32581 + Interview Questions in Mathematics

1.	Question 3 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Answer» Question 3 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Discussion

2.	Please tell me the correct definition of CO-PRIME numbers with examples
Answer» Please tell me the correct definition of CO-PRIME numbers with examples

Discussion

3.	In the given figure, AB and CD are two diameters of a circle (with centre O) Perpendicular to each other and OD is the diameter of the smaller circle, If OA = 7 cm, What the area of the shaded region.
Answer» In the given figure, AB and CD are two diameters of a circle (with centre O) Perpendicular to each other and OD is the diameter of the smaller circle, If OA = 7 cm, What the area of the shaded region.

3.

In the given figure, AB and CD are two diameters of a circle (with centre O) Perpendicular to each other and OD is the diameter of the smaller circle, If OA = 7 cm, What the area of the shaded region.

Answer»

In the given figure, AB and CD are two diameters of a circle (with centre O) Perpendicular to each other and OD is the diameter of the smaller circle, If OA = 7 cm, What the area of the shaded region.

Discussion

4.	A circle has a radius of 5 cm. What is the nature of its perimeter?
Answer» A circle has a radius of 5 cm. What is the nature of its perimeter?

Discussion

5.	The wheel of a motorcycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr ?
Answer» The wheel of a motorcycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr ?

Discussion

6.	If a,b,c are in A.P. and a,c−b,b−a are in G.P., wherea≠b≠c, then a:b:c is ___.
Answer» If $a, b, c$ are in A.P. and $a, c - b, b - a$ are in G.P., where $a \neq b \neq c$ , then $a : b : c$ is ___.

Discussion

7.	Solve each of the following equations by using the method of completing the square: x2−(√2+1)x+√2=0
Answer» Solve each of the following equations by using the method of completing the square: $x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

Discussion

8.	Find the coordinates of the circumcentre of the triangle whose vertices are (8,6) , (8,-2) and (2,-2) also, find its circumradius.
Answer» Find the coordinates of the circumcentre of the triangle whose vertices are (8,6) , (8,-2) and (2,-2) also, find its circumradius.

Discussion

9.	If x=a sinθ and y=btanθ,then prove thata2x2−b2y2=1
Answer» If $x = a s i n θ a n d y = b t a n θ$ ,then prove that $\frac{a^{2}}{x^{2}} - \frac{b^{2}}{y^{2}} = 1$

Discussion

10.	Compute the mode from the following data: Classinterval1−56−1011−1516−2021−2526−3031−3536−4041−4546−50Frequency381318282013864
Answer» Compute the mode from the following data: $\begin{matrix} Class interval & 1 - 5 & 6 - 10 & 11 - 15 & 16 - 20 & 21 - 25 & 26 - 30 & 31 - 35 & 36 - 40 & 41 - 45 & 46 - 50 Frequency & 3 & 8 & 13 & 18 & 28 & 20 & 13 & 8 & 6 & 4 \end{matrix}$

Discussion

11.	ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, show that PQRS is a rhombus.
Answer» ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

Discussion

12.	Find the perimeter of a semicircular protractor whose diameter is 14 cm.
Answer» Find the perimeter of a semicircular protractor whose diameter is 14 cm.

Discussion

13.	If a number 'x' is chosen from the nos. 1,2,3 and number 'y' is selected from the numbers 1,4,9. Find the probability that xy=10
Answer» If a number 'x' is chosen from the nos. 1,2,3 and number 'y' is selected from the numbers 1,4,9. Find the probability that xy=10

Discussion

14.	A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.
Answer» A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

Discussion

15.	The vectors →a=3^i−2^j+2^k and →b=−^i−2^k are the adjacent sides of a parallelogram.Then,angle between its diagonals is
Answer» The vectors $\to a = 3^i - 2^j + 2^k$ and $\to b = -^i - 2^k$ are the adjacent sides of a parallelogram.Then,angle between its diagonals is

Discussion

16.	If f(x) is a polynomial such that f(a) = f(b2) = f(c3) = 0, then which of the following expressions is a factor of f(x)
Answer» If f(x) is a polynomial such that f(a) = f( $\frac{b}{2}$ ) = f( $\frac{c}{3}$ ) = 0, then which of the following expressions is a factor of f(x)

Discussion

17.	Find the HCF of 1190 and 1445 using Euclid's Algorithm. Express the HCF in the form of 1190m+1445n.
Answer» Find the HCF of 1190 and 1445 using Euclid's Algorithm. Express the HCF in the form of 1190m+1445n.

