32581 + Interview Questions in Mathematics

1.	Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is(i) a king (ii) of red colour (iii) a face card (iv) a queen [CBSE 2014]
Answer» Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is (i) a king (ii) of red colour (iii) a face card (iv) a queen [CBSE 2014]

Discussion

2.	Question 4Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
Answer» Question 4 Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Discussion

3.	Adjoint of the matrix N⎡⎢⎣−4−3−3101443⎤⎥⎦ is
Answer» $\begin{matrix} A d j o i n t o f t h e m a t r i x N ⎡ ⎢ ⎣ \begin{matrix} - 4 & - 3 & - 3 1 & 0 & 1 4 & 4 & 3 \end{matrix} ⎤ ⎥ ⎦ \end{matrix}$ is

Discussion

4.	A tent in the form of a square pyramid has a height of 12 cm and the base edge length is 18 cm. Find the total cloth required to build the tent.
Answer» A tent in the form of a square pyramid has a height of 12 cm and the base edge length is 18 cm. Find the total cloth required to build the tent.

Discussion

5.	1 + cot2A= cosec2A is valid for
Answer» 1 + $c o t^{2} A$ = $c o s e c^{2} A$ is valid for

Discussion

6.	The curved surface area of a cone is 440 sq. cm and slant height is 10 cm. Find the radius of the cone.
Answer» The curved surface area of a cone is 440 sq. cm and slant height is 10 cm. Find the radius of the cone.

Discussion

7.	The 12th term of an AP is −13 and the sum of its first four terms is 24. Find the sum of its first 10 terms. [CBSE 2015]
Answer» The 12th term of an AP is −13 and the sum of its first four terms is 24. Find the sum of its first 10 terms. [CBSE 2015]

Discussion

8.	Write the following symbolic statements in words.(i) 43∈ Q (ii) -2∉N (iii) P = {p \| p is an odd number}
Answer» Write the following symbolic statements in words. (i) $\frac{4}{3} \in$ Q (ii) $- 2 \notin$ N (iii) P = {p \| p is an odd number}

Discussion

9.	State the SSS-similarity criterion.
Answer» State the SSS-similarity criterion.

Discussion

10.	A conical shaped container with a height of 30 cm has the area of its base equal to 100 cm2. Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.
Answer» A conical shaped container with a height of 30 cm has the area of its base equal to 100 $c m^{2}$ . Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.

Discussion

11.	If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.
Answer» If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Discussion

12.	In fig., circles C(O,r) and C(O′,r2) touch internally at a point A and AB is a chord of the circle C (O,r) intersecting C(O′,r2) at C. Prove that AC = CB. [3 MARKS]
Answer» In fig., circles C(O,r) and $C (O^{'}, \frac{r}{2})$ touch internally at a point A and AB is a chord of the circle C (O,r) intersecting $C (O^{'}, \frac{r}{2})$ at C. Prove that AC = CB. [3 MARKS]

12.

In fig., circles C(O,r) and C(O′,r2) touch internally at a point A and AB is a chord of the circle C (O,r) intersecting C(O′,r2) at C. Prove that AC = CB. [3 MARKS]

Answer»

In fig., circles C(O,r) and $C (O^{'}, \frac{r}{2})$ touch internally at a point A and AB is a chord of the circle C (O,r) intersecting $C (O^{'}, \frac{r}{2})$ at C. Prove that AC = CB. [3 MARKS]

Discussion

13.	Calculate the median for the following distribution. Marks obtainedNumber of studentsBelow 106Below 2015Below 3029Below 4041Below 5060Below 6070
Answer» Calculate the median for the following distribution. $\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}$

Discussion

14.	if the nth term of an AP is 6n-5 then find the sum of n terms of AP in terms of n
Answer» if the nth term of an AP is 6n-5 then find the sum of n terms of AP in terms of n

Discussion

15.	Find the value of x?x + y = 53x - y = 3
Answer» Find the value of x? x + y = 5 3x - y = 3

Discussion

16.	What is radius-ratio rule?
Answer» What is radius-ratio rule?

Discussion

17.	Solve the following systems of equations:5x+y-2x-y=-115x+y+7x-y=10
Answer» Solve the following systems of equations: $\frac{5}{x + y} - \frac{2}{x - y} = - 1 \frac{15}{x + y} + \frac{7}{x - y} = 10$

Discussion

18.	Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.
Answer» Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.

