24740 + Interview Questions in Mathematics Page 220 InterviewSolution

10951.	2. What is the area of the largest rectangle that can be placed in a semi-circle of diameter 10 cm.
Answer» 2. What is the area of the largest rectangle that can be placed in a semi-circle of diameter 10 cm.

Discussion

10952.	How many intersection points can a line have with a circle depending on its position?
Answer» How many intersection points can a line have with a circle depending on its position?

Discussion

10953.	If the mean of n observations is m. If value of all the observations is increased by y except the last y observations, then the mean of the observations will be
Answer» If the mean of n observations is m. If value of all the observations is increased by y except the last y observations, then the mean of the observations will be

Discussion

10954.	In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE\|\|BC.
Answer» In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE\|\|BC.

10954.

In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE||BC.

Answer»

In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE||BC.

Discussion

10955.	Find the side of the rhombus whose diagonals are 6 cm & 8 cm
Answer» Find the side of the rhombus whose diagonals are 6 cm & 8 cm

Discussion

10956.	A set contains 2n+1 elements. The number of subsets of this set containing more than n elements is equal to
Answer» A set contains 2n+1 elements. The number of subsets of this set containing more than n elements is equal to

Discussion

10957.	The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.
Answer» The string of a kite is 100m long and it makes an angle of $60^{\circ}$ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

10957.

The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Answer»

The string of a kite is 100m long and it makes an angle of $60^{\circ}$ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Discussion

10958.	Question 4BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Answer» Question 4 BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Discussion

10959.	The measure of ∠AOC= ___
Answer» The measure of $∠ A O C =$ ___

Discussion

10960.	A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres? [Assume π=227]
Answer» A conical pit of top diameter $3.5 m$ is $12 m$ deep. What is its capacity in kilolitres? $[A s s u m e π = \frac{22}{7}]$

Discussion

10961.	Why numerical value × unit = constantExplain?
Answer» Why numerical value × unit = constant Explain?

Discussion

10962.	24. The maximum number of points of intersection of 8 circles are
Answer» 24. The maximum number of points of intersection of 8 circles are

Discussion

10963.	Question 2 (iii)Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: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 digits. Find the number.
Answer» Question 2 (iii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: 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 digits. Find the number.

Discussion

10964.	If 21y5 is a multiple of 9, where y is a digit, which digits can take the possible value of y?
Answer» If 21y5 is a multiple of 9, where y is a digit, which digits can take the possible value of y?

Discussion

10965.	In a histogram the area of each rectangle is proportional to(a) the class mark of the corresponding class interval(b) the class size of the corresponding class interval(c) frequency of the corresponding class interval(d) cumulative frequency of the corresponding class interval
Answer» In a histogram the area of each rectangle is proportional to (a) the class mark of the corresponding class interval (b) the class size of the corresponding class interval (c) frequency of the corresponding class interval (d) cumulative frequency of the corresponding class interval

Discussion

10966.	The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45∘. Find the angles of the parallelogram.
Answer» The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is $45^{\circ}$ . Find the angles of the parallelogram.

Discussion

10967.

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.Income (in Rs)Number of familiesMore than 75150More than 85140More than 95115More than 10595More than 11570More than 12560More than 13540More than 14525

Answer»

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.

Income (in Rs)	Number of families
More than 75	150
More than 85	140
More than 95	115
More than 105	95
More than 115	70
More than 125	60
More than 135	40
More than 145	25

Discussion

10968.	The set {x ∈ R : 1 ≤ x < 2} can be written as ____________.
Answer» The set {x ∈ R : 1 ≤ x < 2} can be written as ____________.

Discussion

10969.	Express 0.73 in the form of a fraction
Answer» Express 0.73 in the form of a fraction

Discussion

10970.	The area of the rectangular face of a uniform triangular prism is 60 cm2 and the perimeter of the triangular faces is 18 cm. What is the volume of the prism in cm3?
Answer» The area of the rectangular face of a uniform triangular prism is $60 c m^{2}$ and the perimeter of the triangular faces is $18 c m$ . What is the volume of the prism in $c m^{3}$ ?