Discussion

18.	Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2. Reason : The opposite sides of a parallelogram are equal. Chose from the following alternatives:
Answer» Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2. Reason : The opposite sides of a parallelogram are equal. Chose from the following alternatives:

18.

Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2. Reason : The opposite sides of a parallelogram are equal. Chose from the following alternatives:

Answer»

Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2.

Reason : The opposite sides of a parallelogram are equal.

Chose from the following alternatives:

Discussion

19.	What is the solution for the two lines given in the graph?
Answer» What is the solution for the two lines given in the graph?

Discussion

20.	Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices parallelogram. Show that ABCD is not a rectangle.
Answer» Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices parallelogram. Show that ABCD is not a rectangle.

Discussion

21.	Write the value of cos 1o cos 2o .... cos 180o.
Answer» Write the value of cos $1^{o}$ cos $2^{o}$ .... cos $180^{o}$ .

Discussion

22.	A ladder of length 13 m rests against a wall. If it reaches a height of 12 m from the ground, then the distance of the foot of the ladder from the wall is ___ m.
Answer» A ladder of length 13 m rests against a wall. If it reaches a height of 12 m from the ground, then the distance of the foot of the ladder from the wall is ___ m.

Discussion

23.	A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is (r sin β cosecα2)
Answer» A round balloon of radius r subtends an angle $α$ at the eye of the observer while the angle of elevation of its centre is $β$ . Prove that the height of the centre of the balloon is $(r s i n β c o s e c \frac{α}{2})$

Discussion

24.	If A = {Prime numbers between 19 and 23}, then A is __________.
Answer» If A = {Prime numbers between 19 and 23}, then A is __________.

Discussion

25.	A coin is tossed thrice. What is the probability of getting a Head in the second toss and a Tail in the third? [2 MARKS]
Answer» A coin is tossed thrice. What is the probability of getting a Head in the second toss and a Tail in the third? [2 MARKS]

Discussion

26.	Question 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) a=−1, d=12
Answer» Question 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) $a = - 1, d = \frac{1}{2}$

Discussion

27.	If α and β are the zeros of the quadratic polynomial f(x)=x2−5x+6, then evaluate: α2β2+β2α2 [4 MARKS]
Answer» If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - 5 x + 6$ , then evaluate: $\frac{α^{2}}{β^{2}} + \frac{β^{2}}{α^{2}}$ [4 MARKS]

Discussion

28.	In the given figure, if ∠ACE=43∘ and ∠CAF=62∘, then match the following correctly. ListIListIIA.∠ai.62∘B.∠cii.105∘C.∠biii.13∘
Answer» In the given figure, if $∠ A C E = 43^{\circ}$ and $∠ C A F = 62^{\circ}$ , then match the following correctly. $\begin{matrix} L i s t I & L i s t I I A . ∠ a & i {.62}^{\circ} B . ∠ c & i i . 105^{\circ} C . ∠ b & i i i . 13^{\circ} \end{matrix}$

Discussion

29.	If y=cosθ+isinθ, then the value of y+1y
Answer» If y=cos $θ$ +isin $θ$ , then the value of y+ $\frac{1}{y}$

Discussion

30.	Question 8 Tick the correct answer and justify: ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is (A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4
Answer» Question 8 Tick the correct answer and justify: ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is (A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

Discussion

31.	Question 14 Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm
Answer» Question 14 Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm

Discussion

32.	The sum of two numbers is 15. The sum of their reciprocals is 518. Find the numbers.
Answer» The sum of two numbers is 15. The sum of their reciprocals is $\frac{5}{18}$ . Find the numbers.

32.

The sum of two numbers is 15. The sum of their reciprocals is 518. Find the numbers.

Answer»

The sum of two numbers is 15. The sum of their reciprocals is $\frac{5}{18}$ . Find the numbers.

Discussion

33.	How many spades are present in a deck of cards?
Answer» How many spades are present in a deck of cards?

Discussion

34.	A copper wire when bent in the form of a square encloses an area of 484 cm2. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.
Answer» A copper wire when bent in the form of a square encloses an area of $484 c m^{2}$ . The same wire is now bent in the form of a circle. Find the area enclosed by the circle.

