32581 + Interview Questions in Mathematics

1.	Can line segment AB be divided by drawing 2 parallel rays from A and B constructed at an obtuse angle to it? If yes, how? If not, Why? [2 MARKS]
Answer» Can line segment AB be divided by drawing 2 parallel rays from A and B constructed at an obtuse angle to it? If yes, how? If not, Why? [2 MARKS]

Discussion

2.	A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Answer» A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Discussion

3.	Find the value of:sec 29∘cosec 61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘. ___
Answer» Find the value of: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$ . ___

Discussion

4.	Rashi is going to plant 54 oak trees and 27 pine trees. Rashi would like to plant the trees in all rows that have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Rashi can have in each row? What is the total number of rows she needs to plant? [4 MARKS]
Answer» Rashi is going to plant 54 oak trees and 27 pine trees. Rashi would like to plant the trees in all rows that have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Rashi can have in each row? What is the total number of rows she needs to plant? [4 MARKS]

Discussion

5.	Question 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs. 387 inclusive of taxes of Rs. 43. Find the tax %.
Answer» Question 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs. 387 inclusive of taxes of Rs. 43. Find the tax $%$ .

5.

Question 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs. 387 inclusive of taxes of Rs. 43. Find the tax %.

Answer»

Question 82

Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs. 387 inclusive of taxes of Rs. 43. Find the tax $%$ .

Discussion

6.	Find the sum and the product of the roots of the equation : [1 MARK] 5x2–10x+3=0
Answer» Find the sum and the product of the roots of the equation : [1 MARK] $5 x^{2} - 10 x + 3 = 0$

Discussion

7.	King, queen, ace, and jack of diamonds are removed from a pack of 52 cards. The remaining cards in the pack are well shuffled. A card is drawn randomly from the remaining cards. Find the probability of getting a card of a jack.
Answer» King, queen, ace, and jack of diamonds are removed from a pack of 52 cards. The remaining cards in the pack are well shuffled. A card is drawn randomly from the remaining cards. Find the probability of getting a card of a jack.

Discussion

8.	ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is .
Answer» ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is .

Discussion

9.	Which of the following are correct statements?
Answer» Which of the following are correct statements?

Discussion

10.	If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B.
Answer» If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B.

Discussion

11.	The solution of a linear equation is not affected when
Answer» The solution of a linear equation is not affected when

Discussion

12.	Which of the following statements is/are correct? 1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. 2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.
Answer» Which of the following statements is/are correct? 1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. 2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.

12.

Which of the following statements is/are correct? 1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. 2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.

Answer»

Which of the following statements is/are correct?

1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent.

2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.

Discussion

13.	A rectangular sheet of paper is made to cover a cylinder such that the width of the rectangular sheet is equal to the height of the cylinder and length is just enough to go round the cylinder. Which of the following option correctly represents the curved surface area of the cylinder?
Answer» A rectangular sheet of paper is made to cover a cylinder such that the width of the rectangular sheet is equal to the height of the cylinder and length is just enough to go round the cylinder. Which of the following option correctly represents the curved surface area of the cylinder?

Discussion

14.	Find the volume of a sphere of radius 5.6 cm.
Answer» Find the volume of a sphere of radius 5.6 cm.

Discussion

15.	Find the value of sin(60+θ) - cos(30-θ).
Answer» Find the value of sin(60+ $θ$ ) - cos(30- $θ$ ).

Discussion

16.	The distance between the points (5, 5) and (3, 3) is ___.
Answer» The distance between the points (5, 5) and (3, 3) is ___.

Discussion

17.	Two articles A and B are sold for Rs. 1,167 making 5% profit on A and 7% profit on B. If the two articles are sold for Rs. 1,165, a profit of 7% is made on A and a profit of 5% is made on B. Find the cost price of each article.
Answer» Two articles A and B are sold for Rs. 1,167 making 5% profit on A and 7% profit on B. If the two articles are sold for Rs. 1,165, a profit of 7% is made on A and a profit of 5% is made on B. Find the cost price of each article.

