32581 + Interview Questions in Mathematics

1.	In the figure, AQ, AR and BC are tangents to circle with centre O, if AB = 7 cm, BC = 5 cm, AC = 5 cm, then length of the tangent AQ is:
Answer» In the figure, AQ, AR and BC are tangents to circle with centre O, if AB = 7 cm, BC = 5 cm, AC = 5 cm, then length of the tangent AQ is:

1.

In the figure, AQ, AR and BC are tangents to circle with centre O, if AB = 7 cm, BC = 5 cm, AC = 5 cm, then length of the tangent AQ is:

Answer»

In the figure, AQ, AR and BC are tangents to circle with centre O, if AB = 7 cm, BC = 5 cm, AC = 5 cm, then length of the tangent AQ is:

Discussion

2.	In the given figure, each of PA, QB, RC and SD is perpendicular to l. If AB = 6 cm, BC = 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.
Answer» In the given figure, each of PA, QB, RC and SD is perpendicular to l. If AB = 6 cm, BC = 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.

Discussion

3.	Solve each of the following quadratic equations:3x2-22x-23=0 [CBSE 2011]
Answer» Solve each of the following quadratic equations: $\sqrt{3} x^{2} - 2 \sqrt{2} x - 2 \sqrt{3} = 0$ [CBSE 2011]

Discussion

4.	Question 2 (i)Choose the correct choice in the following and justify.(i) 30th term of the A. P: 10, 7, 4, ….., isA) 97B) 77C) -77D) 87
Answer» Question 2 (i) Choose the correct choice in the following and justify. (i) $30^{t h}$ term of the A. P: 10, 7, 4, ….., is A) 97 B) 77 C) -77 D) 87

Discussion

5.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:4x2+4bx-a2-b2=0 [CBSE 2015]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$ [CBSE 2015]

Discussion

6.	The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.
Answer» The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.

Discussion

7.	Choose the correct answer of the following question:From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of thetower. The height of the tower is(a) 20 m (b) 40 m (c) 60 m (d) 80 m [CBSE 2013C]
Answer» Choose the correct answer of the following question: From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is (a) 20 m (b) 40 m (c) 60 m (d) 80 m [CBSE 2013C]

Discussion

8.	If the radius of both the circles are 5 cm, find the length of AB in the diagram shown below.
Answer» If the radius of both the circles are 5 cm, find the length of AB in the diagram shown below.

Discussion

9.	If a coin is tossed 3 times, what is the probability of getting a tail each time?
Answer» If a coin is tossed 3 times, what is the probability of getting a tail each time?

Discussion

10.	The sub-triplicate ratio of 2744:3375 is _____________
Answer» The sub-triplicate ratio of 2744:3375 is _____________

Discussion

11.	The range of the function f(x) defined by f(x)=x1+x2 is
Answer» The range of the function f(x) defined by $f (x) = \frac{x}{1 + x^{2}}$ is

Discussion

12.	31. CosA-sinA+1÷cosA+sinA-1=cosecA+cotA
Answer» 31. CosA-sinA+1÷cosA+sinA-1=cosecA+cotA

Discussion

13.	A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?
Answer» A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?

Discussion

14.	If the tangents PA and PB from an external point P to circle with centre O are inclined to each other at an angle of 400, then ∠POA =
Answer» If the tangents PA and PB from an external point P to circle with centre O are inclined to each other at an angle of $40^{0}$ , then $∠$ POA =

Discussion

15.	In Triangle ABC,AB=15cm,AC=8cm,∠A=50∘, as shown below.The length of BC will be equal to [sin50∘=0.76,cos50∘=0.64]
Answer» In Triangle $A B C, A B = 15 c m, A C = 8 c m, ∠ A = 50^{\circ},$ as shown below.The length of BC will be equal to $[s i n 50^{\circ} = 0.76, c o s 50^{\circ} = 0.64]$

15.

