32581 + Interview Questions in Mathematics

1.	Solve each of the following systems of equations graphically: 2x−3y+13=0,3x−2y+12=0.
Answer» Solve each of the following systems of equations graphically: $2 x - 3 y + 13 = 0, 3 x - 2 y + 12 = 0.$

1.

Solve each of the following systems of equations graphically: 2x−3y+13=0,3x−2y+12=0.

Answer»

Solve each of the following systems of equations graphically:

$2 x - 3 y + 13 = 0, 3 x - 2 y + 12 = 0.$

2.	The sum of digits of a two number is 9.the digitsin the ones place is 1more than 3 times the digit in the tens place.find the number.
Answer» The sum of digits of a two number is 9.the digitsin the ones place is 1more than 3 times the digit in the tens place.find the number.

Discussion

3.	Question 61In the given figure,a) What is AE + EC?b) What is AC - EC?c) What is BD - BE?d) What is BD - DE?
Answer» Question 61 In the given figure, a) What is AE + EC? b) What is AC - EC? c) What is BD - BE? d) What is BD - DE?

3.

Question 61In the given figure,a) What is AE + EC?b) What is AC - EC?c) What is BD - BE?d) What is BD - DE?

Answer»

Question 61

In the given figure,

a) What is AE + EC?

b) What is AC - EC?

c) What is BD - BE?

d) What is BD - DE?

Discussion

4.	The sum of n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Answer» The sum of n terms of an A.P. is $4 n^{2}$ + 2n. Find the nth term of this A.P.

Discussion

5.	A boy 1.5 metres tall, sees the top of a building under construction at an elevation of 30°. The building is completed, adding 10 more metres to its height; and then the boy sees the top at an elevation of 60° from the same spot. What is the total height of the completed building?
Answer» A boy 1.5 metres tall, sees the top of a building under construction at an elevation of 30°. The building is completed, adding 10 more metres to its height; and then the boy sees the top at an elevation of 60° from the same spot. What is the total height of the completed building?

Discussion

6.	The circumference of a circle of radius π is .
Answer» The circumference of a circle of radius $π$ is .

Discussion

7.	Find the next five terms of each of the following sequences given by:(i) a1 = 1, an = an−1+2, n ≥ 2(ii) a1 = a2 = 2, an = an−1 − 3, n > 2(iii) a1 = -1, an = an-1n, n≥2(iv) a1 = 4, an = 4an−1 + 3, n > 1.
Answer» Find the next five terms of each of the following sequences given by: (i) a₁ = 1, a_n = a_n−1+2, n ≥ 2 (ii) a₁ = a₂ = 2, a_n = a_n−1 − 3, n > 2 (iii) $a_{1} = - 1, a_{n} = \frac{a_{n} - 1}{n}, n \geq 2$ (iv) a₁ = 4, a_n = 4a_n−1 + 3, n > 1.

Discussion

8.

Calculate the median from the following data: Rent (in Rs.): 15−25 25−35 35−45 45−55 55−65 65−75 75−85 85−95 No. of Houses: 8 10 15 25 40 20 15 7

Answer» Calculate the median from the following data:

Rent (in Rs.):	15−25	25−35	35−45	45−55	55−65	65−75	75−85	85−95
No. of Houses:	8	10	15	25	40	20	15	7

Discussion

9.	Write the following sets in the set-builder form:(i) {3,6,9,12}(ii) {2,4,8,16,32}(iii) {5,25,125,625}(iv) {2,4,6,....}(v) {1,4,9,....,100}
Answer» Write the following sets in the set-builder form: $(i)$ ${3, 6, 9, 12}$ $(i i)$ ${2, 4, 8, 16, 32}$ $(i i i)$ ${5, 25, 125, 625}$ $(i v)$ ${2, 4, 6, . . . .}$ $(v)$ ${1, 4, 9, . . . ., 100}$

Discussion

10.	The sequence of all even numbers is a/an ___ arithmetic progression and that of the first 100 odd numbers is a/an ___ arithmetic progression.
Answer» The sequence of all even numbers is a/an ___ arithmetic progression and that of the first 100 odd numbers is a/an ___ arithmetic progression.

