24740 + Interview Questions in Mathematics

1.	Is a square a special type of rhombus? I think that clearly square is a special type of rhombus as it is just a rhombus with angle measuring 90 degrees. But my teacher said that this is wrong because diagonals of rhombus are unequal and diagonals of a square equal. Thus, it is wrong, square can't be called a rhombus. Please clarify.
Answer» Is a square a special type of rhombus? I think that clearly square is a special type of rhombus as it is just a rhombus with angle measuring 90 degrees. But my teacher said that this is wrong because diagonals of rhombus are unequal and diagonals of a square equal. Thus, it is wrong, square can't be called a rhombus. Please clarify.

Discussion

2.	In the given construction ∠MYX=60∘, then ∠AYX is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)
Answer» In the given construction $∠ M Y X = 60^{\circ}$ , then $∠ A Y X$ is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

Discussion

3.	Find the value of x & y, when 25x=5y-1& (32)y=4x8x
Answer» Find the value of x & y, when 25^x=5^y-1& (32)^y=4x8^x

Discussion

4.	In the 5 and 34 h left for the sunset, Harry spent 2 and 14 h to spot a whale and, 1 and 14 h to spot a dolphin.How much time is left?
Answer» In the $5$ and $\frac{3}{4}$ h left for the sunset, Harry spent $2$ and $\frac{1}{4}$ h to spot a whale and, $1$ and $\frac{1}{4}$ h to spot a dolphin. How much time is left?

Discussion

5.	How to find the principal solution for an equation cot X= -root 3
Answer» How to find the principal solution for an equation cot X= -root 3

Discussion

6.	ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?
Answer» ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?

Discussion

7.	If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is
Answer» If a pool has to be constructed with a boundary of width $14 m$ consisting of two straight sections $120 m$ long joining semi-circular ends whose inner radius is $35 m .$ Then, the area of the boundary is

Discussion

8.	In the given figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then(a) x = 55°, y = 40°(b) x = 50°, y = 45°(c) x = 60°, y = 35°(d) x = 35°, y = 60°
Answer» In the given figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then (a) x = 55°, y = 40° (b) x = 50°, y = 45° (c) x = 60°, y = 35° (d) x = 35°, y = 60°

Discussion

9.	Sum of two numbers is 4 more than twice of difference of the two numbers. If one of the two numbers is three more than the other number, find the numbers.
Answer» Sum of two numbers is 4 more than twice of difference of the two numbers. If one of the two numbers is three more than the other number, find the numbers.

Discussion

10.	A coin is tossed 500 times and we getheads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting(i) a head? (ii) a tail?
Answer» A coin is tossed 500 times and we get heads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting (i) a head? (ii) a tail?

10.

A coin is tossed 500 times and we getheads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting(i) a head? (ii) a tail?

Answer»

A coin is tossed 500 times and we get

heads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting

(i) a head? (ii) a tail?

Discussion

11.	Question 3Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Answer» Question 3 Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Discussion

12.	The radius and height of a cone are in the ratio 4: 3. The area of the base is 154cm2. The area of the curved surface in cm2__
Answer» The radius and height of a cone are in the ratio 4: 3. The area of the base is 154cm². The area of the curved surface in $c m^{2}$ __

Discussion

13.	▢MRPN is cyclic, ∠ R = (5x – 13)°, ∠ N = (4x + 4)°. Find measures of ∠ R and ∠ N.
Answer» ▢MRPN is cyclic, ∠ R = (5x – 13)°, ∠ N = (4x + 4)°. Find measures of ∠ R and ∠ N.

Discussion

14.	In Fig. 102, AB \|\| CD \|\| EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is(a) 35(b) 50(c) 30(d) 40
Answer» In Fig. 102, AB \|\| CD \|\| EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is (a) 35 (b) 50 (c) 30 (d) 40

Discussion

15.	In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.
Answer» In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

Discussion

16.	The radii of two cylinders are in the ratio 3:5. Their heights are in the ratio 10:6. Find the ratio of their volumes.
Answer» The radii of two cylinders are in the ratio 3:5. Their heights are in the ratio 10:6. Find the ratio of their volumes.

Discussion

17.	If x2 + x + 1 is a factor of the polynomial 3x3+8x2 + 8x + 3 + 5k, then the value of k is
Answer» If $x^{2}$ + x + 1 is a factor of the polynomial $3 x^{3} + 8 x^{2}$ + 8x + 3 + 5k, then the value of k is

Discussion

18.	If two coins are tossed, find the probability of the following events.(1) Getting at least one head.(2) Getting no head.
Answer» If two coins are tossed, find the probability of the following events. (1) Getting at least one head. (2) Getting no head.

Discussion

19.	Sort steps to construct quadrilateral ABCD with AB, BC, CD, AD, AC as 4 cm, 6 cm, 5.5 cm, 5 cm, 8 cm.
Answer» Sort steps to construct quadrilateral ABCD with AB, BC, CD, AD, AC as 4 cm, 6 cm, 5.5 cm, 5 cm, 8 cm.

