32581 + Interview Questions in Mathematics

1.	P is a point on the -axis whose ordinate is 8. Q is a point on the line 8 – 3 – 8 = 0 whose abscissa is 4. Calculate the length of PQ.
Answer» P is a point on the -axis whose ordinate is 8. Q is a point on the line 8 – 3 – 8 = 0 whose abscissa is 4. Calculate the length of PQ.

Discussion

2.	The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of resulting distribution X + Y?
Answer» The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of resulting distribution X + Y?

Discussion

3.	Evaluate each of the followingcot2 30°-2 cos2 60°-34sec2 45°-4 sec2 30°
Answer» Evaluate each of the following $\cot^{2} 30 ° - 2 \cos^{2} 60 ° - \frac{3}{4} \sec^{2} 45 ° - 4 \sec^{2} 30 °$

Discussion

4.	Sumit Machine Ltd. issued 50,000 shares of Rs. 100 each at premium of 5%. The shares were payable Rs. 25 on application, Rs. 50 on allotment and Rs. 30 on first and final call. The issue was fully subscribed and money was duly received except the final call on 400 shares. The premium was adjusted on allotment.Give journal entries and prepare balance sheet.
Answer» Sumit Machine Ltd. issued 50,000 shares of Rs. 100 each at premium of 5%. The shares were payable Rs. 25 on application, Rs. 50 on allotment and Rs. 30 on first and final call. The issue was fully subscribed and money was duly received except the final call on 400 shares. The premium was adjusted on allotment. Give journal entries and prepare balance sheet.

Discussion

5.	While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100 km/hr. Find the original speed/hour of the plane.
Answer» While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100 km/hr. Find the original speed/hour of the plane.

Discussion

6.	In an A.P., if the common difference d = – 4, and the seventh term a7 is 4, then find the first term.
Answer» In an A.P., if the common difference d = – 4, and the seventh term a₇ is 4, then find the first term.

Discussion

7.	Find value of x in the given pair of equations. 1x+a=3 1x−a=1
Answer» Find value of x in the given pair of equations. $\frac{1}{x} + a = 3$ $\frac{1}{x} - a = 1$

7.

Find value of x in the given pair of equations. 1x+a=3 1x−a=1

Answer»

Find value of x in the given pair of equations.

$\frac{1}{x} + a = 3$

$\frac{1}{x} - a = 1$

Discussion

8.	If alpha and beta are the zeroes of the quadratic polynomial ax2+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta
Answer» If alpha and beta are the zeroes of the quadratic polynomial ax²+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

8.

If alpha and beta are the zeroes of the quadratic polynomial ax2+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

Answer»

If alpha and beta are the zeroes of the quadratic polynomial

ax²+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

Discussion

9.	Maggie invests ₹9600 on ₹100 shares at ₹80. If the company pays her 18% dividend then what is her percentage return?
Answer» Maggie invests ₹9600 on ₹100 shares at ₹80. If the company pays her $18 %$ dividend then what is her percentage return?

Discussion

10.	What is the chief source of credit in an economy?
Answer» What is the chief source of credit in an economy?

Discussion

11.	Which one of the following cannot be the square of a natural number?
Answer» Which one of the following cannot be the square of a natural number?

Discussion

12.	Look at the frequency distribution table given below: Class interval35−4545−5555−6565−75Frequency8122010 The median of the above distribution is (a) 56.5 (b) 57.5 (c) 58.5 (d) 59
Answer» Look at the frequency distribution table given below: $\begin{matrix} C l a s s i n t e r v a l & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 F r e q u e n c y & 8 & 12 & 20 & 10 \end{matrix}$ The median of the above distribution is (a) 56.5 (b) 57.5 (c) 58.5 (d) 59

12.

Look at the frequency distribution table given below: Class interval35−4545−5555−6565−75Frequency8122010 The median of the above distribution is (a) 56.5 (b) 57.5 (c) 58.5 (d) 59

Answer»

Look at the frequency distribution table given below:

$\begin{matrix} C l a s s i n t e r v a l & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 F r e q u e n c y & 8 & 12 & 20 & 10 \end{matrix}$

The median of the above distribution is

(a) 56.5 (b) 57.5 (c) 58.5 (d) 59

Discussion

13.	State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1.(ii) sec A =for some value of angle A.(iii) cos A is the abbreviation used for the cosecant of angle A.(iv) cot A is the product of cot and A(v) sin θ =, for some angle θ
Answer» State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1. (ii) sec A =for some value of angle A. (iii) cos A is the abbreviation used for the cosecant of angle A. (iv) cot A is the product of cot and A (v) sin θ =, for some angle θ

13.