Discussion

11.	Find the sum of the following finite series.(a) 1 + 2 + 4 + ………+ 256(b) (c) 1 + 0.1 + 0.01 + ……. +(0.1)9
Answer» Find the sum of the following finite series. (a) 1 + 2 + 4 + ………+ 256 (b) (c) 1 + 0.1 + 0.01 + ……. +(0.1)⁹

11.

Find the sum of the following finite series.(a) 1 + 2 + 4 + ………+ 256(b) (c) 1 + 0.1 + 0.01 + ……. +(0.1)9

Answer»

Find the sum of the following finite series.

(a) 1 + 2 + 4 + ………+ 256

(b)

(c) 1 + 0.1 + 0.01 + ……. +(0.1)⁹

Discussion

12.	If p and q are two prime number, then what is their HCF?
Answer» If p and q are two prime number, then what is their HCF?

Discussion

13.	A tent is in the form of a cylinder of diameter 4.2 m and height 4m, surmounted by a cone of equal base and height 2.8 m. find the cost of canvas for making the tent at Rs. 100 per sq.m.
Answer» A tent is in the form of a cylinder of diameter 4.2 m and height 4m, surmounted by a cone of equal base and height 2.8 m. find the cost of canvas for making the tent at Rs. 100 per sq.m.

Discussion

14.	In triangle ABC,∠A=130∘,BC=10cm. The diameter of the circumcircle is [sin 50∘=0.76]
Answer» In triangle $A B C, ∠ A = 130^{\circ}, B C = 10 c m$ . The diameter of the circumcircle is $[s i n 50^{\circ} = 0.76]$

14.

In triangle ABC,∠A=130∘,BC=10cm. The diameter of the circumcircle is [sin 50∘=0.76]

Answer»

In triangle $A B C, ∠ A = 130^{\circ}, B C = 10 c m$ . The diameter of the circumcircle is $[s i n 50^{\circ} = 0.76]$

Discussion

15.	An A. P. consists of 60 terms. If the first and last terms be 7 and 125 respectively, find the 31st term.
Answer» An A. P. consists of 60 terms. If the first and last terms be 7 and 125 respectively, find the $31^{s t}$ term.

Discussion

16.	If 2x + 3y = 12 and 3x − 2y = 5 then(a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2
Answer» If 2x + 3y = 12 and 3x − 2y = 5 then (a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2

Discussion

17.	Find the area of triangle ACD in the given figure.
Answer» Find the area of triangle ACD in the given figure.

Discussion

18.	A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank
Answer» A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank

Discussion

19.	Find the area bounded by }y=x^3-x and }y=x^2+x.
Answer» Find the area bounded by }y=x^3-x and }y=x^2+x.

Discussion

20.	Question 4In the figure, if ∠ABC=20∘, then ∠AOC is equal to(A) 20∘(B) 40∘(C) 60∘(D) 10∘
Answer» Question 4 In the figure, if $∠ A B C = 20^{\circ}$ , then $∠ A O C$ is equal to (A) $20^{\circ}$ (B) $40^{\circ}$ (C) $60^{\circ}$ (D) $10^{\circ}$

Discussion

21.	Sonu was making sand pyramids at the beach. He designed his pyramids with a base edge of 10 cm and height 33 cm. He would go collect wet sand with his small cylindrical bucket of radius 5 cm and 7 cm height. How many times does he need to collect the wet sand in order to construct his sand pyramid?
Answer» Sonu was making sand pyramids at the beach. He designed his pyramids with a base edge of 10 cm and height 33 cm. He would go collect wet sand with his small cylindrical bucket of radius 5 cm and 7 cm height. How many times does he need to collect the wet sand in order to construct his sand pyramid?

Discussion

22.	If A = {1, 2, 3}, B = {0, 1, 2, 4, 6, 8} and f: A→B be a function defined by f(x) = 2x. Represent this function as a set of ordered pairs.
Answer» If A = {1, 2, 3}, B = {0, 1, 2, 4, 6, 8} and f: A $\to$ B be a function defined by f(x) = 2x. Represent this function as a set of ordered pairs.

Discussion

23.	What is the angle of elevation of a vertical flagstaff of height 100√3 m from a point 100 m from its foot?
Answer» What is the angle of elevation of a vertical flagstaff of height 100 $\sqrt{3}$ m from a point 100 m from its foot?