In Triangle ABC,AB=15cm,AC=8cm,∠A=50∘, as shown below.The length of BC will be equal to [sin50∘=0.76,cos50∘=0.64]

Answer»

In Triangle $A B C, A B = 15 c m, A C = 8 c m, ∠ A = 50^{\circ},$ as shown below.The length of BC will be equal to $[s i n 50^{\circ} = 0.76, c o s 50^{\circ} = 0.64]$

Discussion

16.	A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used in Rs 20 per 100 cm2 .(Use π = 3.14)
Answer» A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used in Rs 20 per 100 cm² . (Use π = 3.14)

Discussion

17.	If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is(a) 310(b) 29100(c) 13(d) 725
Answer» If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is (a) $\frac{3}{10}$ (b) $\frac{29}{100}$ (c) $\frac{1}{3}$ (d) $\frac{7}{25}$

Discussion

18.	Question 49 Which ratio is larger 10 : 21 and 21 : 93?
Answer» Question 49 Which ratio is larger 10 : 21 and 21 : 93?

18.

Question 49 Which ratio is larger 10 : 21 and 21 : 93?

Answer»

Question 49

Which ratio is larger 10 : 21 and 21 : 93?

Discussion

19.	If the circumference of a circle and the perimeter of a square are equal , then(a) Area of the circle = Area of the square (b) Area of the circle < Area of the square(c) Area of the circle > Area of the square (d) nothing definite can be said
Answer» If the circumference of a circle and the perimeter of a square are equal , then (a) Area of the circle = Area of the square (b) Area of the circle < Area of the square (c) Area of the circle > Area of the square (d) nothing definite can be said

Discussion

20.	The total surface area of hollow cylinder having the inner and outer radii as R2 and R is xπR(R+L4). Find x.3
Answer» The total surface area of hollow cylinder having the inner and outer radii as $\frac{R}{2}$ and $R$ is $x π R (R + \frac{L}{4})$ . Find x. 3

Discussion

21.	In the previous question
Answer» In the previous question

Discussion

22.	If the sum of 99 terms of AP is 198, then what is the value of the 50th term? [1 MARK]
Answer» If the sum of 99 terms of AP is 198, then what is the value of the 50th term? [1 MARK]

Discussion

23.	From the given figure, find the unknown x.
Answer» From the given figure, find the unknown x.

23.

From the given figure, find the unknown x.

Answer»

From the given figure, find the unknown x.

Discussion

24.	In a single throw of a die,the probability of getting a number greater than 6 is___
Answer» In a single throw of a die,the probability of getting a number greater than 6 is___

Discussion

25.	Prove that the area of a trapezium ABCD =12× (sum of parallel sides) × distance between parallel sides.
Answer» Prove that the area of a trapezium ABCD $= \frac{1}{2} \times$ (sum of parallel sides) × distance between parallel sides.

Discussion

26.	Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(-5, -5), B(5, -4), C(4, 8) and D(-4, 6). (ii) Construct the locus of points equidistant from B and C. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PB = PC and P is equidistant from AB and AC. Then P lies in
Answer» Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(-5, -5), B(5, -4), C(4, 8) and D(-4, 6). (ii) Construct the locus of points equidistant from B and C. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PB = PC and P is equidistant from AB and AC. Then P lies in

26.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Plot the points A(-5, -5), B(5, -4), C(4, 8) and D(-4, 6). (ii) Construct the locus of points equidistant from B and C. (iii) Construct the locus of points equidistant from AB and AC. (iv) Locate the point P such that PB = PC and P is equidistant from AB and AC. Then P lies in

Answer»

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

(i) Plot the points A(-5, -5), B(5, -4), C(4, 8) and D(-4, 6).

(ii) Construct the locus of points equidistant from B and C.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Locate the point P such that PB = PC and P is equidistant from AB and AC.