State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1.(ii) sec A =for some value of angle A.(iii) cos A is the abbreviation used for the cosecant of angle A.(iv) cot A is the product of cot and A(v) sin θ =, for some angle θ

Answer»

State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii) sec A =for some value of angle A.

(iii) cos A is the abbreviation used for the cosecant of angle A.

(iv) cot A is the product of cot and A

(v) sin θ =, for some angle θ

Discussion

14.	Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the even ''three tails show'' and D denote the event ‘a head shows on the first coin”.i. Which events are mutually exclusive ?ii. Which events are simple ?iii. Which events are compound ?
Answer» Three coins are tossed once. Let $A$ denote the event ‘three heads show”, $B$ denote the event “two heads and one tail show”, $C$ denote the even ''three tails show'' and $D$ denote the event ‘a head shows on the first coin”. $i .$ Which events are mutually exclusive ? $i i .$ Which events are simple ? $i i i .$ Which events are compound ?

Discussion

15.	In given figure, the length of BC is
Answer» In given figure, the length of BC is

15.

In given figure, the length of BC is

Answer»

In given figure, the length of BC is

Discussion

16.	The dimensions of a rectangular field are 50 m by 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square meter, respectively, is Rs. 52,000. Find width of the gravel path.
Answer» The dimensions of a rectangular field are 50 m by 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square meter, respectively, is Rs. 52,000. Find width of the gravel path.

Discussion

17.	A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.
Answer» A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string, assuming that there is no slack in the string.

Discussion

18.	What quantity must be added to each term of the ratio x : y so that it may become equal to c : d ?
Answer» What quantity must be added to each term of the ratio x : y so that it may become equal to c : d ?

Discussion

19.	If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Answer» If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

Discussion

20.	OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region (in cm2). ___
Answer» OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region (in $c m^{2}$ ). ___

20.

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region (in cm2). ___

Answer»

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region (in $c m^{2}$ ).

___

Discussion

21.	If the mean of the following data is 17 then the value of p is ___xi10p182125fi1015799
Answer» If the mean of the following data is 17 then the value of p is ___ $\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

21.

If the mean of the following data is 17 then the value of p is ___xi10p182125fi1015799

Answer»

If the mean of the following data is 17 then the value of p is

___

$\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

Discussion

22.	The number of proper subsets of the set {1, 2, 3} is ___.
Answer» The number of proper subsets of the set {1, 2, 3} is ___.

Discussion

23.	How many three digit numbers are divisible by 7
Answer» How many three digit numbers are divisible by 7

Discussion

24.	Find the area of the triangle with coordinates A(-2, 1), B(3, 3) and C(1, -2).
Answer» Find the area of the triangle with coordinates A(-2, 1), B(3, 3) and C(1, -2).

Discussion

25.	Question 10A capsule of medicine is in the shape of a sphere of diameter 3.5 mm.How much medicine in mm3 is needed to fill this capsule?[Assume π=227]
Answer» Question 10 A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine $i n m m^{3}$ is needed to fill this capsule? $[A s s u m e π = \frac{22}{7}]$

Discussion

26.	Find the 11 th term of the arithmetic sequence −9, −2, 5, 12, …
Answer» Find the 11 th term of the arithmetic sequence −9, −2, 5, 12, …

Discussion

27.	Q2. The hypotenuse of a right-angled triangle is 17 cm and the difference between other two sides is 7 cm. find the other two unknown sides.
Answer» Q2. The hypotenuse of a right-angled triangle is 17 cm and the difference between other two sides is 7 cm. find the other two unknown sides.

Discussion

28.	If m times the mth term of an AP is equal to n times the nth term prove that (m+n)th term of AP is 0
Answer» If m times the mth term of an AP is equal to n times the nth term prove that (m+n)th term of AP is 0

Discussion

29.	A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets ₹ 10,206 on maturity, find the value of monthly installments.
Answer» A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets ₹ 10,206 on maturity, find the value of monthly installments.