Discussion

10971.	You know that 17=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯142587 .Can you predict the decimal expansion of 27,37,47,57,67 without actually doing the long division? If so, how?
Answer» You know that $\frac{1}{7} = 0. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 142587$ .Can you predict the decimal expansion of $\frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}$ without actually doing the long division? If so, how?

Discussion

10972.	The pair of equations: x + 2y = 5 and -3x - 6y + 1 = 0, have ______.
Answer» The pair of equations: x + 2y = 5 and -3x - 6y + 1 = 0, have ______.

Discussion

10973.	If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either _______ or _______.
Answer» If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either _______ or _______.

Discussion

10974.	Factorise the polynomial x2n+ 5xn + 6
Answer» Factorise the polynomial x²ⁿ+ 5xⁿ + 6

Discussion

10975.	Find the volume of a cube whose side is 4 cm long.
Answer» Find the volume of a cube whose side is 4 cm long.

Discussion

10976.	In a ∆ABC, if a = 4, b = 3, A=π3. Then side C is given by ____________.
Answer» In a ∆ABC, if a = 4, b = 3, $A = \frac{π}{3} .$ Then side C is given by ____________.

Discussion

10977.	54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?
Answer» 54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

Discussion

10978.	The following figure shows a histogram and corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.
Answer» The following figure shows a histogram and corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.

Discussion

10979.	28. The distance of a variable plane from the origin is p. It intersects the co-ordinate axes at A, B, C then prove that the centroid of Δ ABC is on (1/x²) + (1/y²) + (1/z²) = (9/p²).
Answer» 28. The distance of a variable plane from the origin is p. It intersects the co-ordinate axes at A, B, C then prove that the centroid of Δ ABC is on (1/x²) + (1/y²) + (1/z²) = (9/p²).

Discussion

10980.	Prove that ΔPAB is an equilateral triangle.
Answer» Prove that $Δ P A B$ is an equilateral triangle.

Discussion

10981.	If the diagonal of a rectangle is 17 cm and its perimeter is 46 cm, the area of the rectangle is(a) 100 cm2 (b) 110 cm2 (c) 120 cm2 (d) 240 cm2
Answer» If the diagonal of a rectangle is 17 cm and its perimeter is 46 cm, the area of the rectangle is (a) 100 cm² (b) 110 cm² (c) 120 cm² (d) 240 cm²

Discussion

10982.	5+√25−√2=m+n√2 Find the value of m and n
Answer» $\frac{5 + \sqrt{2}}{5 - \sqrt{2}} = m + n \sqrt{2}$ Find the value of m and n

10982.

5+√25−√2=m+n√2 Find the value of m and n

Answer»

$\frac{5 + \sqrt{2}}{5 - \sqrt{2}} = m + n \sqrt{2}$

Find the value of m and n

Discussion

10983.	Let a,b and c be distinct positive numbers. If the vectors a^i+a^j+c^k, ^i+^k and c^i+c^j+b^k are co-planar, then c is equal to
Answer» Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a^i + a^j + c^k,^i +^k$ and $c^i + c^j + b^k$ are co-planar, then $c$ is equal to

Discussion

10984.	The distance of the point P (0, 0) from the line x + y + 1 = 0 measured parallel to the line y = 2x + 1 is
Answer» The distance of the point P (0, 0) from the line x + y + 1 = 0 measured parallel to the line y = 2x + 1 is

Discussion

10985.	Find the value of \sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}
Answer» Find the value of \sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}