Discussion

19.	25×34 = 2592
Answer» $2^{5} \times 3^{4}$ = 2592

Discussion

20.	Find the median from the following data: MarksNo. of studentsBelow 1012Below 2032Below 3057Below 4080Below 5092Below 60116Below 70164Below 80200
Answer» Find the median from the following data: $\begin{matrix} Marks & No. of students Below 10 & 12 Below 20 & 32 Below 30 & 57 Below 40 & 80 Below 50 & 92 Below 60 & 116 Below 70 & 164 Below 80 & 200 \end{matrix}$

Discussion

21.	Is sin + cos =√2,then evaluate: tan + cot
Answer» Is sin + cos =√2,then evaluate: tan + cot

Discussion

22.	Prove that the tangent of any point of a circle is perpendicular to the radius through the point of contact.
Answer» Prove that the tangent of any point of a circle is perpendicular to the radius through the point of contact.

Discussion

23.	If a = 2b, then a : b =(a) 2 : 1(b) 1 : 2(c) 3 : 4(d) 4 : 3
Answer» If a = 2b, then a : b = (a) 2 : 1 (b) 1 : 2 (c) 3 : 4 (d) 4 : 3

Discussion

24.	find the value of limx→∞2x2−3x+117x3+8x2+15x+6
Answer» find the value of $lim x \to \infty \frac{2 x^{2} - 3 x + 11}{7 x^{3} + 8 x^{2} + 15 x + 6}$

Discussion

25.	In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,
Answer» In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,

25.

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,

Answer»

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,

Discussion

26.	What is the product of (x2–9x)/(x+5) and (3x+15)/(x–9)?
Answer» What is the product of $(x^{2} - 9 x) / (x + 5)$ and $(3 x + 15) / (x - 9)$ ?

Discussion

27.	A sector of a circle of radius 4 cm contains an angle of 30°. Find the area of the sector.
Answer» A sector of a circle of radius 4 cm contains an angle of 30°. Find the area of the sector.

Discussion

28.	Find the sum of first 24 terms of an AP whose nth term is given by an=3+2n.
Answer» Find the sum of first $24$ terms of an AP whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$ .

Discussion

29.	The sum of the first 1000 positive integers is ___.
Answer» The sum of the first 1000 positive integers is ___.

Discussion

30.	By increasing the list price of a book by ₹10, a person can buy 10 books less for ₹1200. The original price of the book was :
Answer» By increasing the list price of a book by ₹10, a person can buy 10 books less for ₹1200. The original price of the book was :

Discussion

31.	Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
Answer» Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).

Discussion

32.	In the given figure O is the centre of circle, ∠BAD = 750 & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.
Answer» In the given figure O is the centre of circle, ∠BAD = 75⁰ & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.

32.

In the given figure O is the centre of circle, ∠BAD = 750 & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.

Answer»

In the given figure O is the centre of circle, ∠BAD = 75⁰ & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.

Discussion

33.	Sailor Raju covered a distance of 8 km. in 1 hr. and 40 minutes down stream and return to the starting point. If the speed of the stream is 2 km/hr, find the speed of the boat is still water.
Answer» Sailor Raju covered a distance of 8 km. in 1 hr. and 40 minutes down stream and return to the starting point. If the speed of the stream is 2 km/hr, find the speed of the boat is still water.

Discussion

34.	LCM of 60, 45 is
Answer» LCM of 60, 45 is

Discussion

35.	A cyclic quadrilateral ABCD is such that AB= BC, AD = DC. If AC⊥BD and ∠CAD = 30°, then ∠ABC equals1) 15°2) 30°3) 60°4) 120°
Answer» A cyclic quadrilateral ABCD is such that AB= BC, AD = DC. If AC⊥BD and ∠CAD = 30°, then ∠ABC equals 1) 15° 2) 30° 3) 60° 4) 120°

Discussion

36.	Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(i) 2, 4, 8, 16 …(ii) (iii) − 1.2, − 3.2, − 5.2, − 7.2 …(iv) − 10, − 6, − 2, 2 …(v) (vi) 0.2, 0.22, 0.222, 0.2222 ….(vii) 0, − 4, − 8, − 12 …(viii) (ix) 1, 3, 9, 27 …(x) a, 2a, 3a, 4a …(xi) a, a2, a3, a4 …(xii) (xiii) (xiv) 12, 32, 52, 72 …(xv) 12, 52, 72, 73 …
Answer» Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 … (ii) (iii) − 1.2, − 3.2, − 5.2, − 7.2 … (iv) − 10, − 6, − 2, 2 … (v) (vi) 0.2, 0.22, 0.222, 0.2222 …. (vii) 0, − 4, − 8, − 12 … (viii) (ix) 1, 3, 9, 27 … (x) a, 2a, 3a, 4a … (xi) a, a², a³, a⁴ … (xii) (xiii) (xiv) 1², 3², 5², 7² … (xv) 1², 5², 7², 73 …

36.