Discussion

18.	The following is known about an AP: Sp=a,Sq=b,Sr=c What is the value of E=ap(q−r)+bq(r−p)+cr(p−q)? [4 MARKS]
Answer» The following is known about an AP: $S_{p} = a, S_{q} = b, S_{r} = c$ What is the value of $E = \frac{a}{p} (q - r) + \frac{b}{q} (r - p) + \frac{c}{r} (p - q)$ ? [4 MARKS]

Discussion

19.	The following table gives the frequency distribution of marks obtained by 28 students. Marks30313233Frequency57106 Construct the cumulative frequency table for the given data.
Answer» The following table gives the frequency distribution of marks obtained by $28$ students. $\begin{matrix} Marks & 30 & 31 & 32 & 33 Frequency & 5 & 7 & 10 & 6 \end{matrix}$ Construct the cumulative frequency table for the given data.

19.

The following table gives the frequency distribution of marks obtained by 28 students. Marks30313233Frequency57106 Construct the cumulative frequency table for the given data.

Answer»

The following table gives the frequency distribution of marks obtained by $28$ students.

$\begin{matrix} Marks & 30 & 31 & 32 & 33 Frequency & 5 & 7 & 10 & 6 \end{matrix}$

Construct the cumulative frequency table for the given data.

Discussion

20.	The value of x in the factor tree is:
Answer» The value of x in the factor tree is:

20.

The value of x in the factor tree is:

Answer»

The value of x in the factor tree is:

Discussion

21.	The following table shows marks secured by 140 students in an examination: MarksNumber of students0−102010−202420−304030−403640−5020 Calculate mean marks by the step deviation method.
Answer» The following table shows marks secured by 140 students in an examination: $\begin{matrix} Marks & Number of students 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$ Calculate mean marks by the step deviation method.

Discussion

22.	PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=1200, then ∠OPQ is
Answer» PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120⁰, then ∠OPQ is

Discussion

23.	Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………
Answer» Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

23.

Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Answer»

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

Discussion

24.	Evaluate 2x2+5x−32x2+7x−6÷2x2+5x−32x2−x−6
Answer» Evaluate $\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 7 x - 6} \div \frac{2 x^{2} + 5 x - 3}{2 x^{2} - x - 6}$

Discussion

25.	A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?
Answer» A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?

25.

A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?

Answer»

A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?

Discussion

26.	Numbers that can be expressed as a ratio of p and q where p and q are integers and q≠0 are called __numbers.
Answer» Numbers that can be expressed as a ratio of p and q where p and q are integers and $q \neq 0$ are called __numbers.

Discussion

27.	Question 1 In a ΔPQR, PR2−PQ2=QR2 and M is a point on side PR such that QM⊥PR. Prove that QM2=PM×MR .
Answer» Question 1 In a $Δ P Q R,$ $P R^{2} - P Q^{2} = Q R^{2}$ and M is a point on side PR such that $Q M ⊥ P R$ . Prove that $Q M^{2} = P M \times M R$ .

Discussion

28.	Question 1 (ii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x - 2y = 2
Answer» Question 1 (ii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x - 2y = 2

Discussion

29.	If α and β are the zeros of the quadratic polynomial f(x)=x2−x−4, then evaluate: [4 MARKS] (i) α3+β3 (ii) 1α3+1β3
Answer» If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - x - 4$ , then evaluate: [4 MARKS] (i) $α^{3} + β^{3}$ (ii) $\frac{1}{α^{3}} + \frac{1}{β^{3}}$

Discussion

30.	Find the probability of getting at least two heads if three coins are tossed simultaneously.
Answer» Find the probability of getting at least two heads if three coins are tossed simultaneously.

Discussion

31.	By selling an item for ₹75, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.
Answer» By selling an item for ₹75, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.

Discussion

32.	Each of letters of the word PILOTS is on separate cards, face down on the table. If you pick a card at random, what is the probability that the letter will be a T or a L?
Answer» Each of letters of the word PILOTS is on separate cards, face down on the table. If you pick a card at random, what is the probability that the letter will be a T or a L?

Discussion

33.	In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?
Answer» In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

33.

In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

Answer»

In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

Discussion

34.	A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per m2 is X. Find X
Answer» A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per $m^{2}$ is X. Find X

34.

