24740 + Interview Questions in Mathematics

1.	A trapezium has an area of 570 cm2. The height of the trapezium is 5 cm and the larger parallel side is twice in length of the smaller parallel side. Choose the correct option.
Answer» A trapezium has an area of $570 c m^{2} .$ The height of the trapezium is $5 c m$ and the larger parallel side is twice in length of the smaller parallel side. Choose the correct option.

Discussion

2.	Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.
Answer» Construct the quadrilateral GOLD where OL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

2.

Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

Answer»

Construct the quadrilateral GOLD where

OL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

Discussion

3.	Number of points at which the graph of functionye k(k> 0) intersects the x-axis is
Answer» Number of points at which the graph of functionye k(k> 0) intersects the x-axis is

Discussion

4.	In the given figure, chords AB=CD, ∠COD=60∘ and ∠AOD=170∘.Find the value of ∠BOC.
Answer» In the given figure, chords $A B = C D, ∠ C O D = 60^{\circ}$ and $∠ A O D = 170^{\circ}$ . Find the value of $∠ B O C$ .

4.

In the given figure, chords AB=CD, ∠COD=60∘ and ∠AOD=170∘.Find the value of ∠BOC.

Answer»

In the given figure, chords $A B = C D, ∠ C O D = 60^{\circ}$ and $∠ A O D = 170^{\circ}$ .

Find the value of $∠ B O C$ .

Discussion

5.	In a right angled triangle ABC, right angled at C, if tanA=cotB, then what is value of A + B?
Answer» In a right angled triangle ABC, right angled at C, if $tan A = cot B$ , then what is value of A + B?

Discussion

6.	Factorise: (2a+1)3+(a−1)3
Answer» Factorise: $(2 a + 1)^{3} + (a - 1)^{3}$

Discussion

7.	An ox is tied to a pole situated at the center of a field, with a 10 m long rope. The ox moves keeping the rope tight. Find the area of the ground swept by the rope.( Use π=3.14)
Answer» An ox is tied to a pole situated at the center of a field, with a 10 m long rope. The ox moves keeping the rope tight. Find the area of the ground swept by the rope.( Use $π = 3.14$ )

Discussion

8.	factorise : 7√2x2-10x+4√2
Answer» factorise : 7√2x²-10x+4√2

Discussion

9.	In the standard form of an equation, ax2 + bx + c = 0, both roots of the equation are 0 if
Answer» $I n t h e s t a n d a r d f o r m o f a n e q u a t i o n, a x^{2} + b x + c = 0, b o t h r o o t s o f t h e e q u a t i o n a r e 0 i f$

Discussion

10.	Find the area of a trapezium whose parallel sides are 32 cm and 27 cm, and the distance between them is 15 cm.
Answer» Find the area of a trapezium whose parallel sides are 32 cm and 27 cm, and the distance between them is 15 cm.

Discussion

11.	The given graph shows the weekly earnings of workers of a factory. The weekly earnings of Rs 170 are received by how many workers?
Answer» The given graph shows the weekly earnings of workers of a factory. The weekly earnings of Rs 170 are received by how many workers?

11.

The given graph shows the weekly earnings of workers of a factory. The weekly earnings of Rs 170 are received by how many workers?

Answer»

The given graph shows the weekly earnings of workers of a factory.

The weekly earnings of Rs 170 are received by how many workers?

