point L is the point of intersection of RAY RP and a line through T, parallel to PQ. `triangle LTR` is the required triangle SIMILAR to `triangle PQR`.

Discussion

73.	A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Answer» ANSWER :400

Discussion

74.	Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.
Answer» ANSWER :6,18,30 and 42 or 42, 30, 18 and 6

Discussion

75.	A right angle triangle with sides 3 cm and 4 cm is revolved around its hypotenuse . Find the volume of the double cone thus generated.
Answer» Solution :`triangleAOB triangleABC` `(AO)/(AB)=(OB)/(BC)=(AB)/(AC)` `(R )/(4)=(3)/(5)RARR r=(12)/(5) cm` `AC^(2)=AB^(2)+BC^(2)` =9+16 =25 AC=5=`h_(1)+h_(2)` REQUIRED area `=(1)/(3)PIR^(2)+(1)/(3)pir^(2)h_(2)=(1)/(3)(h_(1)+h_(2))` `=(1)/(3)xx(22)/(7)xx((12)/(5))^(2)xx5=30.17 cm^(3)`

Discussion

76.	Divide 3x^(2)-x^(3)-3x+5 by x-1-c^(2), and verify the division algorithm.
Answer» ANSWER :In this WAY, the DIVISION ALGORITHM is VERIFIED.

Discussion

77.	A farmer connects a pipe of internal diameter 20cm from a canal into a cylinder tank in her field, which is 10m in diameter and 2m deep. If water flows through the pipe at the rate of 3km // h , in how much time will the tank be filled ?
Answer» ANSWER :100 MINUTES

Discussion

78.	A comet is heading for jupiter with axxeleration a = 50 kms^(-2) . The velocity of the comet at time "t" is given by f(t) = at^(2)- at + 1. then the velocity at time t = 5 seconds is ............... .
Answer» 900 `KMS^(-1)` 1001`kms^(-1)` 2001 `kms^(-1)` 50 `kms^(-1)` Answer :A

Discussion

79.	If z_1 and z_2 are complex numbers such that, \|1-bar z_1z_2\|^(2)-\|z_1-z_(2^(2))\|^(2)=k(1-\|z_1\|^(2)) (1-\|z_2\|^(2)).Find value of k.
Answer» ANSWER :k=1

Discussion

80.	Find the 9^(th) term of the series : 1,4,16,64. . . . . . . . . . .
Answer» ANSWER :65536

Discussion

81.	Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6 cm from its centre.
Answer» <P> Solution :Given, a point M' is at a DISTANCE of 6 cm from the centre of a circle of radius 4 cm. STEP of construction 1. Draw a circle of radius 4 cm. Let centre of this circle is O. 2. Join OM' and bisect it. Let M be mid-point of OM'. 3. TAKING M as centre and MO as radius draw a circel to intersect circle (0,4) at two points, P and Q. Join PM' and QM'. PM' and QM' are the required tangents from M' to circle C(0,4).

Discussion

82.	Using Remainder Theorem, factorise : x^(3)+10x^2-37x+26 completely.
Answer» ANSWER :(x-1) (x-2) (x+13)

Discussion

83.	Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
Answer» Mist Cloud Rain VAPOUR ANSWER :C

Discussion

84.	Find two consecutive odd positive integers sum of whose square is 290.
Answer» ANSWER :`11,13`

Discussion

85.	Solve for a,b and c, if, (i) [{:(,-4,a+5),(,3,2):}]=[{:(,b+4,2),(,3,c-1):}] (ii) [{:(,a,a-b),(,b+c,0):}]=[{:(,3,-1),(,2,0):}]
Answer» ANSWER :(i) a=-3, b=-8 and c=3 (II) a=3, b=4 and c=-2

Discussion

86.	Find the number of rectangles in the following figure.
Answer» 6 7 8 18 Answer :D

Discussion

87.	Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? Snake, Lizard, Turtle, Whale
Answer» SNAKE LIZARD TURTLE WHALE ANSWER :D

Discussion

88.	If A , B and C are interior angles of triangle ABC ,then show that sin((B+C)/( 2) )=cos (A) /(2)
Answer» Answer :`SIN ((B+C) /( 2)) =COS (A)/(2) `,HENCE proved

Discussion

89.	Statements: 1. Raman is always successful. 2. No fool is always successful.Conclusions: 1. Raman is a fool. 2. Raman is not a fool.
Answer» If only conclusion I FOLLOWS, If only conclusion 2 follows, If either conclusion 1 or 2 follows, If NEITHER conclusion 1 nor 2 follows, SOLUTION :Clearlyonlyconclusion2 follows .