A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per m2 is X. Find X

Answer»

A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per $m^{2}$ is X. Find X

Discussion

35.	If x + y = 6 and x - y = 2 , then x =___.
Answer» If x + y = 6 and x - y = 2 , then x =___.

Discussion

36.	If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram where A and C are opposite vertices. Find the values of a and b.
Answer» If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram where A and C are opposite vertices. Find the values of a and b.

Discussion

37.	IF A and B are two events such that P(A)=14,P(B)=12 and P(A∩B)=18 Find P (not A and not B)
Answer» IF A and B are two events such that $P (A) = \frac{1}{4}, P (B) = \frac{1}{2}$ and $P (A \cap B) = \frac{1}{8}$ Find P (not A and not B)

Discussion

38.	Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
Answer» Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Discussion

39.	In a G.P., 3rd term is 16 and the 6th term is 128. Find the 10th term.
Answer» In a G.P., 3rd term is 16 and the 6th term is 128. Find the 10th term.

Discussion

40.	Two sides of a ΔABC are 18cm and 20 cm, and the angle between them is 100∘ as shown in the figure. The area of the ΔABC will be equal to ___ [sin 80∘=0.98]
Answer» Two sides of a $Δ A B C$ are 18cm and 20 cm, and the angle between them is $100^{\circ}$ as shown in the figure. The area of the $Δ A B C$ will be equal to ___ $[s i n 80^{\circ} = 0.98]$

40.

Two sides of a ΔABC are 18cm and 20 cm, and the angle between them is 100∘ as shown in the figure. The area of the ΔABC will be equal to ___ [sin 80∘=0.98]

Answer»

Two sides of a $Δ A B C$ are 18cm and 20 cm, and the angle between them is $100^{\circ}$ as shown in the figure. The area of the $Δ A B C$ will be equal to ___ $[s i n 80^{\circ} = 0.98]$

Discussion

41.	Question 25 (ii) Is the following argument correct? Give reasons for your answer. If a die is thrown, there are two possible outcomes – an odd number or an even number. Therefore, the probability of getting an odd number is 12.
Answer» Question 25 (ii) Is the following argument correct? Give reasons for your answer. If a die is thrown, there are two possible outcomes – an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$ .

Discussion

42.	Which of the following given sequences can be represented as a polynomial in one variable?
Answer» Which of the following given sequences can be represented as a polynomial in one variable?

Discussion

43.	What is the number of arcs drawn during construction when the method of Triangle Construction 1 is used? __
Answer» What is the number of arcs drawn during construction when the method of Triangle Construction 1 is used? __

Discussion

44.	Circles with the same centre and different radii are called __ circles.
Answer» Circles with the same centre and different radii are called __ circles.

Discussion

45.	An AP consists of 50 terms of which the third term is 12 and the last term is 106. 29th term of this AP will be ___
Answer» An AP consists of 50 terms of which the third term is 12 and the last term is 106. $29^{t h}$ term of this AP will be ___

Discussion

46.	The number of obtuse angles in the given figure is a) 2 b) 3 c) 4 d) 5
Answer» The number of obtuse angles in the given figure is a) $2$ b) $3$ c) $4$ d) $5$

46.

The number of obtuse angles in the given figure is a) 2 b) 3 c) 4 d) 5

Answer»

The number of obtuse angles in the given figure is
a) $2$
b) $3$
c) $4$
d) $5$

Discussion

47.	If the third and the 9th terms of an A. P. be 4 and -8 respectively, find which term is zero ?
Answer» If the third and the $9^{t h}$ terms of an A. P. be 4 and -8 respectively, find which term is zero ?

Discussion

48.	Question 8 A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.
Answer» Question 8 A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$ . Find the height of the pedestal.

Discussion

49.	Which of the following options is equal to tan A1−cot A+cot A1−tan A ?
Answer» Which of the following options is equal to $\frac{tan A}{1 - cot A} + \frac{cot A}{1 - tan A}$ ?

