32581 + Interview Questions in Mathematics

1.	What is the least number that must be subtracted from 1160 so that the sum of the 1160 and the resulting number is completely divisible by 19?
Answer» What is the least number that must be subtracted from 1160 so that the sum of the 1160 and the resulting number is completely divisible by 19?

Discussion

2.	The length of a medicine capsule is 14mm and the diameter is 5mm. Find its surface area in mm2.220
Answer» The length of a medicine capsule is 14mm and the diameter is 5mm. Find its surface area in $m m^{2}$ . 220

Discussion

3.	Find the area of copper sheet required to make a frustum shaped bucket of height 8 cm and radii 9 cm and 3 cm.
Answer» Find the area of copper sheet required to make a frustum shaped bucket of height 8 cm and radii 9 cm and 3 cm.

Discussion

4.	2tan245∘+3cos230∘−sin260∘=___
Answer» $2 t a n^{2} 45^{\circ} + 3 c o s^{2} 30^{\circ} - s i n^{2} 60^{\circ} =$ ___

Discussion

5.	cosec a + cot a =3 find cos a
Answer» cosec a + cot a =3 find cos a

Discussion

6.	From a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the sshaded region. (Use π=227)
Answer» From a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the sshaded region. (Use $π = \frac{22}{7}$ )

6.

From a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the sshaded region. (Use π=227)

Answer»

From a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the sshaded region. (Use $π = \frac{22}{7}$ )

Discussion

7.	In the given figure, in ∆ABC, seg AD and seg BE are altitudes and AE = BD. Prove that seg AD ≅seg BE
Answer» In the given figure, in $∆$ ABC, seg AD and seg BE are altitudes and AE = BD. Prove that seg AD $≅$ seg BE

Discussion

8.	The radius of sphere is increased by 12.5% , Prove that the volume is increased by 42.38% approximately.
Answer» The radius of sphere is increased by 12.5% , Prove that the volume is increased by 42.38% approximately.

Discussion

9.	Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iii) 4x2+4√3x+3=0
Answer» Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iii) $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

10.	What are the uses if LCM and HCF?
Answer» What are the uses if LCM and HCF?

Discussion

11.	A dice is rolled. The probability of getting an even prime is(a) 16 (b) 13 (c) 12 (d) 56
Answer» A dice is rolled. The probability of getting an even prime is (a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{5}{6}$

Discussion

12.	Find the value of x for which (8x+4), (6x-2) and (2x+7) are in A.P.
Answer» Find the value of x for which (8x+4), (6x-2) and (2x+7) are in A.P.

Discussion

13.	While finding the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The value of (a × c)
Answer» While finding the roots of the quadratic equation 3 $x^{2}$ - 2 $\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The value of (a $\times$ c)

Discussion

14.	Find the HCF of 24, 32 and 36.
Answer» Find the HCF of 24, 32 and 36.

Discussion

15.	Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
Answer» Write the formula for the area of the triangle having its vertices at (x₁, y₁), (x2, y₂) and (x₃, y₃).

Discussion

16.	If a1,a2,a3,a4 are terms of an AP, then the relation between them is
Answer» If $a_{1}, a_{2}, a_{3}, a_{4}$ are terms of an AP, then the relation between them is

Discussion

17.	Find the roots of the following quadratic equations by the factorization method. 25x2−x−35=0
Answer» Find the roots of the following quadratic equations by the factorization method. $\frac{2}{5} x^{2} - x - \frac{3}{5} = 0$

Discussion

18.	Construct triangle ABC in which AB = 3 cm, B = 3.5 cm and CA = 5 cm. Construct ΔDEF similar to ΔABC, having 10 cm as its longest side.
Answer» Construct triangle ABC in which AB = 3 cm, B = 3.5 cm and CA = 5 cm. Construct ΔDEF similar to ΔABC, having 10 cm as its longest side.

Discussion

19.	Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?
Answer» Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?

Discussion

20.	27. If x=at+bt2 where x is in meters and t is in seconds what are the units of a and b
Answer» 27. If x=at+bt2 where x is in meters and t is in seconds what are the units of a and b

Discussion

21.	Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square .
Answer» Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square .