Discussion

12.	In the method of regrouping, we ________ .
Answer» In the method of regrouping, we ________ .

Discussion

13.	Write True' or False' and justify your answer in each of the following :(i) The value of sin θ is x + 1x, where 'x' is a positive real number .(ii) cos θ = a2 + b22ab, where a and b are two distinct numbers such that ab > 0.(iii) The value of cos223 - sin267 is positive .(iv) The value of the expression sin 80° - cos 80° is negative .(v) The value of sin θ + cos θ is always greater than 1 .
Answer» Write True' or False' and justify your answer in each of the following : (i) The value of $\sin θ$ is $x + \frac{1}{x}$ , where 'x' is a positive real number . (ii) $\cos θ = \frac{a^{2} + b^{2}}{2 ab}$ , where a and b are two distinct numbers such that ab > 0. (iii) The value of $\cos^{2} 23 - \sin^{2} 67$ is positive . (iv) The value of the expression $\sin 80^{°} - \cos 80^{°}$ is negative . (v) The value of $\sin θ + \cos θ$ is always greater than 1 .

Discussion

14.	Question 11 In the following figure AD is the bisector of ∠BAC. Prove that AB > BD.
Answer» Question 11 In the following figure AD is the bisector of $∠ B A C$ . Prove that AB > BD.

Discussion

15.	Capacity of water tank is 1000 l. If the shape of tank is cube then find the side of the cube.
Answer» Capacity of water tank is 1000 $l$ . If the shape of tank is cube then find the side of the cube.

Discussion

16.	In the figure given below, if ∠AOP=75∘ and ∠AOB=120∘, then ∠AQP= ___.
Answer» In the figure given below, if $∠ A O P = 75^{\circ}$ and $∠ A O B = 120^{\circ}$ , then $∠ A Q P$ = ___.

Discussion

17.	The number of cartoons drawn by a cartoonist is given by the equation, y = 10x + 5, where x is the number of days, y is the total number of cartoons. Which of the following graph shows the correct data for this situation?
Answer» The number of cartoons drawn by a cartoonist is given by the equation, y = 10x + 5, where x is the number of days, y is the total number of cartoons. Which of the following graph shows the correct data for this situation?

Discussion

18.	The line graph below shows people in a store at various times of the day. How many people are there in the store at 2:30 pm?
Answer» The line graph below shows people in a store at various times of the day. How many people are there in the store at 2:30 pm?

18.

The line graph below shows people in a store at various times of the day. How many people are there in the store at 2:30 pm?

Answer»

The line graph below shows people in a store at various times of the day. How many people are there in the store at 2:30 pm?

Discussion

19.	Let A and B be two events for which P(A) = a, P(B) = b, PA∩B=c, then P(A∩B) = __________________.
Answer» Let A and B be two events for which P(A) = a, P(B) = b, $P (A \cap B) = c, then P (A \cap B)$ = __________________.

Discussion

20.	The value of sin2ϕ+cos2θ is equal to
Answer» The value of $s i n^{2} ϕ + c o s^{2} θ$ is equal to

Discussion

21.	Factorise (n2+22n+96)
Answer» Factorise $(n^{2} + 22 n + 96)$

Discussion

22.	Check whether the linear equation 3x + 5 = 11 is true for x = 2.
Answer» Check whether the linear equation 3x + 5 = 11 is true for x = 2.

Discussion

23.	Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.
Answer» Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.

23.

Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.

Answer»

Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.

Discussion

24.	(i) Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.(ii) Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.
Answer» (i) Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square. (ii) Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.

Discussion

25.	ABCD is a rhombus. IF ∠BAC=38∘,find(1) ∠ACB(2) ∠DAC(3) ∠ADC
Answer» ABCD is a rhombus. IF $∠ B A C = 38^{\circ},$ find (1) $∠$ ACB (2) $∠$ DAC (3) $∠$ ADC

Discussion

26.	In the given figure, ABCD is a square and DEC is equilateral. The value of x is:
Answer» In the given figure, ABCD is a square and DEC is equilateral. The value of x is:

26.

In the given figure, ABCD is a square and DEC is equilateral. The value of x is:

Answer»

In the given figure, ABCD is a square and DEC is equilateral.

The value of x is:

Discussion

27.	Tangents are drawn from origin to the curve y=sinx+cosx. Then their points of contact lie on the curve.
Answer» Tangents are drawn from origin to the curve $y = sin x + cos x .$ Then their points of contact lie on the curve.