Discussion

35.	Which of the following is reduced form of the equation (2x−1)2 = x2 + 2.
Answer» Which of the following is reduced form of the equation $(2 x - 1)^{2}$ = $x^{2}$ + 2.

Discussion

36.	The radius of a circle is 7π cm. Then the area of the circle in cm2 is ?
Answer» The radius of a circle is $\frac{7}{π}$ cm. Then the area of the circle in $c m^{2}$ is ?

Discussion

37.	In figure, AOOC=BOOD=12 and AB = 5cm. Find the value of DC.
Answer» In figure, $\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}$ and AB = 5cm. Find the value of DC.

37.

In figure, AOOC=BOOD=12 and AB = 5cm. Find the value of DC.

Answer»

In figure, $\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}$ and AB = 5cm. Find the value of DC.

Discussion

38.	Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (iv) 40,36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36
Answer» Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (iv) 40,36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36

Discussion

39.	From the ogive curve, answer the following question. How many students secured marks between 50% and 70% ? ___
Answer» From the ogive curve, answer the following question. How many students secured marks between 50% and 70% ? ___

39.

From the ogive curve, answer the following question. How many students secured marks between 50% and 70% ? ___

Answer»

From the ogive curve, answer the following question.

How many students secured marks between 50% and 70% ?

___

Discussion

40.	The first term of an A. P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A. P.
Answer» The first term of an A. P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A. P.

Discussion

41.	4x3+4x2−x−1 is a multiple of-
Answer» $4 x^{3} + 4 x^{2} - x - 1$ is a multiple of-

Discussion

42.	To reach playground Ramu has to travel 4 km from his home. Ramu travelled 2 km by bus with a speed of 40 km/hr and remaining 2 km by bicycle with speed of 8 km/hr. Find the average speed.
Answer» To reach playground Ramu has to travel 4 km from his home. Ramu travelled 2 km by bus with a speed of 40 km/hr and remaining 2 km by bicycle with speed of 8 km/hr. Find the average speed.

Discussion

43.	What is the simplest way to do mid term splitting for larger digit no. Like x^2+2x-195 plzz explain via more examples.
Answer» What is the simplest way to do mid term splitting for larger digit no. Like x^2+2x-195 plzz explain via more examples.

Discussion

44.	The unit's digit in the expansion of 2317^759
Answer» The unit's digit in the expansion of 2317^759

Discussion

45.	All three sides of a right triangle are integers and one side has a length of 11 units. Area of the triangle in square units lies between: 1) 1 and 100 2) 100 and 200 3) 200 and 300 4) More than 300
Answer» All three sides of a right triangle are integers and one side has a length of 11 units. Area of the triangle in square units lies between: 1) 1 and 100 2) 100 and 200 3) 200 and 300 4) More than 300

Discussion

46.	A man is a watching a bulb glow which is 3 meters above him. If he is standing 3 m away from the point directly below the bulb, what is the angle of elevation in degrees? ___
Answer» A man is a watching a bulb glow which is 3 meters above him. If he is standing 3 m away from the point directly below the bulb, what is the angle of elevation in degrees? ___

Discussion

47.	Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals.
Answer» Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals.

Discussion

48.	Consider the expansion of (x+y)20. 12th term from the end = pth term from the beginning. Find the value of p
Answer» Consider the expansion of $(x + y)^{20}$ . $12^{t h}$ term from the end = $p^{t h}$ term from the beginning. Find the value of p

Discussion

49.	Find the value of k for which the system kx + 2y = 5 3x + y = 1 has (i) a unique solution, and (ii) no solution.
Answer» Find the value of k for which the system kx + 2y = 5 3x + y = 1 has (i) a unique solution, and (ii) no solution.

49.

Find the value of k for which the system kx + 2y = 5 3x + y = 1 has (i) a unique solution, and (ii) no solution.

Answer»

Find the value of k for which the system

kx + 2y = 5

3x + y = 1

has (i) a unique solution, and (ii) no solution.

Discussion

50.	Pikachu tells the truth on Mondays, Thursdays, and Saturdays, but lies on all the other days of the week. One day he said, “I will tell the truth tomorrow.” On which day of the week did he make this statement?
Answer» Pikachu tells the truth on Mondays, Thursdays, and Saturdays, but lies on all the other days of the week. One day he said, “I will tell the truth tomorrow.” On which day of the week did he make this statement?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 3 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Please tell me the correct definition of CO-PRIME numbers with examples

In the given figure, AB and CD are two diameters of a circle (with centre O) Perpendicular to each other and OD is the diameter of the smaller circle, If OA = 7 cm, What the area of the shaded region.