Then P lies in

Discussion

27.	What is the net of the given shape?
Answer» What is the net of the given shape?

Discussion

28.	Choose the right answer from the options given after every question.The three angle bisectors of a triangle are concurrent. Their point of concurrence is called the ....................... .(i) circumcentre (ii) apex (iii) incentre (iv) point of intersection.
Answer» Choose the right answer from the options given after every question. The three angle bisectors of a triangle are concurrent. Their point of concurrence is called the ....................... . (i) circumcentre (ii) apex (iii) incentre (iv) point of intersection.

Discussion

29.	150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel. [CBSE 2014]
Answer» 150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel. [CBSE 2014]

Discussion

30.	Arun has a recurring deposit account in a bank. He deposited 2500 per month for 2 years. If he gets ₹ 66250 at the time of maturity. Find the rate of interest will be equal to ___ %.
Answer» Arun has a recurring deposit account in a bank. He deposited 2500 per month for 2 years. If he gets ₹ 66250 at the time of maturity. Find the rate of interest will be equal to ___ %.

Discussion

31.	P and Q be the points of trisection of the line segment joining points A(2,-2) and B(-7,4) such that P is nearer to A. Then find the coordinates of P and Q.
Answer» P and Q be the points of trisection of the line segment joining points A(2,-2) and B(-7,4) such that P is nearer to A. Then find the coordinates of P and Q.

Discussion

32.	Draw a circle of radius 6 cm. Construct the two tangents to the circle from a P which is at the distance of 9 cm from centre. Measure the length of the tangents.
Answer» Draw a circle of radius 6 cm. Construct the two tangents to the circle from a P which is at the distance of 9 cm from centre. Measure the length of the tangents.

Discussion

33.	The graph for the following system of equations : 2x+3y=5 and 6x+9y=40 is shown S1: a1a2= b1b2 ≠ c1c2 S2 : The two lines intersect each other.
Answer» The graph for the following system of equations : $2 x + 3 y = 5 a n d 6 x + 9 y = 40$ is shown S1: $\frac{a_{1}}{a_{2}}$ = $\frac{b_{1}}{b_{2}}$ ≠ $\frac{c_{1}}{c_{2}}$ S2 : The two lines intersect each other.

33.

The graph for the following system of equations : 2x+3y=5 and 6x+9y=40 is shown S1: a1a2= b1b2 ≠ c1c2 S2 : The two lines intersect each other.

Answer»

The graph for the following system of equations :

$2 x + 3 y = 5 a n d 6 x + 9 y = 40$ is shown

S1: $\frac{a_{1}}{a_{2}}$ = $\frac{b_{1}}{b_{2}}$ ≠ $\frac{c_{1}}{c_{2}}$

S2 : The two lines intersect each other.

Discussion

34.	Question 1 (ii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(ii) 3x2+4x–4
Answer» Question 1 (ii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (ii) $3 x^{2} + 4 x - 4$

Discussion

35.	Using factor theorem factorise the expression completely: 33 + 22 – 19 + 6
Answer» Using factor theorem factorise the expression completely: 3³ + 2² – 19 + 6

Discussion

36.	A container shaped like a right circular cylinder has a diameter (d) equal to 12 cm and height (h) equal to 15 cm is full of ice cream. The ice cream is to be filled into 10 equal cons having a hemispherical shape on the top. If the height of the cone is 4 times its radius, find the height of the cone.
Answer» A container shaped like a right circular cylinder has a diameter (d) equal to 12 cm and height (h) equal to 15 cm is full of ice cream. The ice cream is to be filled into 10 equal cons having a hemispherical shape on the top. If the height of the cone is 4 times its radius, find the height of the cone.

Discussion

37.	Question 7. A positive integer when divided by the smallest odd prime, leaves a remainder r. Which of the following CANNOT be ? (a) 0 (b) 1 (c) 2 (d) 3 From byju's maths workbook..
Answer» Question 7. A positive integer when divided by the smallest odd prime, leaves a remainder r. Which of the following CANNOT be ? (a) 0 (b) 1 (c) 2 (d) 3 From byju's maths workbook..

37.