Discussion

28.	If height of equilateral triangle is 3 cm Find area
Answer» If height of equilateral triangle is 3 cm Find area

Discussion

29.	Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:(i)(ii)(iii)(iv)(v)(vi)
Answer» Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels: (i) (ii) (iii) (iv) (v) (vi)

29.

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:(i)(ii)(iii)(iv)(v)(vi)

Answer» Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Discussion

30.	The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m2.
Answer» The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m².

Discussion

31.	In a triangle ABC, if b + c = 2a and ∠ A=600, then Δ ABC is
Answer» In a triangle ABC, if b + c = 2a and $∠$ $A = 60^{0}$ , then $Δ$ ABC is

Discussion

32.	Simplify (2x-5y)3-(2x+5y)3
Answer» Simplify (2x-5y)³-(2x+5y)³

Discussion

33.	Examine the figure and identify which of the following are collinear points.
Answer» Examine the figure and identify which of the following are collinear points.

Discussion

34.	The decimal expansion of pi is:
Answer» The decimal expansion of pi is:

Discussion

35.	Three unbiased coins are tossed together. The probability of getting at least two heads is
Answer» Three unbiased coins are tossed together. The probability of getting at least two heads is

Discussion

36.	Mark the correct answer in each of the following:The converse of the statement "If x > y, then x + a > y + a", is(a) If x < y, then x + a < y + a(b) If x + a > y + a, then x > y(c) If x < y, then x + a > y + a(d) If x > y, then x + a < y + a
Answer» Mark the correct answer in each of the following: The converse of the statement "If x > y, then x + a > y + a", is (a) If x < y, then x + a < y + a (b) If x + a > y + a, then x > y (c) If x < y, then x + a > y + a (d) If x > y, then x + a < y + a

Discussion

37.	Tiwari & Sons find that the bank balance shown by their Cash Book on 31st March, 2019 is ₹ 40,500 (credit) but the Pass Book shows a difference due to the following reasons:(i) A cheque for ₹ 5,000 drawn in favour of Manohar has not yet been presented for payment.(ii) A post-dated cheque for ₹ 900 has been debited in the bank column of the Cash Book but it could not have been presented in any case.(iii) Cheques totalling ₹ 10,200 deposited with the bank have not yet been collected and a cheque for ₹ 4,000 has been dishonoured.(iv) A bill for ₹ 10,000 was retired by the Bank under a rebate of ₹ 150 but the full amount of the bill was credited in the bank column of the Cash Book.Prepare Bank Reconciliation Statement and find out the balance as per Pass Book.
Answer» Tiwari & Sons find that the bank balance shown by their Cash Book on 31st March, 2019 is ₹ 40,500 (credit) but the Pass Book shows a difference due to the following reasons: (i) A cheque for ₹ 5,000 drawn in favour of Manohar has not yet been presented for payment. (ii) A post-dated cheque for ₹ 900 has been debited in the bank column of the Cash Book but it could not have been presented in any case. (iii) Cheques totalling ₹ 10,200 deposited with the bank have not yet been collected and a cheque for ₹ 4,000 has been dishonoured. (iv) A bill for ₹ 10,000 was retired by the Bank under a rebate of ₹ 150 but the full amount of the bill was credited in the bank column of the Cash Book. Prepare Bank Reconciliation Statement and find out the balance as per Pass Book.