Discussion

24.	11.2 friends jhon and daisy ,both have one dice each.both of them toss the dice.if the highest number among the two dice is less than 5 ,jhon wins otherwise daisy wins.who has the highest chance of winning?
Answer» 11.2 friends jhon and daisy ,both have one dice each.both of them toss the dice.if the highest number among the two dice is less than 5 ,jhon wins otherwise daisy wins.who has the highest chance of winning?

Discussion

25.	When we divide the estimated value of company into small part, each part so obtained is called ___
Answer» When we divide the estimated value of company into small part, each part so obtained is called ___

Discussion

26.	If a:b = 2:5 and x:y = 9:15 then the value of 5ay−2bx7bx−3ay
Answer» If a:b = 2:5 and x:y = 9:15 then the value of $\frac{5 a y - 2 b x}{7 b x - 3 a y}$

Discussion

27.	Let Xn={1,2,3,....,n} and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3. (For example, if n=5,A can be ϕ,{2} or {1,5} among others). When n=10, let the probability that 1∈A be p and let the probability that 2∈A be q. Then
Answer» Let $X_{n} = {1, 2, 3, . . . ., n}$ and let a subset $A$ of $X_{n}$ be chosen so that every pair of elements of $A$ differ by at least $3.$ (For example, if $n = 5, A$ can be $ϕ, {2} or {1, 5}$ among others). When $n = 10,$ let the probability that $1 \in A$ be $p$ and let the probability that $2 \in A$ be $q .$ Then

Discussion

28.	If the point P(x, y) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Answer» If the point P(x, y) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.

Discussion

29.	A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.
Answer» A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.

Discussion

30.	The tops of two poles of heights 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:
Answer» The tops of two poles of heights 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

Discussion

31.	Find the first term and common difference for each of the A.P.(1) 5, 1, –3, –7,...(2) 0.6, 0.9, 1.2,1.5,...(3) 127, 135, 143, 151,...(4) 14,34,54,74,....
Answer» Find the first term and common difference for each of the A.P. (1) 5, 1, –3, –7,... (2) 0.6, 0.9, 1.2,1.5,... (3) 127, 135, 143, 151,... (4) $\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, . . . .$

Discussion

32.	The system kx-y=2 and 6x-2y=3 has a unique solution only when (a) k=0 (b)k≠0 (c) k=3 (d) k≠3
Answer» The system kx-y=2 and 6x-2y=3 has a unique solution only when (a) k=0 (b) $k \neq 0$ (c) k=3 (d) $k \neq 3$

32.

The system kx-y=2 and 6x-2y=3 has a unique solution only when (a) k=0 (b)k≠0 (c) k=3 (d) k≠3

Answer»

The system kx-y=2 and 6x-2y=3 has a unique solution only when

(a) k=0 (b) $k \neq 0$ (c) k=3 (d) $k \neq 3$

Discussion

33.	Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.
Answer» Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Discussion

34.	on dividing a polynomial p(x)by a 3x+1the quotient and the remainder were 2x-3 and -2 find p(x)
Answer» on dividing a polynomial p(x)by a 3x+1the quotient and the remainder were 2x-3 and -2 find p(x)

Discussion

35.	find the value o \sqrt[3]{25/16} +\sqrt[3]{49/16} +\sqrt[3]{35/16}
Answer» find the value o \sqrt[3]{25/16} +\sqrt[3]{49/16} +\sqrt[3]{35/16}

Discussion

36.	If sinθ=a2-b2a2+b2, find the values of all T-ratios of θ.
Answer» If $\sin θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}$ , find the values of all T-ratios of $θ$ .

Discussion

37.	What is the trigonometric ratio that connects the opposite side to adjacent side?
Answer» What is the trigonometric ratio that connects the opposite side to adjacent side?

Discussion

38.	The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Answer» The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

Discussion

39.	The difference between two positive numbers is 8. Their product is 180. Find the numbers.
Answer» The difference between two positive numbers is 8. Their product is 180. Find the numbers.

Discussion

40.	The prefixes ‘suc’, ‘sur’ and ‘sus’ mean _________.
Answer» The prefixes ‘suc’, ‘sur’ and ‘sus’ mean _________.

40.

The prefixes ‘suc’, ‘sur’ and ‘sus’ mean _________.

Answer»

The prefixes ‘suc’, ‘sur’ and ‘sus’ mean _________.