Discussion

10986.	The coordinates of the foot of the perpendicular drawn from a point (3, 4, 5) on the xy-plane are(a) (3, 0, 0)(b) (0, 4, 5)(c) (3, 0, 5)(d) none of these
Answer» The coordinates of the foot of the perpendicular drawn from a point (3, 4, 5) on the xy-plane are (a) (3, 0, 0) (b) (0, 4, 5) (c) (3, 0, 5) (d) none of these

Discussion

10987.	Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area (in sq cms) of the figure formed by these points. 49
Answer» Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area (in sq cms) of the figure formed by these points. 49

Discussion

10988.	The height and radius of cone are 4 cm and 3 cm respectively. Fnd the curved surface area of cone.
Answer» The height and radius of cone are 4 cm and 3 cm respectively. Fnd the curved surface area of cone.

Discussion

10989.	Question 2 (iv) Find : 125−13
Answer» Question 2 (iv) Find : $125^{\frac{- 1}{3}}$

Discussion

10990.	A hollow cylindrical copper pipe is 21 dm long . Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe
Answer» A hollow cylindrical copper pipe is 21 dm long . Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe

Discussion

10991.	Question 9Two chords AB and AC of a circle subtends angles equal to 90∘ and 150∘ respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.
Answer» Question 9 Two chords AB and AC of a circle subtends angles equal to $90^{\circ} a n d 150^{\circ}$ respectively at the centre. Find $∠ B A C$ , if AB and AC lie on the opposite sides of the centre.

Discussion

10992.	An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is
Answer» An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

10992.

An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

Answer»

An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

Discussion

10993.	The figure given below shows a circle with centre O. Diameter AB bisects the chord CD perpendicularly at point E . If CD = 16 cm and EB = 4 cm, find the radius of the circle.
Answer» The figure given below shows a circle with centre O. Diameter AB bisects the chord CD perpendicularly at point E . If CD = 16 cm and EB = 4 cm, find the radius of the circle.

10993.

The figure given below shows a circle with centre O. Diameter AB bisects the chord CD perpendicularly at point E . If CD = 16 cm and EB = 4 cm, find the radius of the circle.

Answer»

The figure given below shows a circle with centre O. Diameter AB bisects the chord CD perpendicularly at point E . If CD = 16 cm and EB = 4 cm, find the radius of the circle.

Discussion

10994.	Which of the following is a cubic polynomial?
Answer» Which of the following is a cubic polynomial?

Discussion

10995.	Ram had five matchsticks of equal length. He made a closed figure with those matchsticks, then this figure will have ____sides and ___diagonals.
Answer» Ram had five matchsticks of equal length. He made a closed figure with those matchsticks, then this figure will have ____sides and ___diagonals.

Discussion

10996.	Question 4Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.
Answer» Question 4 Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Discussion

10997.	The graph of a polynomial P(x) is as shown. The number of its zeroes are
Answer» The graph of a polynomial P(x) is as shown. The number of its zeroes are

Discussion

10998.	By using the method of contradiction, prove that the sum of an irrational number and a rational number is irrational.
Answer» By using the method of contradiction, prove that the sum of an irrational number and a rational number is irrational.

Discussion

10999.	The expansion of the algebraic identity ( x + a ) ( x + b ) is:
Answer» The expansion of the algebraic identity ( x + a ) ( x + b ) is:

Discussion

11000.

Anil got the following marks in his mid term exam (Out of 100) : Maths - 74 Science - 82 Social Studies - 90 ComputerScience - 94 English - 70 What was his average percentage marks?

Answer»

Anil got the following marks in his mid term exam (Out of 100) :

Maths - 74

Science - 82

Social Studies - 90

ComputerScience - 94

English - 70

What was his average percentage marks?

Discussion

Explore topic-wise InterviewSolutions in .

2. What is the area of the largest rectangle that can be placed in a semi-circle of diameter 10 cm.

How many intersection points can a line have with a circle depending on its position?

If the mean of n observations is m. If value of all the observations is increased by y except the last y observations, then the mean of the observations will be

In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE||BC.