Discussion

38.	15. Two points P (2,0) and Q (-2,0) are given. R is a variable point on one side of the line PQ such that (angleRPQ)-(angleRQP) is a positive constant (2alpha). The locus of R is
Answer» 15. Two points P (2,0) and Q (-2,0) are given. R is a variable point on one side of the line PQ such that (angleRPQ)-(angleRQP) is a positive constant (2alpha). The locus of R is

Discussion

39.	How to repersent √5 on a number line
Answer» How to repersent √5 on a number line

Discussion

40.	Prove by vector method that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.
Answer» Prove by vector method that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Discussion

41.	If x3+6x2+4x+k is exactly divisible by (x+2), then the value of k is -
Answer» If $x^{3} + 6 x^{2} + 4 x + k$ is exactly divisible by $(x + 2)$ , then the value of k is -

Discussion

42.	If (x+1) is a factor of the polynomial 2x^3+8x^2+3x+k. Then find the value of k
Answer» If (x+1) is a factor of the polynomial 2x^3+8x^2+3x+k. Then find the value of k

Discussion

43.	Question 16If two adjacent angles of a parallelogram are (5x−5)∘ and (10x+35)∘, then the ratio of these angles is ___________.a) 1 : 3b) 2 : 3c) 1 : 4d) 1 : 2
Answer» Question 16 If two adjacent angles of a parallelogram are $(5 x - 5)^{\circ}$ and $(10 x + 35)^{\circ}$ , then the ratio of these angles is ___________. a) 1 : 3 b) 2 : 3 c) 1 : 4 d) 1 : 2

Discussion

44.	The cross- area of a pipe is 42 cm2, and water is pouring out of it at the rate of 1.25 m per sec. If the pipe remains full , find the number of litres discharged per minute?
Answer» The cross- area of a pipe is 42 cm², and water is pouring out of it at the rate of 1.25 m per sec. If the pipe remains full , find the number of litres discharged per minute?

Discussion

45.	In the given figure, AC: CB is
Answer» In the given figure, AC: CB is

45.

In the given figure, AC: CB is

Answer»

In the given figure, AC: CB is

Discussion

46.	A cubical box can hold maximum 8 litres of water, what is the length its side?
Answer» A cubical box can hold maximum 8 litres of water, what is the length its side?

Discussion

47.	In ΔPQR, MN\|\|QR and MN divides the triangle into two parts of equal areas. QMPQ=??
Answer» In $Δ P Q R$ , MN\|\|QR and MN divides the triangle into two parts of equal areas. $\frac{Q M}{P Q} = ? ?$

47.

In ΔPQR, MN||QR and MN divides the triangle into two parts of equal areas. QMPQ=??

Answer»

In $Δ P Q R$ , MN||QR and MN divides the triangle into two parts of equal areas. $\frac{Q M}{P Q} = ? ?$

Discussion

48.	20. A cricketer has a mean score of 58 run in 9 innings.Find out how many runs are to be scored in the 10 th inning to raise the mean score to 61
Answer» 20. A cricketer has a mean score of 58 run in 9 innings.Find out how many runs are to be scored in the 10 th inning to raise the mean score to 61

Discussion

49.	The product of a nonzero rational number with an irrational number is always a/an (a) irrational number (b) rational number (c) whole number (d) natural number
Answer» The product of a nonzero rational number with an irrational number is always a/an (a) irrational number (b) rational number (c) whole number (d) natural number

49.

The product of a nonzero rational number with an irrational number is always a/an (a) irrational number (b) rational number (c) whole number (d) natural number

Answer»

The product of a nonzero rational number with an irrational number is always a/an

(a) irrational number

(b) rational number

(c) whole number

(d) natural number

Discussion

50.	If 2cos2A=√3 and A is acute, find sin3A.
Answer» If $2 cos 2 A = \sqrt{3}$ and A is acute, find $sin 3 A$ .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A trapezium has an area of 570 cm2. The height of the trapezium is 5 cm and the larger parallel side is twice in length of the smaller parallel side. Choose the correct option.

Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

Number of points at which the graph of functionye k(k> 0) intersects the x-axis is

In the given figure, chords AB=CD, ∠COD=60∘ and ∠AOD=170∘.Find the value of ∠BOC.

In a right angled triangle ABC, right angled at C, if tanA=cotB, then what is value of A + B?