Discussion

20.	If two acute angles of a right triangle are equal, then each acute is equal to(a) 30°(b) 45°(c) 60°(d) 90°
Answer» If two acute angles of a right triangle are equal, then each acute is equal to (a) 30° (b) 45° (c) 60° (d) 90°

Discussion

21.	Which of the following shows the visualization of the subtraction of 3x from 9x?
Answer» Which of the following shows the visualization of the subtraction of 3x from 9x?

Discussion

22.	If class mark is 10 and class width is 6 then find the class.
Answer» If class mark is $10$ and class width is $6$ then find the class.

Discussion

23.	Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.Reason: Angles in the same segment are equal.Which of the following options is correct?
Answer» Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC. Reason: Angles in the same segment are equal. Which of the following options is correct?

23.

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.Reason: Angles in the same segment are equal.Which of the following options is correct?

Answer»

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.

Reason: Angles in the same segment are equal.

Which of the following options is correct?

Discussion

24.	The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.
Answer» The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

Discussion

25.	ABC is a triangle, D is the mid-point on side BC. Given, AB=5 cm, AC=5 cm and BD=3 cmFind the value of AD.
Answer» ABC is a triangle, D is the mid-point on side BC. Given, AB=5 cm, AC=5 cm and BD=3 cm Find the value of AD.

Discussion

26.	A number is chosen at random from the set {1,2,3,⋯,2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is
Answer» A number is chosen at random from the set ${1, 2, 3, \dots, 2000}$ . Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500 p$ is

Discussion

27.	The sum of two numbers is 45 and one is twice the other. What is the smaller number?
Answer» The sum of two numbers is 45 and one is twice the other. What is the smaller number?

Discussion

28.	Solve for x x2−(1+√5)x+√5=0
Answer» Solve for x $x^{2} - (1 + \sqrt{5}) x + \sqrt{5} = 0$

Discussion

29.	"The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. How many pants were purchased?1
Answer» "The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. How many pants were purchased? 1

Discussion

30.	If α,β and γ are the zeroes of the polynomial f(x)=ax3+bx2+cx+d, then 1α+1β+1γ is _____.
Answer» If $α, β$ and $γ$ are the zeroes of the polynomial $f (x) = a x^{3} + b x^{2} + c x + d$ , then $\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}$ is _____.

Discussion

31.	Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, then CD = ___________.
Answer» Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, then CD = ___________.

Discussion

32.	Question 77 (ii)From the following table determine if x and y are in direct proportion or not.
Answer» Question 77 (ii) From the following table determine if x and y are in direct proportion or not.

32.

Question 77 (ii)From the following table determine if x and y are in direct proportion or not.

Answer»

Question 77 (ii)

From the following table determine if x and y are in direct proportion or not.

Discussion

33.	If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD
Answer» If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD

Discussion

34.	The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is 127 of the volume of the given cone, at what height above the base is the section made?
Answer» The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is $\frac{1}{27}$ of the volume of the given cone, at what height above the base is the section made?

Discussion

35.	Question 7In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use π=3.14)
Answer» Question 7 In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use $π = 3.14$ )

Discussion

36.	Question 1 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Answer» Question 1 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Discussion

37.	Question 1 (ii) Classify (3+√23)−√23 as rational or irrational.
Answer» Question 1 (ii) Classify $(3 + \sqrt{23}) - \sqrt{23}$ as rational or irrational.

Discussion

38.	The poem is full of images that come alive through skilful use of words. List out any two images that appeal to you the most, quoting the lines from the poem.
Answer» The poem is full of images that come alive through skilful use of words. List out any two images that appeal to you the most, quoting the lines from the poem.

Discussion

39.	The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 gm.
Answer» The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 gm.

Discussion

40.	If p=2a×3b×5c and a>b>c are natural numbers, then what is the unit digit of p?
Answer» If $p = 2^{a} \times 3^{b} \times 5^{c}$ and $a > b > c$ are natural numbers, then what is the unit digit of $p$ ?

Discussion

41.	Are all rational number Integers?
Answer» Are all rational number Integers?

Discussion

42.	Simplify (3125243)45
Answer» Simplify ${(\frac{3125}{243})}^{\frac{4}{5}}$

Discussion

43.	Which of the following is irrational?(i) 0.14(ii) 0.1416¯(iii) 0.1416¯(iv) 0.1014001400014...
Answer» Which of the following is irrational? (i) 0.14 (ii) $0.14 \bar{16}$ (iii) $0 . \bar{1416}$ (iv) 0.1014001400014...

Discussion

44.	(√a − √b)×(√a + √b) =
Answer» $(\sqrt{a} - \sqrt{b}) \times (\sqrt{a} + \sqrt{b}) =$

Discussion

45.	If (x - 2 ) is a factor of the polynomial x2 - 3x + 5a , find the value of ‘a’
Answer» If (x - 2 ) is a factor of the polynomial x² - 3x + 5a , find the value of ‘a’

Discussion

46.	If the pair of linear equations x+2y−4=0 and 2x+4y−12=0 are plotted graphically, How many solution(s) do we get.
Answer» If the pair of linear equations $x + 2 y - 4 = 0$ and $2 x + 4 y - 12 = 0$ are plotted graphically, How many solution(s) do we get.