Discussion

41.	ABCD is a rectangle with AD = 20cm. If the shaded area is 400 cm2, then the shortest distance between the semi-circles is :
Answer» ABCD is a rectangle with AD = 20cm. If the shaded area is 400 cm², then the shortest distance between the semi-circles is :

Discussion

42.	Can y +5 be the remainder on the division of a polynomial f(y) by y -2?
Answer» Can y +5 be the remainder on the division of a polynomial f(y) by y -2?

Discussion

43.	A card is drawn is drawn from a well shuffled pack of 52 cards.what is the probability that it is an ace of heart..?
Answer» A card is drawn is drawn from a well shuffled pack of 52 cards.what is the probability that it is an ace of heart..?

Discussion

44.	Let f:R−(35}→R−(35} be defined by f(x)=3x+25x−3. Then
Answer» Let $f : R - (\frac{3}{5}} \to R - (\frac{3}{5}} b e d e f i n e d b y f (x) = \frac{3 x + 2}{5 x - 3} .$ Then

Discussion

45.	Two adjacent sides of a parallelogram are of lengths 6 cm & 7 cm & the diagonal connecting the ends of these sides is of length 8 cm. Find the area of the parallelogram.
Answer» Two adjacent sides of a parallelogram are of lengths 6 cm & 7 cm & the diagonal connecting the ends of these sides is of length 8 cm. Find the area of the parallelogram.

Discussion

46.	a picnic group for Shimla consists of students whose ages are in AP the common difference being 3 months if the youngest student Neeraj is just 12 years old the sum of Ages of all students is 375 years find the number of students in a group
Answer» a picnic group for Shimla consists of students whose ages are in AP the common difference being 3 months if the youngest student Neeraj is just 12 years old the sum of Ages of all students is 375 years find the number of students in a group

Discussion

47.	The nth term of the sequence 5×(1+6),10×(2+6),15×(3+6)___ is
Answer» The $n^{t h}$ term of the sequence $5 \times (1 + 6), 10 \times (2 + 6), 15 \times (3 + 6)$ ___ is

Discussion

48.	Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles. [CBSE 2011]
Answer» Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles. [CBSE 2011]

Discussion

49.	If ∆ABC is right angled at C , then the value of cos ( A + B ) is
Answer» If $∆ A B C$ is right angled at C , then the value of cos ( $A + B$ ) is

Discussion

50.	The sum of the numerator and denominator of a certain fraction is 8.If 2 is added to the numerator and to the denominator, the value of the fraction is increased by 4/35.Find the fraction.
Answer» The sum of the numerator and denominator of a certain fraction is 8.If 2 is added to the numerator and to the denominator, the value of the fraction is increased by 4/35.Find the fraction.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve each of the following systems of equations graphically: 2x−3y+13=0,3x−2y+12=0.

The sum of digits of a two number is 9.the digitsin the ones place is 1more than 3 times the digit in the tens place.find the number.

Question 61In the given figure,a) What is AE + EC?b) What is AC - EC?c) What is BD - BE?d) What is BD - DE?

The sum of n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.

A boy 1.5 metres tall, sees the top of a building under construction at an elevation of 30°. The building is completed, adding 10 more metres to its height; and then the boy sees the top at an elevation of 60° from the same spot. What is the total height of the completed building?

The circumference of a circle of radius π is .

Find the next five terms of each of the following sequences given by:(i) a1 = 1, an = an−1+2, n ≥ 2(ii) a1 = a2 = 2, an = an−1 − 3, n > 2(iii) a1 = -1, an = an-1n, n≥2(iv) a1 = 4, an = 4an−1 + 3, n > 1.

Calculate the median from the following data: Rent (in Rs.): 15−25 25−35 35−45 45−55 55−65 65−75 75−85 85−95 No. of Houses: 8 10 15 25 40 20 15 7

Write the following sets in the set-builder form:(i) {3,6,9,12}(ii) {2,4,8,16,32}(iii) {5,25,125,625}(iv) {2,4,6,....}(v) {1,4,9,....,100}

The sequence of all even numbers is a/an ___ arithmetic progression and that of the first 100 odd numbers is a/an ___ arithmetic progression.

Find the sum of the following finite series.(a) 1 + 2 + 4 + ………+ 256(b) (c) 1 + 0.1 + 0.01 + ……. +(0.1)9

If p and q are two prime number, then what is their HCF?