Factorise: (2a+1)3+(a−1)3

An ox is tied to a pole situated at the center of a field, with a 10 m long rope. The ox moves keeping the rope tight. Find the area of the ground swept by the rope.( Use π=3.14)

factorise : 7√2x2-10x+4√2

In the standard form of an equation, ax2 + bx + c = 0, both roots of the equation are 0 if

Find the area of a trapezium whose parallel sides are 32 cm and 27 cm, and the distance between them is 15 cm.

The given graph shows the weekly earnings of workers of a factory. The weekly earnings of Rs 170 are received by how many workers?

In the method of regrouping, we ________ .

Question 11 In the following figure AD is the bisector of ∠BAC. Prove that AB &gt; BD.

Capacity of water tank is 1000 l. If the shape of tank is cube then find the side of the cube.

In the figure given below, if ∠AOP=75∘ and ∠AOB=120∘, then ∠AQP= ___.

The number of cartoons drawn by a cartoonist is given by the equation, y = 10x + 5, where x is the number of days, y is the total number of cartoons. Which of the following graph shows the correct data for this situation?

The line graph below shows people in a store at various times of the day. How many people are there in the store at 2:30 pm?

Let A and B be two events for which P(A) = a, P(B) = b, PA∩B=c, then P(A∩B) = __________________.

The value of sin2ϕ+cos2θ is equal to

Factorise (n2+22n+96)

Check whether the linear equation 3x + 5 = 11 is true for x = 2.

Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.

(i) Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.(ii) Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.

ABCD is a rhombus. IF ∠BAC=38∘,find(1) ∠ACB(2) ∠DAC(3) ∠ADC

In the given figure, ABCD is a square and DEC is equilateral. The value of x is:

Tangents are drawn from origin to the curve y=sinx+cosx. Then their points of contact lie on the curve.

If height of equilateral triangle is 3 cm Find area

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:(i)(ii)(iii)(iv)(v)(vi)

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m2.

In a triangle ABC, if b + c = 2a and ∠ A=600, then Δ ABC is

Simplify (2x-5y)3-(2x+5y)3

Examine the figure and identify which of the following are collinear points.

The decimal expansion of pi is:

Three unbiased coins are tossed together. The probability of getting at least two heads is

Mark the correct answer in each of the following:The converse of the statement "If x > y, then x + a > y + a", is(a) If x < y, then x + a < y + a(b) If x + a > y + a, then x > y(c) If x < y, then x + a > y + a(d) If x > y, then x + a < y + a

15. Two points P (2,0) and Q (-2,0) are given. R is a variable point on one side of the line PQ such that (angleRPQ)-(angleRQP) is a positive constant (2alpha). The locus of R is

How to repersent √5 on a number line

Prove by vector method that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

If x3+6x2+4x+k is exactly divisible by (x+2), then the value of k is -

If (x+1) is a factor of the polynomial 2x^3+8x^2+3x+k. Then find the value of k

Question 16If two adjacent angles of a parallelogram are (5x−5)∘ and (10x+35)∘, then the ratio of these angles is ___________.a) 1 : 3b) 2 : 3c) 1 : 4d) 1 : 2

The cross- area of a pipe is 42 cm2, and water is pouring out of it at the rate of 1.25 m per sec. If the pipe remains full , find the number of litres discharged per minute?

In the given figure, AC: CB is

A cubical box can hold maximum 8 litres of water, what is the length its side?

In ΔPQR, MN||QR and MN divides the triangle into two parts of equal areas. QMPQ=??

20. A cricketer has a mean score of 58 run in 9 innings.Find out how many runs are to be scored in the 10 th inning to raise the mean score to 61

The product of a nonzero rational number with an irrational number is always a/an (a) irrational number (b) rational number (c) whole number (d) natural number

If 2cos2A=√3 and A is acute, find sin3A.

Question 11 In the following figure AD is the bisector of ∠BAC. Prove that AB > BD.