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(i) 2, 4, 8, 16 …(ii) (iii) − 1.2, − 3.2, − 5.2, − 7.2 …(iv) − 10, − 6, − 2, 2 …(v) (vi) 0.2, 0.22, 0.222, 0.2222 ….(vii) 0, − 4, − 8, − 12 …(viii) (ix) 1, 3, 9, 27 …(x) a, 2a, 3a, 4a …(xi) a, a2, a3, a4 …(xii) (xiii) (xiv) 12, 32, 52, 72 …(xv) 12, 52, 72, 73 …

Answer»

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(i) 2, 4, 8, 16 …

(ii)

(iii) − 1.2, − 3.2, − 5.2, − 7.2 …

(iv) − 10, − 6, − 2, 2 …

(v)

(vi) 0.2, 0.22, 0.222, 0.2222 ….

(vii) 0, − 4, − 8, − 12 …

(viii)

(ix) 1, 3, 9, 27 …

(x) a, 2a, 3a, 4a …

(xi) a, a², a³, a⁴ …

(xii)

(xiii)

(xiv) 1², 3², 5², 7² …

(xv) 1², 5², 7², 73 …

Discussion

37.	If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?(a) 26th(b) 27th(c) 28th(d) none of these.
Answer» If the sum of n terms of an A.P. is 3n² + 5n then which of its terms is 164? (a) 26th (b) 27th (c) 28th (d) none of these.

Discussion

38.	If a=4^i+6^j and b=3^j+4^k, then the vector form of the component of a along b is
Answer» If $a = 4^i + 6^j$ and $b = 3^j + 4^k$ , then the vector form of the component of a along b is

Discussion

39.	Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a - 1) x + 3y - 5 = 0 3x + (b-1) y - 2 = 0
Answer» Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a - 1) x + 3y - 5 = 0 3x + (b-1) y - 2 = 0

39.

Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a - 1) x + 3y - 5 = 0 3x + (b-1) y - 2 = 0

Answer»

Determine the values of a and b so that the following system of linear equations have infinitely many solutions:

(2a - 1) x + 3y - 5 = 0

3x + (b-1) y - 2 = 0

Discussion

40.	If x = 2t3 and y = 3t2, then value of is
Answer» If x = 2t3 and y = 3t2, then value of is

Discussion

41.	What is the difference between mesomeric and inductive effect
Answer» What is the difference between mesomeric and inductive effect

Discussion

42.	8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by one man alone and one boy alone to finish the work
Answer» 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by one man alone and one boy alone to finish the work

Discussion

43.	∑ fx=5x+2, ∑ f=12. If the mean of the distribution is 6, what is the value of x?
Answer» $\sum f x = 5 x + 2$ , $\sum f = 12$ . If the mean of the distribution is 6, what is the value of x?

Discussion

44.	Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner
Answer» Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

44.

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

Answer»

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x

Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

Discussion

45.	In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?
Answer» In the figure $△ A B C$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

45.

In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Answer»

In the figure $△ A B C$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Discussion

46.	If the nth term of an A.P. is (2n + 1), then the sum, of its first three terms is(a) 6n + 3(b) 15(c) 12(d) 21
Answer» If the n^th term of an A.P. is (2n + 1), then the sum, of its first three terms is (a) 6n + 3 (b) 15 (c) 12 (d) 21

Discussion

47.	42.If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the former of an equatoon in two variable and draw the graph of the taking the constant force as 5 unit. Also read from the graph the graphone the work done when the distance travelled by the body is (1) 2 unit (2) 0 unit
Answer» 42.If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the former of an equatoon in two variable and draw the graph of the taking the constant force as 5 unit. Also read from the graph the graphone the work done when the distance travelled by the body is (1) 2 unit (2) 0 unit

Discussion

48.	Red balls are arranged in rows to form an equilateral triangle. The first row consists of one ball; second row consists of two and so on up to n rows. If 669 more red balls are added, then all the balls can be arranged in the shape of a square and each of its sides then contains 8 balls less than each side of the triangle. Find the initial number of balls.
Answer» Red balls are arranged in rows to form an equilateral triangle. The first row consists of one ball; second row consists of two and so on up to n rows. If 669 more red balls are added, then all the balls can be arranged in the shape of a square and each of its sides then contains 8 balls less than each side of the triangle. Find the initial number of balls.

