32581 + Interview Questions in Mathematics

1.	A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The original speed of the train is ___ km/hr.
Answer» A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h r$ less, then it would have taken $3$ hours more to cover the same distance. The original speed of the train is ___ km/hr.

Discussion

2.	Question 7 (iv) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (d) What do you observe?
Answer» Question 7 (iv) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (d) What do you observe?

Discussion

3.	If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are
Answer» If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are

Discussion

4.	In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2. Find the area of △ DEF. (Note: The given figures are not to scale.) __ cm2
Answer» In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ . Find the area of $△$ DEF. (Note: The given figures are not to scale.) __ $c m^{2}$

4.

In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2. Find the area of △ DEF. (Note: The given figures are not to scale.) __ cm2

Answer»

In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ . Find the area of $△$ DEF. (Note: The given figures are not to scale.)

__

c m^{2}

Discussion

5.	Find the number in the position of ‘?’.
Answer» Find the number in the position of ‘?’.

5.

Find the number in the position of ‘?’.

Answer»

Find the number in the position of ‘?’.

Discussion

6.	In an isosceles triangle ABC, if AB = AC=13 cm and the altitude from A on BC is 5 cm find BC.
Answer» In an isosceles triangle ABC, if AB = AC=13 cm and the altitude from A on BC is 5 cm find BC.

Discussion

7.	In a \Delta ABC, prove that: (i)cos (A+B)+cos C =0 (ii)cos(A+B2)=sinC2 (iii)tanA+B2=cotC2
Answer» In a \Delta ABC, prove that: (i)cos (A+B)+cos C =0 $(i i) c o s (\frac{A + B}{2}) = s i n \frac{C}{2}$ $(i i i) t a n \frac{A + B}{2} = c o t \frac{C}{2}$

7.

In a \Delta ABC, prove that: (i)cos (A+B)+cos C =0 (ii)cos(A+B2)=sinC2 (iii)tanA+B2=cotC2

Answer»

In a \Delta ABC, prove that:

(i)cos (A+B)+cos C =0

$(i i) c o s (\frac{A + B}{2}) = s i n \frac{C}{2}$

$(i i i) t a n \frac{A + B}{2} = c o t \frac{C}{2}$

Discussion

8.	If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?
Answer» If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?

Discussion

9.	How do you start off to construct a rhombus inside a parallelogram in which the smaller side is two-third the larger side?
Answer» How do you start off to construct a rhombus inside a parallelogram in which the smaller side is two-third the larger side?

Discussion

10.	What property would you use to find angle PTQ?
Answer» What property would you use to find angle PTQ?

Discussion

11.	The sum of four consecutive numbers in an A.P. with common difference d>0 is 20. If the sum of their squares is 120, then the middle terms are __ and __.
Answer» The sum of four consecutive numbers in an A.P. with common difference $d > 0$ is 20. If the sum of their squares is 120, then the middle terms are __ and __.

Discussion

12.	In similar triangles, 1. The corresponding angles are equal. 2. The corresponding sides are always equal. 3. The corresponding sides are always proportional.
Answer» In similar triangles, 1. The corresponding angles are equal. 2. The corresponding sides are always equal. 3. The corresponding sides are always proportional.

Discussion

13.	Which of the following is/are not a quadratic equation?
Answer» Which of the following is/are not a quadratic equation?

Discussion

14.	In Fig. 7.138, XY \|\| BC. Find the length of XY.
Answer» In Fig. 7.138, XY \|\| BC. Find the length of XY.

14.

In Fig. 7.138, XY || BC. Find the length of XY.

Answer»

In Fig. 7.138, XY || BC. Find the length of XY.

Discussion

15.	What is the total surface area of a hemisphere?
Answer» What is the total surface area of a hemisphere?

Discussion

16.	Using Euclid's division algorithm, find the HCF of 1650 and 847.
Answer» Using Euclid's division algorithm, find the HCF of 1650 and 847.

Discussion

17.	Find the roots of the quadratic equation ax2+bx+c in terms of a, b, c
Answer» Find the roots of the quadratic equation $a x^{2} + b x + c$ in terms of a, b, c

Discussion

18.	What is the value sin θ in the given right triangle, right angled at B?
Answer» What is the value sin $θ$ in the given right triangle, right angled at B?