Discussion

50.	Solve 15x=10y=6z 7x+9y+9z=344
Answer» Solve $15 x = 10 y = 6 z$ $7 x + 9 y + 9 z = 344$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Can line segment AB be divided by drawing 2 parallel rays from A and B constructed at an obtuse angle to it? If yes, how? If not, Why? [2 MARKS]

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Find the value of:sec 29∘cosec 61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘. ___

Question 82 Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs. 387 inclusive of taxes of Rs. 43. Find the tax %.

Find the sum and the product of the roots of the equation : [1 MARK] 5x2–10x+3=0

King, queen, ace, and jack of diamonds are removed from a pack of 52 cards. The remaining cards in the pack are well shuffled. A card is drawn randomly from the remaining cards. Find the probability of getting a card of a jack.

ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is .

Which of the following are correct statements?

If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B.

The solution of a linear equation is not affected when

Which of the following statements is/are correct? 1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. 2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.

A rectangular sheet of paper is made to cover a cylinder such that the width of the rectangular sheet is equal to the height of the cylinder and length is just enough to go round the cylinder. Which of the following option correctly represents the curved surface area of the cylinder?

Find the volume of a sphere of radius 5.6 cm.

Find the value of sin(60+θ) - cos(30-θ).

The distance between the points (5, 5) and (3, 3) is ___.

Two articles A and B are sold for Rs. 1,167 making 5% profit on A and 7% profit on B. If the two articles are sold for Rs. 1,165, a profit of 7% is made on A and a profit of 5% is made on B. Find the cost price of each article.

The following is known about an AP: Sp=a,Sq=b,Sr=c What is the value of E=ap(q−r)+bq(r−p)+cr(p−q)? [4 MARKS]

The following table gives the frequency distribution of marks obtained by 28 students. Marks30313233Frequency57106 Construct the cumulative frequency table for the given data.

The value of x in the factor tree is:

The following table shows marks secured by 140 students in an examination: MarksNumber of students0−102010−202420−304030−403640−5020 Calculate mean marks by the step deviation method.

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=1200, then ∠OPQ is

Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Evaluate 2x2+5x−32x2+7x−6÷2x2+5x−32x2−x−6

A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?

Numbers that can be expressed as a ratio of p and q where p and q are integers and q≠0 are called __numbers.

Question 1 In a ΔPQR, PR2−PQ2=QR2 and M is a point on side PR such that QM⊥PR. Prove that QM2=PM×MR .

Question 1 (ii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x - 2y = 2

If α and β are the zeros of the quadratic polynomial f(x)=x2−x−4, then evaluate: [4 MARKS] (i) α3+β3 (ii) 1α3+1β3

Find the probability of getting at least two heads if three coins are tossed simultaneously.

By selling an item for ₹75, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.

Each of letters of the word PILOTS is on separate cards, face down on the table. If you pick a card at random, what is the probability that the letter will be a T or a L?

In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per m2 is X. Find X

If x + y = 6 and x - y = 2 , then x =___.

If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram where A and C are opposite vertices. Find the values of a and b.

IF A and B are two events such that P(A)=14,P(B)=12 and P(A∩B)=18 Find P (not A and not B)

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

In a G.P., 3rd term is 16 and the 6th term is 128. Find the 10th term.

Two sides of a ΔABC are 18cm and 20 cm, and the angle between them is 100∘ as shown in the figure. The area of the ΔABC will be equal to ___ [sin 80∘=0.98]

Question 25 (ii) Is the following argument correct? Give reasons for your answer. If a die is thrown, there are two possible outcomes – an odd number or an even number. Therefore, the probability of getting an odd number is 12.

Which of the following given sequences can be represented as a polynomial in one variable?

What is the number of arcs drawn during construction when the method of Triangle Construction 1 is used? __

Circles with the same centre and different radii are called __ circles.

An AP consists of 50 terms of which the third term is 12 and the last term is 106. 29th term of this AP will be ___

The number of obtuse angles in the given figure is a) 2 b) 3 c) 4 d) 5

If the third and the 9th terms of an A. P. be 4 and -8 respectively, find which term is zero ?

Question 8 A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.

Which of the following options is equal to tan A1−cot A+cot A1−tan A ?

Solve 15x=10y=6z 7x+9y+9z=344