Discussion

22.	Let S = {1, 2, 3, 4, 5, 6} be the sample space associated to a random experiment and A = {1, 3, 5} be an event, then A =__________.
Answer» Let S = {1, 2, 3, 4, 5, 6} be the sample space associated to a random experiment and A = {1, 3, 5} be an event, then $A$ =__________.

Discussion

23.	Black aces and black cards are removed from a pack of 52cards. Remaining cards are reshuffled and a card is drawn. Find the probability of getting 1) A black card 2) An ace
Answer» Black aces and black cards are removed from a pack of 52cards. Remaining cards are reshuffled and a card is drawn. Find the probability of getting 1) A black card 2) An ace

23.

Black aces and black cards are removed from a pack of 52cards. Remaining cards are reshuffled and a card is drawn. Find the probability of getting 1) A black card 2) An ace

Answer»

Black aces and black cards are removed from a pack of 52cards. Remaining cards are reshuffled and a card is drawn. Find the probability of getting

1) A black card

2) An ace

Discussion

24.	In ΔABC, AC=15 cm and DE∥BC. If ADDB=12, then AE= ___
Answer» In $Δ A B C, A C = 15 c m$ and $D E ∥ B C$ . If $\frac{A D}{D B} = \frac{1}{2}$ , then $A E =$ ___

Discussion

25.	Consider the following frequency distributions:Class: 65-85 85-105 105-125 125-145 145-165 165-185 - 185-205Frequency: 4 5 13 20 14 7 4The difference of the upper limit of the median class and the lower limit of the modal class is (a) 0 (b) 19 (c) 20 (d) 38
Answer» Consider the following frequency distributions: Class: 65-85 85-105 105-125 125-145 145-165 165-185 - 185-205 Frequency: 4 5 13 20 14 7 4 The difference of the upper limit of the median class and the lower limit of the modal class is (a) 0 (b) 19 (c) 20 (d) 38

Discussion

26.	Prove that √5 is an irrational number. Hence show that 3+2√5 is also an irrational number.
Answer» Prove that $\sqrt{5}$ is an irrational number. Hence show that $3 + 2 \sqrt{5}$ is also an irrational number.

Discussion

27.	Use the Venn diagram to find A∪B.
Answer» Use the Venn diagram to find $A \cup B$ .

27.

Use the Venn diagram to find A∪B.

Answer»

Use the Venn diagram to find $A \cup B$ .

Discussion

28.	The value of π upto 50 decimal places is given below :.14159265358979323846264338327950288419716939937510 From this information prepare an ungrouped frequency distribution table of digits appearing after the decimal point.
Answer» The value of π upto 50 decimal places is given below : .14159265358979323846264338327950288419716939937510 From this information prepare an ungrouped frequency distribution table of digits appearing after the decimal point.

Discussion

29.	Question 1 (vii)Solve the following pairs of equations by reducing them to a pair of linear equations:10x+y+2x−y=415x+y−5x−y=−2
Answer» Question 1 (vii) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{10}{x + y} + \frac{2}{x - y} = 4$ $\frac{15}{x + y} - \frac{5}{x - y} = - 2$

Discussion

30.	The pair of equations x = a and y = b has solution ________.
Answer» The pair of equations x = a and y = b has solution ________.

Discussion

31.	Question 1Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).
Answer» Question 1 Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Discussion

32.	Following real number has decimal expansion as given below. Decide whether rational, or not. If rational, and of the form pq, what can you say about the prime factors of q? 43.123456789
Answer» Following real number has decimal expansion as given below. Decide whether rational, or not. If rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q? 43.123456789

Discussion

33.	(1) Draw a graph of y = x2 and find the value of.(2) Draw the graph of y = 2x2 and find the value of.(3) Draw the graph of and find the value of.
Answer» (1) Draw a graph of y = x² and find the value of. (2) Draw the graph of y = 2x² and find the value of. (3) Draw the graph of and find the value of.

33.

(1) Draw a graph of y = x2 and find the value of.(2) Draw the graph of y = 2x2 and find the value of.(3) Draw the graph of and find the value of.