Discussion

90.	If sky is called sea, sea is called water, water is caled air, air is called cloud and cloud is called river, then what do we drink when thirsty?
Answer» Sky Air Water Sea Solution :ONE DRINKS .water. when thirsty and as GIVEN .water. is called air. So we DRINK air when thirsty.

Discussion

91.	If x=sec^2 theta + cos^2 theta ,theta ne theta , then the value of x is
Answer» 0 `le 2` `ge -2` `NE 2` Answer :D

Discussion

92.	the difference between the circumference and the radius of a circle is 37 cm. then using pi = (22)/(7) find the circumference (in cm) of the circle .
Answer» ANSWER :44 CM

Discussion

93.	Find the remainder when x^(29) is divided by x^(2)-2x-3.
Answer» ANSWER :`((3^(29)+1)/(4))x+((3^(29)-3)/(4))`

Discussion

94.	Find the number of terms of an AP whose first and last terms are 5 and 80 respectively and the common difference is 3.
Answer» ANSWER :26

Discussion

95.	Find the ratio of which the line segment joining the points A(3,8) and B(-9,3) is divided by the Y-axis.
Answer» ANSWER :`3 : 1`

Discussion

96.	The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the number. Find the number.
Answer» ANSWER :18

Discussion

97.	Prepare Business to Business (B2B) Tax Invoice as per the details given below. Name of the supplier, adress, Date etc. as per your choice. Supplier-Name, Adress,State,GSTIN,Invoice No., Date Recipient-Name,Adress,State,GSTIN Items: (i) Pencil boxes 100, HSN-3924, Rate- 20, GST 12% (ii) Jigsaw Puzzles 50, HSN 9503, Rate -100 GST 12%.
Answer» ANSWER :`THEREFORE CGST=SGST=300`

Discussion

98.	Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.
Answer» ANSWER :(i) 625 (II) 546

Discussion

99.	If the height and the base area of a right circular cone are 5cm and 48sq.cm respectively. Then the volume of the cone is equal to……… .
Answer» `240cm^(3)` `120cm^(3)` `80CM^(3)` `480CM^(3)` ANSWER :C

Discussion

100.	PA and PB are the two tangents drawn to a circle centered at o. from an external point. If lfloorAOB=150^(@) then lfloorAPB is
Answer» `20^(@)` `30^(@)` `50^(@)` `100^(@)` ANSWER :B::C

Discussion

Explore topic-wise InterviewSolutions in .

In the following frequency distribution, find the median class. What is the value of median height ?

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

For what values of a and b the following pair of linear equations have infinite number of solutions? 2x+3y=7 a(x+y)-b(x-y)=3a+b-2

Prove that: (a)(1+sintheta)/(1-sintheta)=(sectheta+tantheta)^(2) (b)(cosA)/(1-tanA)+(sinA)/(1-cotA)=sinA+cosA.

Write the reciprocals of the above numbers and add them. You will get a number of the form (p)/(q).

Determine graphically whether the following pair of linear equations :3x-y=72x+5y+1=0 has :(i) a unique solution(ii) infinitely many solutions or(iii) no solution.

If the points A (k +1, 2k), B (3k, 2k + 3) and C (5k-1, 5k) are collinear, then find the value of k.

How many multiple of 4 lie between 10 and 250 ?

Using the factor theorem, show that (x-2) is a factor of 3x^(2)-5x-2. Hence factorise the given expression.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3……., 12 as shown in the Fig. What is the probability that it will point to: (i) 6? (ii) an even number? (iii) a prime number? (iv) a multiple of 4?

If A={2,4,6,8,10} and B={3,6,9,12,15}. Find A-B and B-A.