18.

What is the value sin θ in the given right triangle, right angled at B?

Answer»

What is the value sin $θ$ in the given right triangle, right angled at B?

Discussion

19.	The decimal expansion of 141120 will terminate after how many places?
Answer» The decimal expansion of $\frac{141}{120}$ will terminate after how many places?

Discussion

20.	Express 6' 10” in SI units.
Answer» Express 6^' 10” in SI units.

Discussion

21.	Question 1(e) Find the following product: (−15)×0×(−18)
Answer» Question 1(e) Find the following product: $(- 15) \times 0 \times (- 18)$

Discussion

22.	Question 5(d) Substract: 3a(a+b+c)−2b(a−b+c)from 4c(−a+b+c).
Answer» Question 5(d) Substract: $3 a (a + b + c) - 2 b (a - b + c) f r o m 4 c (- a + b + c) .$

Discussion

23.	Prove that √5 is irrational. [4 MARKS]
Answer» Prove that $\sqrt{5}$ is irrational. [4 MARKS]

Discussion

24.	An ordinary cube has 4 blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is:
Answer» An ordinary cube has 4 blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is:

Discussion

25.	Question 4 Draw an isosceles triangle ABC in which AB=AC = 6 cm and BC=5 cm Construct a triangle PQR similar to ΔABC in which PQ = 8 cm, Also justify the construction. Thinking process (i)Here, for making two similar triangles with one vertex is base We assume that In ΔABC and ΔPQR, vertex B = vertex Q. (ii) In ΔABC and ΔPQR, vertex B = vertex Q. So, we get the required scale factor. Now, construct a ΔABC and then a ΔPBR, similar to ΔABC whose sides are PQAB of the corresponding sides of the ΔABC.
Answer» Question 4 Draw an isosceles triangle ABC in which AB=AC = 6 cm and BC=5 cm Construct a triangle PQR similar to $Δ A B C$ in which PQ = 8 cm, Also justify the construction. Thinking process (i)Here, for making two similar triangles with one vertex is base We assume that In $Δ A B C$ and $Δ P Q R$ , vertex B = vertex Q. (ii) In $Δ A B C$ and $Δ P Q R$ , vertex B = vertex Q. So, we get the required scale factor. Now, construct a $Δ A B C$ and then a $Δ P B R$ , similar to $Δ A B C$ whose sides are $\frac{P Q}{A B}$ of the corresponding sides of the $Δ A B C$ .

Discussion

26.	Find the sum of two consecutive positive integers, such that the sum of their squares is 365.27
Answer» Find the sum of two consecutive positive integers, such that the sum of their squares is 365. 27

Discussion

27.	In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one. He is ………... heir of a rich man.
Answer» In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one. He is ………... heir of a rich man.

27.

In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one. He is ………... heir of a rich man.

Answer»

In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one.

He is ………... heir of a rich man.

Discussion

28.	The radius of a circle and the tangent are perpendicular at the
Answer» The radius of a circle and the tangent are perpendicular at the

Discussion

29.	PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then ∠OPR:∠OPQ =.
Answer» PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then $∠ O P R : ∠ O P Q$ =.

Discussion

30.	From the top of a hill, the angles of depression of two consecutive km stones due east are found to be 30∘ and 45∘. The height of the hill is (a) 12(√3−1) km (b) 12(√3+1) km (c) (√3−1) km (d) (√3+1) km
Answer» From the top of a hill, the angles of depression of two consecutive km stones due east are found to be $30^{\circ}$ and $45^{\circ}$ . The height of the hill is (a) $\frac{1}{2} (\sqrt{3} - 1)$ km (b) $\frac{1}{2} (\sqrt{3} + 1)$ km (c) $(\sqrt{3} - 1)$ km (d) $(\sqrt{3} + 1)$ km

30.