Answer»

(1) Draw a graph of y = x² and find the value of.

(2) Draw the graph of y = 2x² and find the value of.

(3) Draw the graph of and find the value of.

Discussion

34.	In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.
Answer» In the following figure, AD is a straight line. OP $⊥$ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

34.

In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

Answer»

In the following figure, AD is a straight line. OP $⊥$ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

Discussion

35.	If cosecθ−cotθ=12,0<θ<π2, then cosθ is equal to
Answer» If $c o s e c θ - c o t θ = \frac{1}{2}, 0 < θ < \frac{π}{2}$ , then $c o s θ$ is equal to

Discussion

36.	Check whether p(x) = x3 + 5x2 + 2x - 5 is a multiple of g(x) = x + 2.
Answer» Check whether p(x) = $x^{3}$ + 5 $x^{2}$ + 2x - 5 is a multiple of g(x) = x + 2.

Discussion

37.	From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.
Answer» From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

Discussion

38.	7. How To do hcf and lcm of numbers 301 421
Answer» 7. How To do hcf and lcm of numbers 301 421

Discussion

39.	sin A + cos A =p; sec A + cosec A = q; Prove that q(p^2-1)=2p
Answer» sin A + cos A =p; sec A + cosec A = q; Prove that q(p^2-1)=2p

Discussion

40.	In the given figure, O is the centre of the circle, the value of x is
Answer» In the given figure, O is the centre of the circle, the value of x is

Discussion

41.	One leg of a right-angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.
Answer» One leg of a right-angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

Discussion

42.	A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.
Answer» A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.

Discussion

43.	Question 5If sin θ+2 cos θ=1, then prove that 2 sin θ−cos θ=2.
Answer» Question 5 If $s i n θ + 2 c o s θ = 1$ , then prove that $2 s i n θ - c o s θ = 2$ .

Discussion

44.	A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be
Answer» A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

44.

A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

Answer»

A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

Discussion

45.	PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA=35∘, then find ∠POB.
Answer» $PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠ O P A = 35^{\circ}, then find ∠ P O B .$

Discussion

46.	E^°(Cu^{2+}/Cu^+)=x volt; E^°(Cu/Cu^{2+})=y volt; Find E†extdegree_{cell} for Cu^+/Cu^{2+}//Cu^+/Cu. -1) 2x-2y, 2)2x+2y, 3)-2x+2y, 4)-2x-2y, 5)-2x-y, 6)-y, 7)none
Answer» E^°(Cu^{2+}/Cu^+)=x volt; E^°(Cu/Cu^{2+})=y volt; Find E†extdegree_{cell} for Cu^+/Cu^{2+}//Cu^+/Cu. -1) 2x-2y, 2)2x+2y, 3)-2x+2y, 4)-2x-2y, 5)-2x-y, 6)-y, 7)none

Discussion

47.	In Fig. 10, a right circular cone of diameter r cm and height 12 cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12 cm. If the cone is then removed, find the height to which water level will fall.
Answer» In Fig. 10, a right circular cone of diameter r cm and height 12 cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12 cm. If the cone is then removed, find the height to which water level will fall.

Discussion

48.	\|x+4\|=2\|x+3\|
Answer» \|x+4\|=2\|x+3\|

Discussion

49.	Question 6If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Answer» Question 6 If $∠$ A and $∠$ B are acute angles such that cos A = cos B, then show that $∠$ A = $∠$ B.

Discussion

50.	A and B are partners sharing profits in the ratio of 2 : 1. They admit C for 1/4th share in profits. C brings in ₹ 30,000 for his capital and ₹ 8,000 out of his share of ₹ 10,000 for goodwill. Before admission, goodwill appeared in books at ₹ 18,000. Give Journal entries to give effect to the above arrangement.
Answer» A and B are partners sharing profits in the ratio of 2 : 1. They admit C for 1/4th share in profits. C brings in ₹ 30,000 for his capital and ₹ 8,000 out of his share of ₹ 10,000 for goodwill. Before admission, goodwill appeared in books at ₹ 18,000. Give Journal entries to give effect to the above arrangement.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the least number that must be subtracted from 1160 so that the sum of the 1160 and the resulting number is completely divisible by 19?