Find the side of the rhombus whose diagonals are 6 cm &amp; 8 cm

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements is equal to

The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Question 4BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

The measure of ∠AOC= ___

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres? [Assume π=227]

Why numerical value × unit = constantExplain?

24. The maximum number of points of intersection of 8 circles are

If 21y5 is a multiple of 9, where y is a digit, which digits can take the possible value of y?

In a histogram the area of each rectangle is proportional to(a) the class mark of the corresponding class interval(b) the class size of the corresponding class interval(c) frequency of the corresponding class interval(d) cumulative frequency of the corresponding class interval

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45∘. Find the angles of the parallelogram.

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.Income (in Rs)Number of familiesMore than 75150More than 85140More than 95115More than 10595More than 11570More than 12560More than 13540More than 14525

The set {x ∈ R : 1 ≤ x < 2} can be written as ____________.

Express 0.73 in the form of a fraction

The area of the rectangular face of a uniform triangular prism is 60 cm2 and the perimeter of the triangular faces is 18 cm. What is the volume of the prism in cm3?

You know that 17=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯142587 .Can you predict the decimal expansion of 27,37,47,57,67 without actually doing the long division? If so, how?

The pair of equations: x + 2y = 5 and -3x - 6y + 1 = 0, have ______.

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either _______ or _______.

Factorise the polynomial x2n+ 5xn + 6

Find the volume of a cube whose side is 4 cm long.

In a ∆ABC, if a = 4, b = 3, A=π3. Then side C is given by ____________.

54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

The following figure shows a histogram and corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.

28. The distance of a variable plane from the origin is p. It intersects the co-ordinate axes at A, B, C then prove that the centroid of Δ ABC is on (1/x²) + (1/y²) + (1/z²) = (9/p²).

Prove that ΔPAB is an equilateral triangle.

If the diagonal of a rectangle is 17 cm and its perimeter is 46 cm, the area of the rectangle is(a) 100 cm2 (b) 110 cm2 (c) 120 cm2 (d) 240 cm2

5+√25−√2=m+n√2 Find the value of m and n

Let a,b and c be distinct positive numbers. If the vectors a^i+a^j+c^k, ^i+^k and c^i+c^j+b^k are co-planar, then c is equal to

The distance of the point P (0, 0) from the line x + y + 1 = 0 measured parallel to the line y = 2x + 1 is

Find the value of \sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}

The coordinates of the foot of the perpendicular drawn from a point (3, 4, 5) on the xy-plane are(a) (3, 0, 0)(b) (0, 4, 5)(c) (3, 0, 5)(d) none of these

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area (in sq cms) of the figure formed by these points. 49

The height and radius of cone are 4 cm and 3 cm respectively. Fnd the curved surface area of cone.

Question 2 (iv) Find : 125−13

A hollow cylindrical copper pipe is 21 dm long . Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe

Question 9Two chords AB and AC of a circle subtends angles equal to 90∘ and 150∘ respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

The figure given below shows a circle with centre O. Diameter AB bisects the chord CD perpendicularly at point E . If CD = 16 cm and EB = 4 cm, find the radius of the circle.

Which of the following is a cubic polynomial?

Ram had five matchsticks of equal length. He made a closed figure with those matchsticks, then this figure will have ____sides and ___diagonals.

Question 4Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

The graph of a polynomial P(x) is as shown. The number of its zeroes are

By using the method of contradiction, prove that the sum of an irrational number and a rational number is irrational.

The expansion of the algebraic identity ( x + a ) ( x + b ) is:

Anil got the following marks in his mid term exam (Out of 100) : Maths - 74 Science - 82 Social Studies - 90 ComputerScience - 94 English - 70 What was his average percentage marks?

Find the side of the rhombus whose diagonals are 6 cm & 8 cm

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either _ or _.

Ram had five matchsticks of equal length. He made a closed figure with those matchsticks, then this figure will have __sides and _diagonals.