From the top of a hill, the angles of depression of two consecutive km stones due east are found to be 30∘ and 45∘. The height of the hill is (a) 12(√3−1) km (b) 12(√3+1) km (c) (√3−1) km (d) (√3+1) km

Answer»

From the top of a hill, the angles of depression of two consecutive km stones due east are found to be $30^{\circ}$ and $45^{\circ}$ . The height of the hill is

(a) $\frac{1}{2} (\sqrt{3} - 1)$ km

(b) $\frac{1}{2} (\sqrt{3} + 1)$ km

(c) $(\sqrt{3} - 1)$ km

(d) $(\sqrt{3} + 1)$ km

Discussion

31.	Find the fourth proportional to 9, 6, and 3.
Answer» Find the fourth proportional to 9, 6, and 3.

Discussion

32.	The larger of the two supplementary angles exceeds the smaller by 18∘. Find them.
Answer» The larger of the two supplementary angles exceeds the smaller by $18^{\circ}$ . Find them.

Discussion

33.	Three consecutive natural numbers are added and their sum is divided by 3. What is the remainder obtained?
Answer» Three consecutive natural numbers are added and their sum is divided by 3. What is the remainder obtained?

Discussion

34.	The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Answer» The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

Discussion

35.	The area of a circle is 38.5 cm2. The circumference of the circle is (a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm
Answer» The area of a circle is 38.5 $c m^{2}$ . The circumference of the circle is (a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm

35.

The area of a circle is 38.5 cm2. The circumference of the circle is (a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm

Answer»

The area of a circle is 38.5 $c m^{2}$ . The circumference of the circle is

(a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm

Discussion

36.	Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer» Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Discussion

37.	Kiran deposited Rs 200 per month for 36 months in a bank's Recurring Deposit Account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity. [3 MARKS]
Answer» Kiran deposited Rs 200 per month for 36 months in a bank's Recurring Deposit Account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity. [3 MARKS]

Discussion

38.	Question 1 (iii) Evaluate the following: (iii) cos45∘(sec30∘+cosec30∘)
Answer» Question 1 (iii) Evaluate the following: (iii) $\frac{c o s 45^{\circ}}{(s e c 30^{\circ} + c o s e c 30^{\circ})}$

Discussion

39.	Draw two concentric circles of radii 2 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to the other. Measure the lengths of the two tangents. [4 MARKS]
Answer» Draw two concentric circles of radii 2 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to the other. Measure the lengths of the two tangents. [4 MARKS]

Discussion

40.	Prove that a parallelogram circumscribing a circle is a rhombus [4 MARKS]
Answer» Prove that a parallelogram circumscribing a circle is a rhombus [4 MARKS]

Discussion

41.	If one of the zeros of quadratic polynomial (k−1)x2+kx+1 is −3, then find the value of k.
Answer» $If one of the zeros of quadratic polynomial (k - 1) x^{2} + k x + 1 is - 3,$ $then find the value of k .$

Discussion

42.	If cot θ=78, evaluate: (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)
Answer» If $cot θ = \frac{7}{8}$ , evaluate: $\frac{(1 + sin θ) (1 - sin θ)}{(1 + cos θ) (1 - cos θ)}$

Discussion

43.	Dinkar has a recurring deposit account in a bank for a time period of 3.5 years at 9.5 % p.a. He gets Rs 78638 at the time of maturity. What is his monthly installment?
Answer» Dinkar has a recurring deposit account in a bank for a time period of 3.5 years at 9.5 % p.a. He gets Rs 78638 at the time of maturity. What is his monthly installment?

Discussion

44.	If 0∘<θ<90∘, √sec2θ+cosec2θ =
Answer» If $0^{\circ} < θ < 90^{\circ}$ , $\sqrt{s e c^{2} θ + c o s e c^{2} θ}$ =

Discussion

45.	If the polynomials x3 + 3x2 − m and 2x3 − mx + 9 leave the same remainder when they are divided by (x − 2), find the value of m. Also find the remainder.
Answer» If the polynomials $x^{3} + 3 x^{2} - m$ and $2 x^{3} - m x + 9$ leave the same remainder when they are divided by $(x - 2)$ , find the value of $m$ . Also find the remainder.

Discussion

46.	Find the value of x and y for the pair of equations 7x−2yxy = 5 and 8x+6yxy = 15
Answer» Find the value of x and y for the pair of equations $\frac{7 x - 2 y}{x y}$ = 5 and $\frac{8 x + 6 y}{x y}$ = 15

Discussion

47.	Find the inconsistent pair of linear equations from the following.
Answer» Find the inconsistent pair of linear equations from the following.