The length of a medicine capsule is 14mm and the diameter is 5mm. Find its surface area in mm2.220

Find the area of copper sheet required to make a frustum shaped bucket of height 8 cm and radii 9 cm and 3 cm.

2tan245∘+3cos230∘−sin260∘=___

cosec a + cot a =3 find cos a

From a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the sshaded region. (Use π=227)

In the given figure, in ∆ABC, seg AD and seg BE are altitudes and AE = BD. Prove that seg AD ≅seg BE

The radius of sphere is increased by 12.5% , Prove that the volume is increased by 42.38% approximately.

Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iii) 4x2+4√3x+3=0

What are the uses if LCM and HCF?

A dice is rolled. The probability of getting an even prime is(a) 16 (b) 13 (c) 12 (d) 56

Find the value of x for which (8x+4), (6x-2) and (2x+7) are in A.P.

While finding the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The value of (a × c)

Find the HCF of 24, 32 and 36.

Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).

If a1,a2,a3,a4 are terms of an AP, then the relation between them is

Find the roots of the following quadratic equations by the factorization method. 25x2−x−35=0

Construct triangle ABC in which AB = 3 cm, B = 3.5 cm and CA = 5 cm. Construct ΔDEF similar to ΔABC, having 10 cm as its longest side.

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?

27. If x=at+bt2 where x is in meters and t is in seconds what are the units of a and b

Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square .

Let S = {1, 2, 3, 4, 5, 6} be the sample space associated to a random experiment and A = {1, 3, 5} be an event, then A =__________.

Black aces and black cards are removed from a pack of 52cards. Remaining cards are reshuffled and a card is drawn. Find the probability of getting 1) A black card 2) An ace

In ΔABC, AC=15 cm and DE∥BC. If ADDB=12, then AE= ___

Consider the following frequency distributions:Class: 65-85 85-105 105-125 125-145 145-165 165-185 - 185-205Frequency: 4 5 13 20 14 7 4The difference of the upper limit of the median class and the lower limit of the modal class is (a) 0 (b) 19 (c) 20 (d) 38

Prove that √5 is an irrational number. Hence show that 3+2√5 is also an irrational number.

Use the Venn diagram to find A∪B.

The value of π upto 50 decimal places is given below :.14159265358979323846264338327950288419716939937510 From this information prepare an ungrouped frequency distribution table of digits appearing after the decimal point.

Question 1 (vii)Solve the following pairs of equations by reducing them to a pair of linear equations:10x+y+2x−y=415x+y−5x−y=−2

The pair of equations x = a and y = b has solution ________.

Question 1Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Following real number has decimal expansion as given below. Decide whether rational, or not. If rational, and of the form pq, what can you say about the prime factors of q? 43.123456789

(1) Draw a graph of y = x2 and find the value of.(2) Draw the graph of y = 2x2 and find the value of.(3) Draw the graph of and find the value of.

In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

If cosecθ−cotθ=12,0&lt;θ&lt;π2, then cosθ is equal to

Check whether p(x) = x3​ + 5x2 + 2x - 5 is a multiple of g(x) = x + 2.

From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

7. How To do hcf and lcm of numbers 301 421

sin A + cos A =p; sec A + cosec A = q; Prove that q(p^2-1)=2p

In the given figure, O is the centre of the circle, the value of x is

One leg of a right-angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.

Question 5If sin θ+2 cos θ=1, then prove that 2 sin θ−cos θ=2.

A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA=35∘, then find ∠POB.

E^°(Cu^{2+}/Cu^+)=x volt; E^°(Cu/Cu^{2+})=y volt; Find E†extdegree_{cell} for Cu^+/Cu^{2+}//Cu^+/Cu. -1) 2x-2y, 2)2x+2y, 3)-2x+2y, 4)-2x-2y, 5)-2x-y, 6)-y, 7)none

|x+4|=2|x+3|

Question 6If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

If cosecθ−cotθ=12,0<θ<π2, then cosθ is equal to

Check whether p(x) = x3 + 5x2 + 2x - 5 is a multiple of g(x) = x + 2.