Discussion

47.	find the dimensional formula of A/B in given expression W =A+X/B
Answer» find the dimensional formula of A/B in given expression W =A+X/B

Discussion

48.	P and Q are any two points lying on the sides DC and AD respectively of a square ABCD.Show that ar(APB) = ar(BQC).
Answer» P and Q are any two points lying on the sides DC and AD respectively of a square ABCD. Show that ar(APB) = ar(BQC).

Discussion

49.	Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see given Fig.? If she pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Answer» Nazima is fly fishing in a stream. The tip of her fishing rod is $1.8 m$ above the surface of the water and the fly at the end of the string rests on the water $3.6 m$ away and $2.4 m$ from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see given Fig.? If she pills in the string at the rate of $5 c m$ per second, what will be the horizontal distance of the fly from her after $12$ seconds?

Discussion

50.	The lateral surface area of a cuboid with length 5 cm, breadth 4 cm, and height 3 cm is .
Answer» The lateral surface area of a cuboid with length 5 cm, breadth 4 cm, and height 3 cm is .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the given construction ∠MYX=60∘, then ∠AYX is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

Find the value of x &amp; y, when 25x=5y-1&amp; (32)y=4x8x

In the 5 and 34 h left for the sunset, Harry spent 2 and 14 h to spot a whale and, 1 and 14 h to spot a dolphin.How much time is left?

How to find the principal solution for an equation cot X= -root 3

ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?

If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is

In the given figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then(a) x = 55°, y = 40°(b) x = 50°, y = 45°(c) x = 60°, y = 35°(d) x = 35°, y = 60°

Sum of two numbers is 4 more than twice of difference of the two numbers. If one of the two numbers is three more than the other number, find the numbers.

A coin is tossed 500 times and we getheads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting(i) a head? (ii) a tail?

Question 3Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154cm2. The area of the curved surface in cm2__

▢MRPN is cyclic, ∠ R = (5x – 13)°, ∠ N = (4x + 4)°. Find measures of ∠ R and ∠ N.

In Fig. 102, AB || CD || EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is(a) 35(b) 50(c) 30(d) 40

In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

The radii of two cylinders are in the ratio 3:5. Their heights are in the ratio 10:6. Find the ratio of their volumes.

If x2 + x + 1 is a factor of the polynomial 3x3+8x2 + 8x + 3 + 5k, then the value of k is

If two coins are tossed, find the probability of the following events.(1) Getting at least one head.(2) Getting no head.

Sort steps to construct quadrilateral ABCD with AB, BC, CD, AD, AC as 4 cm, 6 cm, 5.5 cm, 5 cm, 8 cm.

If two acute angles of a right triangle are equal, then each acute is equal to(a) 30°(b) 45°(c) 60°(d) 90°

Which of the following shows the visualization of the subtraction of 3x from 9x?

If class mark is 10 and class width is 6 then find the class.

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.Reason: Angles in the same segment are equal.Which of the following options is correct?

The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

ABC is a triangle, D is the mid-point on side BC. Given, AB=5 cm, AC=5 cm and BD=3 cmFind the value of AD.

A number is chosen at random from the set {1,2,3,⋯,2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is

The sum of two numbers is 45 and one is twice the other. What is the smaller number?

Solve for x x2−(1+√5)x+√5=0

"The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. How many pants were purchased?1

If α,β and γ are the zeroes of the polynomial f(x)=ax3+bx2+cx+d, then 1α+1β+1γ is _____.

Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, then CD = ___________.

Question 77 (ii)From the following table determine if x and y are in direct proportion or not.

If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is 127 of the volume of the given cone, at what height above the base is the section made?

Question 7In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use π=3.14)

Question 1 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Question 1 (ii) Classify (3+√23)−√23 as rational or irrational.

The poem is full of images that come alive through skilful use of words. List out any two images that appeal to you the most, quoting the lines from the poem.

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 gm.

If p=2a×3b×5c and a&gt;b&gt;c are natural numbers, then what is the unit digit of p?

Are all rational number Integers?

Simplify (3125243)45

Which of the following is irrational?(i) 0.14(ii) 0.1416¯(iii) 0.1416¯(iv) 0.1014001400014...

(√a − √b)×(√a + √b) =

If (x - 2 ) is a factor of the polynomial x2 - 3x + 5a , find the value of ‘a’

If the pair of linear equations x+2y−4=0 and 2x+4y−12=0 are plotted graphically, How many solution(s) do we get.

find the dimensional formula of A/B in given expression W =A+X/B

P and Q are any two points lying on the sides DC and AD respectively of a square ABCD.Show that ar(APB) = ar(BQC).

The lateral surface area of a cuboid with length 5 cm, breadth 4 cm, and height 3 cm is .

Find the value of x & y, when 25x=5y-1& (32)y=4x8x

If p=2a×3b×5c and a>b>c are natural numbers, then what is the unit digit of p?