24740 + Interview Questions in Mathematics

1.	The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
Answer» The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

Discussion

2.	Find the value of x in the given figure.
Answer» Find the value of $x$ in the given figure.

Discussion

3.	The sum of the deviations of a set of n values x1, x2,...., xn, measured from 15 and −3 are −90 and 54 respectively. Find the value of n and mean.
Answer» The sum of the deviations of a set of n values x₁, x₂,...., x_n, measured from 15 and −3 are −90 and 54 respectively. Find the value of n and mean.

Discussion

4.	A circular hole of 25 mm diameter and depth of 20 mm is machined by the EDM process. The material removal rate inmm3/min is expressed as 4×104IT−1.23 where I = 300 A and the melting point of the material, T = 1600°C. Thetime (in minutes) for machining this hole is____(correct to two decimal places).7.1431
Answer» A circular hole of 25 mm diameter and depth of 20 mm is machined by the EDM process. The material removal rate $i n m m^{3} / m i n$ is expressed as $4 \times 10^{4} I T^{- 1.23}$ where I = 300 A and the melting point of the material, T = 1600°C. The time (in minutes) for machining this hole is____(correct to two decimal places). 7.1431

Discussion

5.	A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to server 250 patients?
Answer» A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to server 250 patients?

Discussion

6.	Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle.
Answer» Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle.

Discussion

7.	x+y=30 and are coincident lines.
Answer» $x + y = 30$ and are coincident lines.

Discussion

8.	In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is:
Answer» In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is:

Discussion

9.	In a parallelogram ABCD, if AB→ = a→ and BC→ =b→, then AC→= _____________ and BD→ = _______________.
Answer» In a parallelogram ABCD, if $\vec{A B} = \vec{a} and \vec{B C} = \vec{b}, then \vec{A C} =_____________and \vec{B D} =_______________.$

Discussion

10.	What's the difference between postulate and axioms.
Answer» What's the difference between postulate and axioms.

Discussion

11.	Find two rational numbers of the form pq between the numbers 0.2121121112....and 0.2020020002....
Answer» Find two rational numbers of the form $\frac{p}{q}$ between the numbers 0.2121121112....and 0.2020020002....

Discussion

12.	Angles made by the line with the positive direction of X–axis are given. Find the slope of these lines.(1) 45° (2) 60° (3) 90°
Answer» Angles made by the line with the positive direction of X–axis are given. Find the slope of these lines. (1) 45° (2) 60° (3) 90°

Discussion

13.	Question 09. A car takes 2 hours to reach a destination by travelling at the speed of 60 km/hr. How long will it take when the car travels at the speed of 80 km/hr?
Answer» Question 09. A car takes 2 hours to reach a destination by travelling at the speed of 60 km/hr. How long will it take when the car travels at the speed of 80 km/hr?

Discussion

14.	In the given figure, ΔABD is an isosceles triangle with AB=AD. A median is drawn from A to side BD at C. Which of the following option(s) is/are correct?
Answer» In the given figure, $Δ A B D$ is an isosceles triangle with AB=AD. A median is drawn from A to side BD at C. Which of the following option(s) is/are correct?

Discussion

15.	In a triangle ABC, D is the midpoint of AB and E is a point on AC such that DE \|\| BC. Then
Answer» In a triangle ABC, D is the midpoint of AB and E is a point on AC such that DE \|\| BC. Then

Discussion

16.	If x=0.¯18, which of the following statements are true?(i) 100x=18.¯18 (ii) 100x−x=17.¯18 (iii) 99x=18
Answer» If $x = 0. ¯ 18$ , which of the following statements are true? (i) $100 x = 18. ¯ 18$ (ii) $100 x - x = 17. ¯ 18$ (iii) $99 x = 18$

16.

If x=0.¯18, which of the following statements are true?(i) 100x=18.¯18 (ii) 100x−x=17.¯18 (iii) 99x=18

Answer»

If $x = 0. ¯ 18$ , which of the following statements are true?