Discussion

49.	The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?
Answer» The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

Discussion

50.	As observed from top of a 150 m tall light house, the angles of depression of two ships approaching it are 30∘ and 45∘. If one ship is directly behind the other, find the distance between the two ships.
Answer» As observed from top of a 150 m tall light house, the angles of depression of two ships approaching it are $30^{\circ}$ and $45^{\circ}$ . If one ship is directly behind the other, find the distance between the two ships.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is(i) a king (ii) of red colour (iii) a face card (iv) a queen [CBSE 2014]

Question 4Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Adjoint of the matrix N⎡⎢⎣−4−3−3101443⎤⎥⎦ is

A tent in the form of a square pyramid has a height of 12 cm and the base edge length is 18 cm. Find the total cloth required to build the tent.

1 + cot2A= cosec2A is valid for

The curved surface area of a cone is 440 sq. cm and slant height is 10 cm. Find the radius of the cone.

The 12th term of an AP is −13 and the sum of its first four terms is 24. Find the sum of its first 10 terms. [CBSE 2015]

Write the following symbolic statements in words.(i) 43∈ Q (ii) -2∉N (iii) P = {p | p is an odd number}

State the SSS-similarity criterion.

A conical shaped container with a height of 30 cm has the area of its base equal to 100 cm2. Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

In fig., circles C(O,r) and C(O′,r2) touch internally at a point A and AB is a chord of the circle C (O,r) intersecting C(O′,r2) at C. Prove that AC = CB. [3 MARKS]

Calculate the median for the following distribution. Marks obtainedNumber of studentsBelow 106Below 2015Below 3029Below 4041Below 5060Below 6070

if the nth term of an AP is 6n-5 then find the sum of n terms of AP in terms of n

Find the value of x?x + y = 53x - y = 3

What is radius-ratio rule?

Solve the following systems of equations:5x+y-2x-y=-115x+y+7x-y=10

Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.

25×34 = 2592

Find the median from the following data: MarksNo. of studentsBelow 1012Below 2032Below 3057Below 4080Below 5092Below 60116Below 70164Below 80200

Is sin + cos =√2,then evaluate: tan + cot

Prove that the tangent of any point of a circle is perpendicular to the radius through the point of contact.

If a = 2b, then a : b =(a) 2 : 1(b) 1 : 2(c) 3 : 4(d) 4 : 3

find the value of limx→∞2x2−3x+117x3+8x2+15x+6

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,

What is the product of (x2–9x)/(x+5) and (3x+15)/(x–9)?

A sector of a circle of radius 4 cm contains an angle of 30°. Find the area of the sector.

Find the sum of first 24 terms of an AP whose nth term is given by an=3+2n.

The sum of the first 1000 positive integers is ___.

By increasing the list price of a book by ₹10, a person can buy 10 books less for ₹1200. The original price of the book was :

Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).

In the given figure O is the centre of circle, ∠BAD = 750 &amp; chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.

Sailor Raju covered a distance of 8 km. in 1 hr. and 40 minutes down stream and return to the starting point. If the speed of the stream is 2 km/hr, find the speed of the boat is still water.

LCM of 60, 45 is

A cyclic quadrilateral ABCD is such that AB= BC, AD = DC. If AC⊥BD and ∠CAD = 30°, then ∠ABC equals1) 15°2) 30°3) 60°4) 120°

If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?(a) 26th(b) 27th(c) 28th(d) none of these.

If a=4^i+6^j and b=3^j+4^k, then the vector form of the component of a along b is

Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a - 1) x + 3y - 5 = 0 3x + (b-1) y - 2 = 0

If x = 2t3 and y = 3t2, then value of is

What is the difference between mesomeric and inductive effect

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by one man alone and one boy alone to finish the work

∑ fx=5x+2, ∑ f=12. If the mean of the distribution is 6, what is the value of x?

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

If the nth term of an A.P. is (2n + 1), then the sum, of its first three terms is(a) 6n + 3(b) 15(c) 12(d) 21

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

As observed from top of a 150 m tall light house, the angles of depression of two ships approaching it are 30∘ and 45∘. If one ship is directly behind the other, find the distance between the two ships.

In the given figure O is the centre of circle, ∠BAD = 750 & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.