Discussion

30.	Explain why 3.1416¯ is a rational number.
Answer» Explain why $3 . \bar{1416}$ is a rational number.

Discussion

31.	nta ball is projected from the ground . it just touches the top of 6m high wall at a distance of 4m and strikes the ground 8m behind the wall. calculate angle of projection and velocity of projectionn
Answer» nta ball is projected from the ground . it just touches the top of 6m high wall at a distance of 4m and strikes the ground 8m behind the wall. calculate angle of projection and velocity of projectionn

Discussion

32.	On Jan. 15, 2017, Kusum sold goods for ₹ 30,000 to Pushpa and drew upon her three bills of exchanges of ₹ 10,000 each payable after one month, two months and three months respectively. The first bill was retained by Kusum till its maturity. The second bill was endorsed by her in favour of her creditor Khushboo and the third bill was discounted by her immediately 6% p.a. All the bills were met by Pushpa. Journalise the above transactions in the books of Kusum and Pushpa.
Answer» On Jan. 15, 2017, Kusum sold goods for ₹ 30,000 to Pushpa and drew upon her three bills of exchanges of ₹ 10,000 each payable after one month, two months and three months respectively. The first bill was retained by Kusum till its maturity. The second bill was endorsed by her in favour of her creditor Khushboo and the third bill was discounted by her immediately 6% p.a. All the bills were met by Pushpa. Journalise the above transactions in the books of Kusum and Pushpa.

Discussion

33.	If θ=tan-1a, ϕ=tan-1b and ab=-1, then θ-ϕ=
Answer» If $θ = \tan^{- 1} a$ , $ϕ = \tan^{- 1} b$ and $a b = - 1$ , then $θ - ϕ =$

Discussion

34.	The perimeter of the figure ABCDEFGHIJ is
Answer» The perimeter of the figure ABCDEFGHIJ is

Discussion

35.	Prove that the length of tangents drawn from an external point to a circle are equal.
Answer» Prove that the length of tangents drawn from an external point to a circle are equal.

Discussion

36.	Question 1 (i)Evaluate :sin 18∘cos 72∘
Answer» Question 1 (i) Evaluate : $\frac{s i n 18^{\circ}}{c o s 72^{\circ}}$

Discussion

37.	Find the distance of the point (6,18) from the X-axis.
Answer» Find the distance of the point (6,18) from the X-axis.

Discussion

38.	of the sum of the squares of the zeroes of the quadratic polynomial f(x) = x^{2 }- px +70 is equal to 149 , then the value of p i
Answer» of the sum of the squares of the zeroes of the quadratic polynomial f(x) = x^{2 }- px +70 is equal to 149 , then the value of p i

Discussion

39.	Construct a triangle ABC in which BC is 4 cm, Angle B is 45∘ and AB-AC=1.75 cm.
Answer» Construct a triangle ABC in which BC is 4 cm, Angle B is $45^{\circ}$ and AB-AC=1.75 cm.

Discussion

40.	In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of AB is(a) 8 cm(b) 14 cm(c) 16 cm(d) 136 cm
Answer» In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of AB is (a) 8 cm (b) 14 cm (c) 16 cm (d) $\sqrt{136}$ cm

Discussion

41.	The difference between the squares of two consecutive numbers is 31. Find the numbers
Answer» The difference between the squares of two consecutive numbers is 31. Find the numbers

Discussion

42.	In the adjoining figure, DE \|\| AB,AD = 7 cm, CD = 5 cm and BC = 18 cmFind (i) BE (ii) CE
Answer» In the adjoining figure, DE \|\| AB, AD = 7 cm, CD = 5 cm and BC = 18 cm Find (i) BE (ii) CE

42.

In the adjoining figure, DE || AB,AD = 7 cm, CD = 5 cm and BC = 18 cmFind (i) BE (ii) CE

Answer»

In the adjoining figure, DE || AB,

AD = 7 cm, CD = 5 cm and BC = 18 cm

Find (i) BE (ii) CE

Discussion

43.	Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6.........
Answer» Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6.........

Discussion

44.	Dinkar has a recurring deposit account in a bank for a time period of 3.5 years at 9.5 % p.a. He gets ₹ 78638 at the time of maturity. What is his monthly installment rounded off to nearest whole number ?
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 ₹ 78638 at the time of maturity. What is his monthly installment rounded off to nearest whole number ?

Discussion

45.	Sin 53
Answer» Sin 53

Discussion

46.	If sum of the n terms of a sequence is (n-1)2, find the nth term of the sequence.
Answer» If sum of the n terms of a sequence is (n-1)2, find the nth term of the sequence.

Discussion

47.	Question 3 (iii) Is 43.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯123446789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?
Answer» Question 3 (iii) Is $43. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 123446789$ rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

Discussion

48.	A number ‘s’ is called irrational if it cannot be written in the form of _____ , where p and q are integers and ______.
Answer» A number ‘s’ is called irrational if it cannot be written in the form of _____ , where p and q are integers and ______.

Discussion

49.	If the quotient on dividing x3–3x2+6 by (x–1) is x2+ax+b, find a, b and also the remainder.
Answer» If the quotient on dividing $x^{3} - 3 x^{2} + 6 b y (x - 1) i s x^{2} + a x + b$ , find a, b and also the remainder.