(i) $100 x = 18. ¯ 18$

(ii) $100 x - x = 17. ¯ 18$

(iii) $99 x = 18$

Discussion

17.	Question 2 A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. The acute angle between the diagonals is (a) 55∘ (b) 50∘ (c) 40∘ (d) 25∘
Answer» Question 2 A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$ . The acute angle between the diagonals is (a) $55^{\circ}$ (b) $50^{\circ}$ (c) $40^{\circ}$ (d) $25^{\circ}$

Discussion

18.	Vector 5^i−2^j,−^i+3^j and 2^i−λ^j have same initial point (−1,2), then the value of (2λ+3) for which all three vectors vanishes on a straight line is
Answer» Vector $5^i - 2^j, -^i + 3^j$ and $2^i - λ^j$ have same initial point $(- 1, 2),$ then the value of $(2 λ + 3)$ for which all three vectors vanishes on a straight line is

Discussion

19.	Find the slope (m) and the y-intercept (c) of the line x+y+5=0.
Answer» Find the slope (m) and the y-intercept (c) of the line $x + y + 5 = 0$ .

Discussion

20.	Question 86A packet of sweet was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?
Answer» Question 86 A packet of sweet was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?

20.

Question 86A packet of sweet was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?

Answer»

Question 86

A packet of sweet was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?

Discussion

21.	The product of a non-zero rational number and an irrational number is(a) always irrational(b) always rational(c) rational or irrational(d) one
Answer» The product of a non-zero rational number and an irrational number is (a) always irrational (b) always rational (c) rational or irrational (d) one

Discussion

22.	Find the value of unknown x in the following isosceles triangle:
Answer» Find the value of unknown x in the following isosceles triangle:

Discussion

23.	If \|→a\|+\|→b\|=\|→c\| and →a+→b=→c, then the angle between vectors →a and →b is
Answer» If $\| \to a \| + \| \to b \| = \| \to c \|$ and $\to a + \to b = \to c,$ then the angle between vectors $\to a$ and $\to b$ is

Discussion

24.	If both x + 1 and x - 1 are factors of ax3+x2 - 2x + b, find the values of a and b.
Answer» If both x + 1 and x - 1 are factors of $a x^{3} + x^{2}$ - 2x + b, find the values of a and b.

Discussion

25.	A 25 m long ladder is placed against a vertical wall, such that the foot of the ladder is 7m from the feet of the wall. If the top of the ladder slides down by 4m, by how much distance will the foot of the ladder slide.
Answer» A 25 m long ladder is placed against a vertical wall, such that the foot of the ladder is 7m from the feet of the wall. If the top of the ladder slides down by 4m, by how much distance will the foot of the ladder slide.

Discussion

26.	Write 7y = 2x as a linear equation of the form ax + by + c = 0. Also, write the values corresponding to a, b, c. Does the graph of this linear equation pass through origin? Give your answer in 'yes' or 'no'.
Answer» Write $\sqrt{7} y = 2 x$ as a linear equation of the form ax + by + c = 0. Also, write the values corresponding to a, b, c. Does the graph of this linear equation pass through origin? Give your answer in 'yes' or 'no'.

Discussion

27.	Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure. Can you identify how many circles and arcs are there in the plan respectively?
Answer» Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure. Can you identify how many circles and arcs are there in the plan respectively?

27.

Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure. Can you identify how many circles and arcs are there in the plan respectively?

Answer»

Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure.

Can you identify how many circles and arcs are there in the plan respectively?

Discussion

28.	X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:
Answer» X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

Discussion

29.	If α and β are zeroes of polynomial6x2−5x+k and α−β=16 find k
Answer» If $α$ and $β$ are zeroes of polynomial $6 x^{2} - 5 x + k a n d α - β = \frac{1}{6}$ find k

Discussion

30.	In a circle of radius 2 centimetres, what is the length of an arc of central angle 300°?
Answer» In a circle of radius 2 centimetres, what is the length of an arc of central angle 300°?

30.

In a circle of radius 2 centimetres, what is the length of an arc of central angle 300°?

Answer»

In a circle of radius 2 centimetres, what is the length of an arc of central angle 300°?