A tent is in the form of a cylinder of diameter 4.2 m and height 4m, surmounted by a cone of equal base and height 2.8 m. find the cost of canvas for making the tent at Rs. 100 per sq.m.

In triangle ABC,∠A=130∘,BC=10cm. The diameter of the circumcircle is [sin 50∘=0.76]

An A. P. consists of 60 terms. If the first and last terms be 7 and 125 respectively, find the 31st term.

If 2x + 3y = 12 and 3x − 2y = 5 then(a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2

Find the area of triangle ACD in the given figure.

A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank

Find the area bounded by }y=x^3-x and }y=x^2+x.

Question 4In the figure, if ∠ABC=20∘, then ∠AOC is equal to(A) 20∘(B) 40∘(C) 60∘(D) 10∘

Sonu was making sand pyramids at the beach. He designed his pyramids with a base edge of 10 cm and height 33 cm. He would go collect wet sand with his small cylindrical bucket of radius 5 cm and 7 cm height. How many times does he need to collect the wet sand in order to construct his sand pyramid?

If A = {1, 2, 3}, B = {0, 1, 2, 4, 6, 8} and f: A→B be a function defined by f(x) = 2x. Represent this function as a set of ordered pairs.

What is the angle of elevation of a vertical flagstaff of height 100√3 m from a point 100 m from its foot?

11.2 friends jhon and daisy ,both have one dice each.both of them toss the dice.if the highest number among the two dice is less than 5 ,jhon wins otherwise daisy wins.who has the highest chance of winning?

When we divide the estimated value of company into small part, each part so obtained is called ___

If a:b = 2:5 and x:y = 9:15 then the value of 5ay−2bx7bx−3ay

Let Xn={1,2,3,....,n} and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3. (For example, if n=5,A can be ϕ,{2} or {1,5} among others). When n=10, let the probability that 1∈A be p and let the probability that 2∈A be q. Then

If the point P(x, y) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.

A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.

The tops of two poles of heights 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

Find the first term and common difference for each of the A.P.(1) 5, 1, –3, –7,...(2) 0.6, 0.9, 1.2,1.5,...(3) 127, 135, 143, 151,...(4) 14,34,54,74,....

The system kx-y=2 and 6x-2y=3 has a unique solution only when (a) k=0 (b)k≠0 (c) k=3 (d) k≠3

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

on dividing a polynomial p(x)by a 3x+1the quotient and the remainder were 2x-3 and -2 find p(x)

find the value o \sqrt[3]{25/16} +\sqrt[3]{49/16} +\sqrt[3]{35/16}

If sinθ=a2-b2a2+b2, find the values of all T-ratios of θ.

What is the trigonometric ratio that connects the opposite side to adjacent side?

The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

The difference between two positive numbers is 8. Their product is 180. Find the numbers.

The prefixes ‘suc’, ‘sur’ and ‘sus’ mean _________.

ABCD is a rectangle with AD = 20cm. If the shaded area is 400 cm2, then the shortest distance between the semi-circles is :

Can y +5 be the remainder on the division of a polynomial f(y) by y​​​​​​ -2?

A card is drawn is drawn from a well shuffled pack of 52 cards.what is the probability that it is an ace of heart..?

Let f:R−(35}→R−(35} be defined by f(x)=3x+25x−3. Then

Two adjacent sides of a parallelogram are of lengths 6 cm &amp; 7 cm &amp; the diagonal connecting the ends of these sides is of length 8 cm. Find the area of the parallelogram.

a picnic group for Shimla consists of students whose ages are in AP the common difference being 3 months if the youngest student Neeraj is just 12 years old the sum of Ages of all students is 375 years find the number of students in a group

The nth term of the sequence 5×(1+6),10×(2+6),15×(3+6)___ is

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles. [CBSE 2011]

If ∆ABC is right angled at C , then the value of cos ( A + B ) is

The sum of the numerator and denominator of a certain fraction is 8.If 2 is added to the numerator and to the denominator, the value of the fraction is increased by 4/35.Find the fraction.

The sequence of all even numbers is a/an _ arithmetic progression and that of the first 100 odd numbers is a/an _ arithmetic progression.

Can y +5 be the remainder on the division of a polynomial f(y) by y -2?

Two adjacent sides of a parallelogram are of lengths 6 cm & 7 cm & the diagonal connecting the ends of these sides is of length 8 cm. Find the area of the parallelogram.