If (a, b) is a point in the solution region for the system of inequalities shown above and a=6, what is the minimu possible value of b? (sqrt(2)*x^((5)/(6))*x)/(root(3)(x))

If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x,y) and Plies on the line x + y -10 = 0, find the value of k.

Water flows at the rate of 10 m/min through a cylinderical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?

The mode of the following series is 36. Find the missing frequency in it :

If P is brother of Q, R is father of P, S is brother of T, T is daughter of Q, then uncle of S is

In triangle ABC, right angled at B, if tanA=1/sqrt(3) find the value ofSin Acos C + cos A sin C OR Prove the identity tan^(2)theta-sin^(2)theta=tan^(2)theta-sin^(2)theta

Find the mean percentage of the work completedfor a presect in a country from the following frequency idstribution by step deviation method. :

What is the perimeter of the triangle formed by the points (0, 0), (1, 0) and (0, 1) ?

In what ratio does the line x - y - 2 = 0 divide the line segment joining the points (3.-1) and (8,9) ? Also, find the co-ordinates of the point of intersection.

The volume of a cube is 64 cm^(3). Find the total sufrace area of the cube.

triangle PQR~ triangle LTR. In triangle PQR,PQ=4.2 cm, QR=5.4 cm, PR=4.8 cm. Construct triangle PQR " and " triangle LTR, such that (PQ)/(LT)=(3)/(4).

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.

Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.

A right angle triangle with sides 3 cm and 4 cm is revolved around its hypotenuse . Find the volume of the double cone thus generated.

Divide 3x^(2)-x^(3)-3x+5 by x-1-c^(2), and verify the division algorithm.

A farmer connects a pipe of internal diameter 20cm from a canal into a cylinder tank in her field, which is 10m in diameter and 2m deep. If water flows through the pipe at the rate of 3km // h , in how much time will the tank be filled ?

A comet is heading for jupiter with axxeleration a = 50 kms^(-2) . The velocity of the comet at time "t" is given by f(t) = at^(2)- at + 1. then the velocity at time t = 5 seconds is ............... .

If z_1 and z_2 are complex numbers such that, |1-bar z_1z_2|^(2)-|z_1-z_(2^(2))|^(2)=k(1-|z_1|^(2)) (1-|z_2|^(2)).Find value of k.

Find the 9^(th) term of the series : 1,4,16,64. . . . . . . . . . .

Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6 cm from its centre.

Using Remainder Theorem, factorise : x^(3)+10x^2-37x+26 completely.

Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ?

Find two consecutive odd positive integers sum of whose square is 290.

Solve for a,b and c, if, (i) [{:(,-4,a+5),(,3,2):}]=[{:(,b+4,2),(,3,c-1):}] (ii) [{:(,a,a-b),(,b+c,0):}]=[{:(,3,-1),(,2,0):}]

Find the number of rectangles in the following figure.

Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? Snake, Lizard, Turtle, Whale

If A , B and C are interior angles of triangle ABC ,then show that sin((B+C)/( 2) )=cos (A) /(2)

Statements: 1. Raman is always successful. 2. No fool is always successful.Conclusions: 1. Raman is a fool. 2. Raman is not a fool.

If sky is called sea, sea is called water, water is caled air, air is called cloud and cloud is called river, then what do we drink when thirsty?

If x=sec^2 theta + cos^2 theta ,theta ne theta , then the value of x is

the difference between the circumference and the radius of a circle is 37 cm. then using pi = (22)/(7) find the circumference (in cm) of the circle .

Find the remainder when x^(29) is divided by x^(2)-2x-3.

Find the number of terms of an AP whose first and last terms are 5 and 80 respectively and the common difference is 3.

Find the ratio of which the line segment joining the points A(3,8) and B(-9,3) is divided by the Y-axis.

The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the number. Find the number.

Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.

If the height and the base area of a right circular cone are 5cm and 48sq.cm respectively. Then the volume of the cone is equal to……… .

PA and PB are the two tangents drawn to a circle centered at o. from an external point. If lfloorAOB=150^(@) then lfloorAPB is

If (a, b) is a point in the solution region for the system of inequalities shown above and a=6, what is the minimu possible value of b? (sqrt(2)x^((5)/(6))x)/(root(3)(x))