Discussion

31.	What is the area of the rhombus ABCD, if AC=12 cm and BE=8 cm
Answer» What is the area of the rhombus $A B C D$ , if $A C = 12 c m$ and $B E = 8 c m$

31.

What is the area of the rhombus ABCD, if AC=12 cm and BE=8 cm

Answer»

What is the area of the rhombus $A B C D$ , if $A C = 12 c m$ and $B E = 8 c m$

Discussion

32.	The straight line x = a (where a is a constant) is parallel to the ___ - axis.
Answer» The straight line x = a (where a is a constant) is parallel to the ___ - axis.

Discussion

33.	If A=[cosα−sinαsinαcosα], then A+A′=I, if the value of α is
Answer» If $A = [\begin{matrix} cos α & - sin α sin α & cos α \end{matrix}]$ , then $A + A^{'} = I$ , if the value of $α$ is

Discussion

34.

From the following particulars relating to the Ramakrishna Mission Charitable Hospital, prepare Income and Expenditure Account for the year ended 31st March, 2019 and Balance Sheet as at that date. RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019 Dr. Cr. Receipts ₹ Payments ₹ To Cash in Hand on 1st April, 2018 71,300 By Medicines 3,05,900 To Subscriptions 4,79,960 By Doctor's Honorarium 90,000 To Donations 1,45,000 By Salaries 2,75,000 To Interest on Investment 7% for full year 70,000 By Petty Expenses 4,610 To Proceeds from Charity Show 1,04,500 By Equipments 1,50,000 By Expenses on Charity Show 7,500 By Cash in Hand on 31st March, 2018 37,750 8,70,760 8,70,760 Additional Information: As at 1st April, 2018 (₹) As at 31st March, 2019 (₹) Subscriptions Due 2,400 2,800 Subscriptions Received in Advance 640 1,000 Stock of Medicines 88,100 97,400 Estimated value of Equipments 2,12,000 3,16,000 Building (cost less depreciation) 4,00,000 3,80,000

Answer» From the following particulars relating to the Ramakrishna Mission Charitable Hospital, prepare Income and Expenditure Account for the year ended 31st March, 2019 and Balance Sheet as at that date.

RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019
Dr.				Cr.
Receipts	₹	Payments	₹
To Cash in Hand on 1st April, 2018	71,300	By Medicines	3,05,900
To Subscriptions	4,79,960	By Doctor's Honorarium	90,000
To Donations	1,45,000	By Salaries	2,75,000
To Interest on Investment 7% for full year	70,000	By Petty Expenses	4,610
To Proceeds from Charity Show	1,04,500	By Equipments	1,50,000
		By Expenses on Charity Show	7,500
		By Cash in Hand on 31st March, 2018	37,750

	8,70,760		8,70,760

Additional Information:	As at 1st April, 2018 (₹)	As at 31st March, 2019 (₹)
Subscriptions Due	2,400	2,800
Subscriptions Received in Advance	640	1,000
Stock of Medicines	88,100	97,400
Estimated value of Equipments	2,12,000	3,16,000
Building (cost less depreciation)	4,00,000	3,80,000

Discussion

35.	In a ΔABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.
Answer» In a ΔABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.

Discussion

36.	Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:(i) A(−1,−2) B(1, 0), C (−1, 2), D(−3, 0)(ii) A(−3, 5) B(3, 1), C (0, 3), D(−1, −4)(iii) A(4, 5) B(7, 6), C (4, 3), D(1, 2)
Answer» Name the quadrilateral formed, if any, by the following points, and given reasons for your answers: (i) A(−1,−2) B(1, 0), C (−1, 2), D(−3, 0) (ii) A(−3, 5) B(3, 1), C (0, 3), D(−1, −4) (iii) A(4, 5) B(7, 6), C (4, 3), D(1, 2)

Discussion

37.	Question 11 Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC).
Answer» Question 11 Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC).

Discussion

38.	PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP.
Answer» PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP.

Discussion

39.	23. An equilateral triangle has area A root 3.Three circles are drawn with their centres at the vertices of the triangle.Diameter of each circle is equal to the length of each side of the triangle.The area of the triangle not included in any of the circles is?
Answer» 23. An equilateral triangle has area A root 3.Three circles are drawn with their centres at the vertices of the triangle.Diameter of each circle is equal to the length of each side of the triangle.The area of the triangle not included in any of the circles is?