Discussion

48.	A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.
Answer» A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

Discussion

49.	The sum of two digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.
Answer» The sum of two digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

Discussion

50.	Which of the following is not true for two non-empty sets A and B?
Answer» Which of the following is not true for two non-empty sets A and B?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The original speed of the train is ___ km/hr.

Question 7 (iv) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (d) What do you observe?

If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are

In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2. Find the area of △ DEF. (Note: The given figures are not to scale.) __ cm2

Find the number in the position of ‘?’.

In an isosceles triangle ABC, if AB = AC=13 cm and the altitude from A on BC is 5 cm find BC.

In a \Delta ABC, prove that: (i)cos (A+B)+cos C =0 (ii)cos(A+B2)=sinC2 (iii)tanA+B2=cotC2

If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?

How do you start off to construct a rhombus inside a parallelogram in which the smaller side is two-third the larger side?

What property would you use to find angle PTQ?

The sum of four consecutive numbers in an A.P. with common difference d&gt;0 is 20. If the sum of their squares is 120, then the middle terms are __ and __.

In similar triangles, 1. The corresponding angles are equal. 2. The corresponding sides are always equal. 3. The corresponding sides are always proportional.

Which of the following is/are not a quadratic equation?

In Fig. 7.138, XY || BC. Find the length of XY.

What is the total surface area of a hemisphere?

Using Euclid's division algorithm, find the HCF of 1650 and 847.

Find the roots of the quadratic equation ax2+bx+c in terms of a, b, c

What is the value sin θ in the given right triangle, right angled at B?

The decimal expansion of 141120 will terminate after how many places?

Express 6' 10” in SI units.

Question 1(e) Find the following product: (−15)×0×(−18)

Question 5(d) Substract: 3a(a+b+c)−2b(a−b+c)from 4c(−a+b+c).

Prove that √5 is irrational. [4 MARKS]

An ordinary cube has 4 blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is:

Find the sum of two consecutive positive integers, such that the sum of their squares is 365.27

In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one. He is ………... heir of a rich man.

The radius of a circle and the tangent are perpendicular at the

PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then ∠OPR:∠OPQ =.

From the top of a hill, the angles of depression of two consecutive km stones due east are found to be 30∘ and 45∘. The height of the hill is (a) 12(√3−1) km (b) 12(√3+1) km (c) (√3−1) km (d) (√3+1) km

Find the fourth proportional to 9, 6, and 3.

The larger of the two supplementary angles exceeds the smaller by 18∘. Find them.

Three consecutive natural numbers are added and their sum is divided by 3. What is the remainder obtained?

The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

The area of a circle is 38.5 cm2. The circumference of the circle is (a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Kiran deposited Rs 200 per month for 36 months in a bank's Recurring Deposit Account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity. [3 MARKS]

Question 1 (iii) Evaluate the following: (iii) cos45∘(sec30∘+cosec30∘)

Draw two concentric circles of radii 2 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to the other. Measure the lengths of the two tangents. [4 MARKS]

Prove that a parallelogram circumscribing a circle is a rhombus [4 MARKS]

If one of the zeros of quadratic polynomial (k−1)x2+kx+1 is −3, then find the value of k.

If cot θ=78, evaluate: (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)

Dinkar has a recurring deposit account in a bank for a time period of 3.5 years at 9.5 % p.a. He gets Rs 78638 at the time of maturity. What is his monthly installment?

If 0∘&lt;θ&lt;90∘, √sec2θ+cosec2θ =

If the polynomials x3 + 3x2 − m and 2x3 − mx + 9 leave the same remainder when they are divided by (x − 2), find the value of m. Also find the remainder.

Find the value of x and y for the pair of equations 7x−2yxy = 5 and 8x+6yxy = 15

Find the inconsistent pair of linear equations from the following.

A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

The sum of two digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

Which of the following is not true for two non-empty sets A and B?

The sum of four consecutive numbers in an A.P. with common difference d>0 is 20. If the sum of their squares is 120, then the middle terms are and .

If 0∘<θ<90∘, √sec2θ+cosec2θ =