A circle has a radius of 5 cm. What is the nature of its perimeter?

The wheel of a motorcycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr ?

If a,b,c are in A.P. and a,c−b,b−a are in G.P., wherea≠b≠c, then a:b:c is ___.

Solve each of the following equations by using the method of completing the square: x2−(√2+1)x+√2=0

Find the coordinates of the circumcentre of the triangle whose vertices are (8,6) , (8,-2) and (2,-2) also, find its circumradius.

If x=a sinθ and y=btanθ,then prove thata2x2−b2y2=1

Compute the mode from the following data: Classinterval1−56−1011−1516−2021−2526−3031−3536−4041−4546−50Frequency381318282013864

ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

Find the perimeter of a semicircular protractor whose diameter is 14 cm.

If a number 'x' is chosen from the nos. 1,2,3 and number 'y' is selected from the numbers 1,4,9. Find the probability that xy=10

A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

The vectors →a=3^i−2^j+2^k and →b=−^i−2^k are the adjacent sides of a parallelogram.Then,angle between its diagonals is

If f(x) is a polynomial such that f(a) = f(b2) = f(c3) = 0, then which of the following expressions is a factor of f(x)

Find the HCF of 1190 and 1445 using Euclid's Algorithm. Express the HCF in the form of 1190m+1445n.

Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2. Reason : The opposite sides of a parallelogram are equal. Chose from the following alternatives:

What is the solution for the two lines given in the graph?

Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices parallelogram. Show that ABCD is not a rectangle.

Write the value of cos 1o cos 2o .... cos 180o.

A ladder of length 13 m rests against a wall. If it reaches a height of 12 m from the ground, then the distance of the foot of the ladder from the wall is ___ m.

A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is (r sin β cosecα2)

If A = {Prime numbers between 19 and 23}, then A is __________.

A coin is tossed thrice. What is the probability of getting a Head in the second toss and a Tail in the third? [2 MARKS]

Question 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) a=−1, d=12

If α and β are the zeros of the quadratic polynomial f(x)=x2−5x+6, then evaluate: α2β2+β2α2 [4 MARKS]

In the given figure, if ∠ACE=43∘ and ∠CAF=62∘, then match the following correctly. ListIListIIA.∠ai.62∘B.∠cii.105∘C.∠biii.13∘

If y=cosθ+isinθ, then the value of y+1y

Question 8 Tick the correct answer and justify: ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is (A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

Question 14 Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm

The sum of two numbers is 15. The sum of their reciprocals is 518. Find the numbers.

How many spades are present in a deck of cards?

A copper wire when bent in the form of a square encloses an area of 484 cm2. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.

Which of the following is reduced form of the equation (2x−1)2 = x2 + 2.

The radius of a circle is 7π cm. Then the area of the circle in cm2 is ?

In figure, AOOC=BOOD=12 and AB = 5cm. Find the value of DC.

Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (iv) 40,36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36

From the ogive curve, answer the following question. How many students secured marks between 50% and 70% ? ___

The first term of an A. P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A. P.

4x3+4x2−x−1 is a multiple of-

To reach playground Ramu has to travel 4 km from his home. Ramu travelled 2 km by bus with a speed of 40 km/hr and remaining 2 km by bicycle with speed of 8 km/hr. Find the average speed.

What is the simplest way to do mid term splitting for larger digit no. Like x^2+2x-195 plzz explain via more examples.

The unit's digit in the expansion of 2317^759

All three sides of a right triangle are integers and one side has a length of 11 units. Area of the triangle in square units lies between: 1) 1 and 100 2) 100 and 200 3) 200 and 300 4) More than 300

A man is a watching a bulb glow which is 3 meters above him. If he is standing 3 m away from the point directly below the bulb, what is the angle of elevation in degrees? ___

Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals.

Consider the expansion of (x+y)20. 12th term from the end = pth term from the beginning. Find the value of p

Find the value of k for which the system kx + 2y = 5 3x + y = 1 has (i) a unique solution, and (ii) no solution.

Pikachu tells the truth on Mondays, Thursdays, and Saturdays, but lies on all the other days of the week. One day he said, “I will tell the truth tomorrow.” On which day of the week did he make this statement?