Discussion

40.	Question 67Extend the line segment on both sides to meet the coordinate axes. What are the coordinates of the points, where this line meets the X-axis and the Y-axis?
Answer» Question 67 Extend the line segment on both sides to meet the coordinate axes. What are the coordinates of the points, where this line meets the X-axis and the Y-axis?

Discussion

41.	The volume of a right circular cone is 9856 cm3.If the diameter of the base is 28 cm,find:(i) height of the cone(ii) slant height of the cone(iii) curved surface area of the cone.
Answer» The volume of a right circular cone is 9856 $c m^{3}$ .If the diameter of the base is 28 cm,find: (i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone.

41.

The volume of a right circular cone is 9856 cm3.If the diameter of the base is 28 cm,find:(i) height of the cone(ii) slant height of the cone(iii) curved surface area of the cone.

Answer»

The volume of a right circular cone is 9856 $c m^{3}$ .If the diameter of the base is 28 cm,find:

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone.

Discussion

42.	If O is the centre of the circle, find the value of x in each of the following figures.
Answer» If O is the centre of the circle, find the value of x in each of the following figures.

42.

If O is the centre of the circle, find the value of x in each of the following figures.

Answer»

If O is the centre of the circle, find the value of x in each of the following figures.

Discussion

43.	10. n(A) =20, n,(B)=18 and n(A intersection B) =5, then n(A-B) is ?
Answer» 10. n(A) =20, n,(B)=18 and n(A intersection B) =5, then n(A-B) is ?

Discussion

44.	Find the solution of the simultaneous system of linear equation by substitution method X/a+y/b=1/2X/√a+y/√b=1/√2 (a>0,b>0
Answer» Find the solution of the simultaneous system of linear equation by substitution method X/a+y/b=1/2 X/√a+y/√b=1/√2 (a>0,b>0

Discussion

45.	In the figure below, two vertices of a parallelogram are joined to the mid points of two sides. Then, the lines divide the diagonal in the picture into _______ equal parts.3
Answer» In the figure below, two vertices of a parallelogram are joined to the mid points of two sides. Then, the lines divide the diagonal in the picture into _______ equal parts. 3

Discussion

46.	With the help of a compass and a ruler draw a circle congruent to the circle shown below:
Answer» With the help of a compass and a ruler draw a circle congruent to the circle shown below:

Discussion

47.	Read the following bar graph and answer the following questions:(i) What information is given by the bar graph?(ii) In which year the export is minimum?(iii) In which year the import is maximum?(iv) In which year the difference of the values of export and import is maximum?
Answer» Read the following bar graph and answer the following questions: (i) What information is given by the bar graph? (ii) In which year the export is minimum? (iii) In which year the import is maximum? (iv) In which year the difference of the values of export and import is maximum?

Discussion

48.	In Figure, PS = QR and ∠SPQ=∠RQP.Prove that PR = QS and ∠QPR=∠PQS.
Answer» In Figure, PS = QR and $∠ S P Q = ∠ R Q P$ . Prove that PR = QS and $∠ Q P R = ∠ P Q S$ .

Discussion

49.

In figure, value of x is:

Answer»

In figure, value of x is:

Discussion

50.	Complete the series -1,6,7,18,23,38,?
Answer» Complete the series -1,6,7,18,23,38,?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

Find the value of x in the given figure.

The sum of the deviations of a set of n values x1, x2,...., xn, measured from 15 and −3 are −90 and 54 respectively. Find the value of n and mean.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to server 250 patients?

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle.

x+y=30 and are coincident lines.

In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is:

In a parallelogram ABCD, if AB→ = a→ and BC→ =b→, then AC→= _____________ and BD→ = _______________.

What's the difference between postulate and axioms.

Find two rational numbers of the form pq between the numbers 0.2121121112....and 0.2020020002....