Question 7. A positive integer when divided by the smallest odd prime, leaves a remainder r. Which of the following CANNOT be ? (a) 0 (b) 1 (c) 2 (d) 3 From byju's maths workbook..

Answer»

Question 7. A positive integer when divided by the smallest odd prime, leaves a remainder r. Which
of the following CANNOT be ?
(a) 0 (b) 1 (c) 2 (d) 3

From byju's maths workbook..

Discussion

38.	Calculate the mean of the following distribution using step - deviation method. Class IntervalFrequency50−55555−602060−651065−701070−75962.3
Answer» Calculate the mean of the following distribution using step - deviation method. $\begin{matrix} Class Interval & Frequency 50 - 55 & 5 55 - 60 & 20 60 - 65 & 10 65 - 70 & 10 70 - 75 & 9 \end{matrix}$ 62.3

Discussion

39.	Which measure of central tendency can you obtain from the intersection point of the less than and greater than ogives?__
Answer» Which measure of central tendency can you obtain from the intersection point of the less than and greater than ogives? __

Discussion

40.	If sum of the first 21 terms of the series log912x+log913x+log914x+..., where x>0 is 504, then x is equal to:
Answer» If sum of the first $21$ terms of the series ${log}_{9^{\frac{1}{2}}} x + {log}_{9^{\frac{1}{3}}} x + {log}_{9^{\frac{1}{4}}} x + . . .,$ where $x > 0$ is $504,$ then $x$ is equal to:

Discussion

41.	Draw a circle of any radius with centre O. Draw two tangents to its inclined at an angle of 75∘ to each other. [3 MARKS]
Answer» Draw a circle of any radius with centre O. Draw two tangents to its inclined at an angle of $75^{\circ}$ to each other. [3 MARKS]

Discussion

42.	If A, B and C are interior angles of a triangle ABC, then what is sin(B+C2) in terms of cosine trigonometric function?
Answer» If A, B and C are interior angles of a triangle ABC, then what is $sin (\frac{B + C}{2})$ in terms of cosine trigonometric function?

Discussion

43.	Question 8 If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.
Answer» Question 8 If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

Discussion

44.	A triangle has integer sides. One side is three times a second side. The length of the third side is 15.The greatest possible perimeter of the triangle is
Answer» A triangle has integer sides. One side is three times a second side. The length of the third side is 15. The greatest possible perimeter of the triangle is

Discussion

45.	The mean of 1, 2, 3, 4 ...n is given by
Answer» The mean of 1, 2, 3, 4 ...n is given by

Discussion

46.	Why the x, y, z axes are to be denoted by i cap, j cap, and k cap respectively in case of vectors?
Answer» Why the x, y, z axes are to be denoted by i cap, j cap, and k cap respectively in case of vectors?

Discussion

47.	The figure shows the graph of y=x2. This graph is shifted downward by 9 units. Find the new roots of the equation.
Answer» The figure shows the graph of $y = x^{2}$ . This graph is shifted downward by 9 units. Find the new roots of the equation.

Discussion

48.	15. ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced atQ. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.
Answer» 15. ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced atQ. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

Discussion

49.	A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .
Answer» A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .

Discussion

50.	What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?
Answer» What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the figure, AQ, AR and BC are tangents to circle with centre O, if AB = 7 cm, BC = 5 cm, AC = 5 cm, then length of the tangent AQ is:

In the given figure, each of PA, QB, RC and SD is perpendicular to l. If AB = 6 cm, BC = 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.

Solve each of the following quadratic equations:3x2-22x-23=0 [CBSE 2011]

Question 2 (i)Choose the correct choice in the following and justify.(i) 30th term of the A. P: 10, 7, 4, ….., isA) 97B) 77C) -77D) 87

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:4x2+4bx-a2-b2=0 [CBSE 2015]

The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.

Choose the correct answer of the following question:From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of thetower. The height of the tower is(a) 20 m (b) 40 m (c) 60 m (d) 80 m [CBSE 2013C]

If the radius of both the circles are 5 cm, find the length of AB in the diagram shown below.