Discussion

50.	Question 14A 15m high tower casts a shadow 24m long at a certain time and at the same time, a telephone pole casts a shadow 16m long. Find the height of the telephone pole.
Answer» Question 14 A 15m high tower casts a shadow 24m long at a certain time and at the same time, a telephone pole casts a shadow 16m long. Find the height of the telephone pole.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

P is a point on the -axis whose ordinate is 8. Q is a point on the line 8 – 3 – 8 = 0 whose abscissa is 4. Calculate the length of PQ.

The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of resulting distribution X + Y?

Evaluate each of the followingcot2 30°-2 cos2 60°-34sec2 45°-4 sec2 30°

In an A.P., if the common difference d = – 4, and the seventh term a7 is 4, then find the first term.

Find value of x in the given pair of equations. 1x+a=3 1x−a=1

If alpha and beta are the zeroes of the quadratic polynomial ax​​​​2+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

Maggie invests ₹9600 on ₹100 shares at ₹80. If the company pays her 18% dividend then what is her percentage return?

What is the chief source of credit in an economy?

Which one of the following cannot be the square of a natural number?

Look at the frequency distribution table given below: Class interval35−4545−5555−6565−75Frequency8122010 The median of the above distribution is (a) 56.5 (b) 57.5 (c) 58.5 (d) 59

State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1.(ii) sec A =for some value of angle A.(iii) cos A is the abbreviation used for the cosecant of angle A.(iv) cot A is the product of cot and A(v) sin θ =, for some angle θ

In given figure, the length of BC is

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.

What quantity must be added to each term of the ratio x : y so that it may become equal to c : d ?

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region (in cm2). ___

If the mean of the following data is 17 then the value of p is ___xi10p182125fi1015799

The number of proper subsets of the set {1, 2, 3} is ___.

How many three digit numbers are divisible by 7

Find the area of the triangle with coordinates A(-2, 1), B(3, 3) and C(1, -2).

Question 10A capsule of medicine is in the shape of a sphere of diameter 3.5 mm.How much medicine in mm3 is needed to fill this capsule?[Assume π=227]

Find the 11 th term of the arithmetic sequence −9, −2, 5, 12, …

Q2. The hypotenuse of a right-angled triangle is 17 cm and the difference between other two sides is 7 cm. find the other two unknown sides.

If m times the mth term of an AP is equal to n times the nth term prove that (m+n)th term of AP is 0

A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets ₹ 10,206 on maturity, find the value of monthly installments.

Explain why 3.1416¯ is a rational number.

nta ball is projected from the ground . it just touches the top of 6m high wall at a distance of 4m and strikes the ground 8m behind the wall. calculate angle of projection and velocity of projectionn

If θ=tan-1a, ϕ=tan-1b and ab=-1, then θ-ϕ=

The perimeter of the figure ABCDEFGHIJ is

Prove that the length of tangents drawn from an external point to a circle are equal.

Question 1 (i)Evaluate :sin 18∘cos 72∘

Find the distance of the point (6,18) from the X-axis.

of the sum of the squares of the zeroes of the quadratic polynomial f(x) = x^{2 }- px +70 is equal to 149 , then the value of p i

Construct a triangle ABC in which BC is 4 cm, Angle B is 45∘ and AB-AC=1.75 cm.

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of AB is(a) 8 cm(b) 14 cm(c) 16 cm(d) 136 cm

The difference between the squares of two consecutive numbers is 31. Find the numbers

In the adjoining figure, DE || AB,AD = 7 cm, CD = 5 cm and BC = 18 cmFind (i) BE (ii) CE

Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6.........

Dinkar has a recurring deposit account in a bank for a time period of 3.5 years at 9.5 % p.a. He gets ₹ 78638 at the time of maturity. What is his monthly installment rounded off to nearest whole number ?

Sin 53

If sum of the n terms of a sequence is (n-1)2, find the nth term of the sequence.

Question 3 (iii) Is 43.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯123446789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

A number ‘s’ is called irrational if it cannot be written in the form of _____ , where p and q are integers and ______.

If the quotient on dividing x3–3x2+6 by (x–1) is x2+ax+b, find a, b and also the remainder.

Question 14A 15m high tower casts a shadow 24m long at a certain time and at the same time, a telephone pole casts a shadow 16m long. Find the height of the telephone pole.

If alpha and beta are the zeroes of the quadratic polynomial ax2+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

A number ‘s’ is called irrational if it cannot be written in the form of _ , where p and q are integers and __.