Angles made by the line with the positive direction of X–axis are given. Find the slope of these lines.(1) 45° (2) 60° (3) 90°

Question 09. A car takes 2 hours to reach a destination by travelling at the speed of 60 km/hr. How long will it take when the car travels at the speed of 80 km/hr?

In the given figure, ΔABD is an isosceles triangle with AB=AD. A median is drawn from A to side BD at C. Which of the following option(s) is/are correct?

In a triangle ABC, D is the midpoint of AB and E is a point on AC such that DE || BC. Then

If x=0.¯18, which of the following statements are true?(i) 100x=18.¯18 (ii) 100x−x=17.¯18 (iii) 99x=18

Question 2 A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. The acute angle between the diagonals is (a) 55∘ (b) 50∘ (c) 40∘ (d) 25∘

Vector 5^i−2^j,−^i+3^j and 2^i−λ^j have same initial point (−1,2), then the value of (2λ+3) for which all three vectors vanishes on a straight line is

Find the slope (m) and the y-intercept (c) of the line x+y+5=0.

Question 86A packet of sweet was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?

The product of a non-zero rational number and an irrational number is(a) always irrational(b) always rational(c) rational or irrational(d) one

Find the value of unknown x in the following isosceles triangle:

If |→a|+|→b|=|→c| and →a+→b=→c, then the angle between vectors →a and →b is

If both x + 1 and x - 1 are factors of ax3+x2 - 2x + b, find the values of a and b.

A 25 m long ladder is placed against a vertical wall, such that the foot of the ladder is 7m from the feet of the wall. If the top of the ladder slides down by 4m, by how much distance will the foot of the ladder slide.

Write 7y = 2x as a linear equation of the form ax + by + c = 0. Also, write the values corresponding to a, b, c. Does the graph of this linear equation pass through origin? Give your answer in 'yes' or 'no'.

Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure. Can you identify how many circles and arcs are there in the plan respectively?

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

If α and β are zeroes of polynomial6x2−5x+k and α−β=16 find k

In a circle of radius 2 centimetres, what is the length of an arc of central angle 300°?

What is the area of the rhombus ABCD, if AC=12 cm and BE=8 cm

The straight line x = a (where a is a constant) is parallel to the ___ - axis.

If A=[cosα−sinαsinαcosα], then A+A′=I, if the value of α is

In a ΔABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.

Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:(i) A(−1,−2) B(1, 0), C (−1, 2), D(−3, 0)(ii) A(−3, 5) B(3, 1), C (0, 3), D(−1, −4)(iii) A(4, 5) B(7, 6), C (4, 3), D(1, 2)

Question 11 Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC).

PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP.

23. An equilateral triangle has area A root 3.Three circles are drawn with their centres at the vertices of the triangle.Diameter of each circle is equal to the length of each side of the triangle.The area of the triangle not included in any of the circles is?

Question 67Extend the line segment on both sides to meet the coordinate axes. What are the coordinates of the points, where this line meets the X-axis and the Y-axis?

The volume of a right circular cone is 9856 cm3.If the diameter of the base is 28 cm,find:(i) height of the cone(ii) slant height of the cone(iii) curved surface area of the cone.

If O is the centre of the circle, find the value of x in each of the following figures.

10. n(A) =20, n,(B)=18 and n(A intersection B) =5, then n(A-B) is ?

Find the solution of the simultaneous system of linear equation by substitution method X/a+y/b=1/2X/√a+y/√b=1/√2 (a>0,b>0

In the figure below, two vertices of a parallelogram are joined to the mid points of two sides. Then, the lines divide the diagonal in the picture into _______ equal parts.3

With the help of a compass and a ruler draw a circle congruent to the circle shown below:

Read the following bar graph and answer the following questions:(i) What information is given by the bar graph?(ii) In which year the export is minimum?(iii) In which year the import is maximum?(iv) In which year the difference of the values of export and import is maximum?

In Figure, PS = QR and ∠SPQ=∠RQP.Prove that PR = QS and ∠QPR=∠PQS.

In figure, value of x is:

Complete the series -1,6,7,18,23,38,?

In a parallelogram ABCD, if AB→ = a→ and BC→ =b→, then AC→= _ and BD→ = ___.