If a coin is tossed 3 times, what is the probability of getting a tail each time?

The sub-triplicate ratio of 2744:3375 is _____________

The range of the function f(x) defined by f(x)=x1+x2 is

31. CosA-sinA+1÷cosA+sinA-1=cosecA+cotA

A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?

If the tangents PA and PB from an external point P to circle with centre O are inclined to each other at an angle of 400, then ∠POA =

In Triangle ABC,AB=15cm,AC=8cm,∠A=50∘, as shown below.The length of BC will be equal to [sin50∘=0.76,cos50∘=0.64]

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used in Rs 20 per 100 cm2 .(Use π = 3.14)

If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is(a) 310(b) 29100(c) 13(d) 725

Question 49 Which ratio is larger 10 : 21 and 21 : 93?

If the circumference of a circle and the perimeter of a square are equal , then(a) Area of the circle = Area of the square (b) Area of the circle < Area of the square(c) Area of the circle > Area of the square (d) nothing definite can be said

The total surface area of hollow cylinder having the inner and outer radii as R2 and R is xπR(R+L4). Find x.3

In the previous question

If the sum of 99 terms of AP is 198, then what is the value of the 50th term? [1 MARK]

From the given figure, find the unknown x.

In a single throw of a die,the probability of getting a number greater than 6 is___

Prove that the area of a trapezium ABCD =12× (sum of parallel sides) × distance between parallel sides.

What is the net of the given shape?​​​​

Choose the right answer from the options given after every question.The three angle bisectors of a triangle are concurrent. Their point of concurrence is called the ....................... .(i) circumcentre (ii) apex (iii) incentre (iv) point of intersection.

150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel. [CBSE 2014]

Arun has a recurring deposit account in a bank. He deposited 2500 per month for 2 years. If he gets ₹ 66250 at the time of maturity. Find the rate of interest will be equal to ___ %.

P and Q be the points of trisection of the line segment joining points A(2,-2) and B(-7,4) such that P is nearer to A. Then find the coordinates of P and Q.

Draw a circle of radius 6 cm. Construct the two tangents to the circle from a P which is at the distance of 9 cm from centre. Measure the length of the tangents.

The graph for the following system of equations : 2x+3y=5 and 6x+9y=40 is shown S1: a1a2= b1b2 ≠ c1c2 S2 : The two lines intersect each other.

Question 1 (ii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(ii) 3x2+4x–4

Using factor theorem factorise the expression completely: 33 + 22 – 19 + 6

Question 7. A positive integer when divided by the smallest odd prime, leaves a remainder r. Which of the following CANNOT be ? (a) 0 (b) 1 (c) 2 (d) 3 From byju's maths workbook..

Calculate the mean of the following distribution using step - deviation method. Class IntervalFrequency50−55555−602060−651065−701070−75962.3

Which measure of central tendency can you obtain from the intersection point of the less than and greater than ogives?__

If sum of the first 21 terms of the series log912x+log913x+log914x+..., where x&gt;0 is 504, then x is equal to:

Draw a circle of any radius with centre O. Draw two tangents to its inclined at an angle of 75∘ to each other. [3 MARKS]

If A, B and C are interior angles of a triangle ABC, then what is sin(B+C2) in terms of cosine trigonometric function?

Question 8 If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.

A triangle has integer sides. One side is three times a second side. The length of the third side is 15.The greatest possible perimeter of the triangle is

The mean of 1, 2, 3, 4 ...n is given by

Why the x, y, z axes are to be denoted by i cap, j cap, and k cap respectively in case of vectors?

The figure shows the graph of y=x2. This graph is shifted downward by 9 units. Find the new roots of the equation.

15. ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced atQ. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .

What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively?

What is the net of the given shape?

If sum of the first 21 terms of the series log912x+log913x+log914x+..., where x>0 is 504, then x is equal to: