32581 + Interview Questions in Mathematics

1.	In the given fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).
Answer» In the given fig. a circle is inscribed in a quadrilateral ABCD in which $∠$ B = $90^{0}$ . If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

1.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

Answer»

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $∠$ B = $90^{0}$ . If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

Discussion

2.	The coordinates of the orthocentre of the triangle with vertices 2, 3-12, 12, -12 and 2, -12 are ________.
Answer» The coordinates of the orthocentre of the triangle with vertices $(2, \frac{\sqrt{3} - 1}{2}), (\frac{1}{2}, - \frac{1}{2})$ and $(2, - \frac{1}{2})$ are ________.

Discussion

3.	If surface area of a cube is changing at a rate of 5m^{2/s},find the rate of change of body diagonal at the moment when side length is 1m.
Answer» If surface area of a cube is changing at a rate of 5m^{2/s},find the rate of change of body diagonal at the moment when side length is 1m.

Discussion

4.	Question 9 If sinA+sin2A=1, then the value of (cos2A+cos4A) is (A) 1 (B) 12 (C) 2 (D) 3
Answer» Question 9 If $s i n A + s i n^{2} A = 1$ , then the value of $(c o s^{2} A + c o s^{4} A)$ is (A) $1$ (B) $\frac{1}{2}$ (C) $2$ (D) $3$

Discussion

5.	In figure, ABCD is a trapezium with AB\|\|DC, If △AED is similar to △BEC, prove that AD = BC
Answer» In figure, ABCD is a trapezium with AB\|\|DC, If $△$ AED is similar to $△$ BEC, prove that AD = BC

5.

In figure, ABCD is a trapezium with AB||DC, If △AED is similar to △BEC, prove that AD = BC

Answer»

In figure, ABCD is a trapezium with AB||DC, If $△$ AED is similar to $△$ BEC, prove that AD = BC

Discussion

6.	AB is a diameter and AC is chord of a circle with centre O such that ∠BAC=30∘. The tangent at C intersects AB at a point D. Prove that BC =BD.
Answer» AB is a diameter and AC is chord of a circle with centre O such that $∠ B A C = 30^{\circ}$ . The tangent at C intersects AB at a point D. Prove that BC =BD.

Discussion

7.	A Boat goes upstream at 2 km per hour and downstream at 5 km per hour. Represent the situation algebraically.
Answer» A Boat goes upstream at 2 km per hour and downstream at 5 km per hour. Represent the situation algebraically.

Discussion

8.	Find the value of k for which the following system of equations has no solution: (20-25): 2x + ky = 11 5x - 7y = 5
Answer» Find the value of k for which the following system of equations has no solution: (20-25): 2x + ky = 11 5x - 7y = 5

8.

Find the value of k for which the following system of equations has no solution: (20-25): 2x + ky = 11 5x - 7y = 5

Answer»

Find the value of k for which the following system of equations has no solution: (20-25):

2x + ky = 11

5x - 7y = 5

Discussion

9.	If the product of two numbers is 1050 and their HCF is 25, find their LCM.
Answer» If the product of two numbers is 1050 and their HCF is 25, find their LCM.

Discussion

10.	A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then perimeter of ∆ ABC = ___ AR.
Answer» A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then perimeter of ∆ ABC = ___ AR.

10.

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then perimeter of ∆ ABC = ___ AR.

Answer»

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then perimeter of ∆ ABC = ___ AR.

Discussion

11.	Question 2 (v) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. −14,14
Answer» Question 2 (v) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. $\frac{- 1}{4}, \frac{1}{4}$

11.

Question 2 (v) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. −14,14

Answer»

Question 2 (v)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$\frac{- 1}{4}, \frac{1}{4}$

Discussion

12.	Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation.(1) x − 4 = 3, x =−1, 7,−7(2) 9m = 81, m = 3, 9, −3(3) 2a + 4 = 0, a = 2, −2, 1(4) 3 − y = 4, y = −1, 1, 2
Answer» Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation. (1) x − 4 = 3, x =−1, 7,−7 (2) 9m = 81, m = 3, 9, −3 (3) 2a + 4 = 0, a = 2, −2, 1 (4) 3 − y = 4, y = −1, 1, 2

Discussion

13.	The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder ?
Answer» The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder ?

Discussion

14.	Two customers A and B are visiting a particular shop in the same week (Monday to Friday). Each of them is equally likely to visit the shop on any of these days. The probability that both will visit the shop on consecutive days is:[1 mark]
Answer» Two customers A and B are visiting a particular shop in the same week (Monday to Friday). Each of them is equally likely to visit the shop on any of these days. The probability that both will visit the shop on consecutive days is: [1 mark]

Discussion

15.	Solve the following simultaneous equations:14x+y=11;x+15y=6
Answer» Solve the following simultaneous equations: $\frac{1}{4} x + y = 11; x + \frac{1}{5} y = 6$

Discussion

16.	13. If (2n)!/3!(2n-3)! and n!/2!(n-2)! are in the ratio 44:3 then n is equal to
Answer» 13. If (2n)!/3!(2n-3)! and n!/2!(n-2)! are in the ratio 44:3 then n is equal to

Discussion

17.	What is a control setup ?
Answer» What is a control setup ?

Discussion

18.	There are 40 passengers on a bus. Some have tickets worth Rs 3 and remaining worth Rs 10. The total collection of these passengers is Rs 295. Find how many passengers have tickets worth Rs 3?
Answer» There are 40 passengers on a bus. Some have tickets worth Rs 3 and remaining worth Rs 10. The total collection of these passengers is Rs 295. Find how many passengers have tickets worth Rs 3?

Discussion

19.	The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.
Answer» The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.

Discussion

20.	Find area of quadrilateral ABCD
Answer» Find area of quadrilateral ABCD

Discussion

21.	A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use π = 3.14)
Answer» A bucket is in the form of a frustum of a cone with a capacity of 12308.8 $c m^{3}$ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use $π$ = 3.14)

Discussion

22.	The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by l2−a2k−(l+a), then k =
Answer» The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by $\frac{l^{2} - a^{2}}{k - (l + a)}$ , then k =

Discussion

23.	If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =(a) −1(b) 1(c) 0(d) None of these
Answer» If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ = (a) −1 (b) 1 (c) 0 (d) None of these

Discussion

24.	6.Find the total number of ways in which a person can buy 6 chocolates,if ther are 3 types of chocolates available. (Chocolate of same type are identical)
Answer» 6.Find the total number of ways in which a person can buy 6 chocolates,if ther are 3 types of chocolates available. (Chocolate of same type are identical)

Discussion

25.	A number consists of 2 digits whose sum is 5. If we add 9 with the number, the digits in the number are interchanged. Find the numbers
Answer» A number consists of 2 digits whose sum is 5. If we add 9 with the number, the digits in the number are interchanged. Find the numbers

Discussion

26.	Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.
Answer» Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.

Discussion

27.	Five years hence, a man's age will be three times the age of his son. Five years ago, the man was seven times as old as his son.Find their present ages.
Answer» Five years hence, a man's age will be three times the age of his son. Five years ago, the man was seven times as old as his son. Find their present ages.

Discussion

28.	Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: x6+y15=4 x3−y12=434
Answer» Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: $\frac{x}{6} + \frac{y}{15} = 4$ $\frac{x}{3} - \frac{y}{12} = 4 \frac{3}{4}$

28.

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: x6+y15=4 x3−y12=434

Answer»

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$\frac{x}{6} + \frac{y}{15} = 4$

$\frac{x}{3} - \frac{y}{12} = 4 \frac{3}{4}$

Discussion

29.	If -1 and 2 are the zeroes of polynomial 2x³-x²-5x-2 then what are it's other zeroes?
Answer» If -1 and 2 are the zeroes of polynomial 2x³-x²-5x-2 then what are it's other zeroes?

Discussion

30.	Howto plot y= 3x with step-by -step
Answer» Howto plot y= 3x with step-by -step

Discussion

31.	The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is(a) 321 π cm2(b) 300 π cm2(c) 260 π cm2(d) 250 π cm2
Answer» The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is (a) 321 π cm² (b) 300 π cm² (c) 260 π cm² (d) 250 π cm²

Discussion

32.	The product of two expressions is (a4 − 9a2 + 4a + 12) and their H.C.F. is (a − 2) find their L.C.M.
Answer» The product of two expressions is (a⁴ − 9a² + 4a + 12) and their H.C.F. is (a − 2) find their L.C.M.

Discussion

33.	Euclid’s division lemma states “Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r".Which of the following is true for r?
Answer» Euclid’s division lemma states “Given positive integers a and b, there exist unique integers q and r satisfying $a = b q + r$ ". Which of the following is true for r?

Discussion

34.	18. If tanθ =1+ 2tanα , prove that sinθ =(1+ sinα )
Answer» 18. If tanθ =1+ 2tanα , prove that sinθ =(1+ sinα )

Discussion

35.	Question 12Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y - axis, find the area of this triangle?
Answer» Question 12 Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y - axis, find the area of this triangle?

Discussion

36.	The minute hand of a clock is 21 cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.
Answer» The minute hand of a clock is $\sqrt{21}$ cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Discussion

37.	A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 143 m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.
Answer» A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $\frac{14}{3}$ m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

Discussion

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

Discussion

39.	the angle of elevation of the top of a tower at a point on the ground is 30. if on walkinf 20m towards the tower, the angle of elevation become 60, then the height of the tower is
Answer» the angle of elevation of the top of a tower at a point on the ground is 30. if on walkinf 20m towards the tower, the angle of elevation become 60, then the height of the tower is

Discussion

40.	If the sum of circumference of three circles with radii r1,r2 and r3 is equal to the circumference of a circle of radius R, then which of the following is true?
Answer» If the sum of circumference of three circles with radii $r_{1}, r_{2}$ and $r_{3}$ is equal to the circumference of a circle of radius $R$ , then which of the following is true?

Discussion

41.	In the given figure, the tangent from A touches the circle at B. BC is a diameter. The Line AC cuts the circle at P. The tangent at P cuts AB at M. If ∠PCB = x∘ , then ∠BPM = ____.
Answer» In the given figure, the tangent from A touches the circle at B. BC is a diameter. The Line AC cuts the circle at P. The tangent at P cuts AB at M. If $∠ P C B$ = $x^{\circ}$ , then $∠ B P M$ = ____.

41.

In the given figure, the tangent from A touches the circle at B. BC is a diameter. The Line AC cuts the circle at P. The tangent at P cuts AB at M. If ∠PCB = x∘ , then ∠BPM = ____.

Answer»

In the given figure, the tangent from A touches the circle at B. BC is a diameter.

The Line AC cuts the circle at P. The tangent at P cuts AB at M. If $∠ P C B$ = $x^{\circ}$ , then $∠ B P M$ = ____.

Discussion

42.

Find the missing frequencies and the median for the following distribution if the mean is 1.46. No. of accidents: 0 1 2 3 4 5 Total Frequency: 46 ? ? 25 10 5 200

Answer» Find the missing frequencies and the median for the following distribution if the mean is 1.46.

No. of accidents:	0	1	2	3	4	5	Total
Frequency:	46	?	?	25	10	5	200

Discussion

43.	A natural number, when increased by 12, equals 160 times its reciprocal find the number.
Answer» A natural number, when increased by 12, equals 160 times its reciprocal find the number.

Discussion

44.	24. The perimeters of two similar triangles are 25 cm and 15cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle? Also, derive the formula used.
Answer» 24. The perimeters of two similar triangles are 25 cm and 15cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle? Also, derive the formula used.

Discussion

45.	If A=[543−1],B=[2104] and C=[−3210] then find A + B - C
Answer» If $A = [\begin{matrix} 5 & 4 3 & - 1 \end{matrix}], B = [\begin{matrix} 2 & 1 0 & 4 \end{matrix}]$ and $C = [\begin{matrix} - 3 & 2 1 & 0 \end{matrix}]$ then find A + B - C

Discussion

46.	Gopal has a cumulative deposit account and deposits Rs 900 per month for a period of 4 years. If he gets Rs 52,020 at the time of maturity, find the rate of interest.
Answer» Gopal has a cumulative deposit account and deposits Rs 900 per month for a period of 4 years. If he gets Rs 52,020 at the time of maturity, find the rate of interest.

Discussion

47.	Choose the correct answer of the following question:If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2012]
Answer» Choose the correct answer of the following question: If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is (a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2012]

Discussion

48.	Solve each of the following quadratic equations:x2+6x+5=0
Answer» Solve each of the following quadratic equations: $x^{2} + 6 x + 5 = 0$

Discussion

49.	If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 + bx + 1 = 0 having real roots is(a) 10(b) 7(c) 6(d) 12
Answer» If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax² + bx + 1 = 0 having real roots is (a) 10 (b) 7 (c) 6 (d) 12

Discussion

50.	Mark the number of terms of the polynomial 3a−2a2+3+4a3.4
Answer» Mark the number of terms of the polynomial $3 a - 2 a^{2} + 3 + 4 a^{3}$ . 4

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

The coordinates of the orthocentre of the triangle with vertices 2, 3-12, 12, -12 and 2, -12 are ________.

If surface area of a cube is changing at a rate of 5m^{2/s},find the rate of change of body diagonal at the moment when side length is 1m.

Question 9 If sinA+sin2A=1, then the value of (cos2A+cos4A) is (A) 1 (B) 12 (C) 2 (D) 3

In figure, ABCD is a trapezium with AB||DC, If △AED is similar to △BEC, prove that AD = BC

AB is a diameter and AC is chord of a circle with centre O such that ∠BAC=30∘. The tangent at C intersects AB at a point D. Prove that BC =BD.

A Boat goes upstream at 2 km per hour and downstream at 5 km per hour. Represent the situation algebraically.

Find the value of k for which the following system of equations has no solution: (20-25): 2x + ky = 11 5x - 7y = 5

If the product of two numbers is 1050 and their HCF is 25, find their LCM.

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then perimeter of ∆ ABC = ___ AR.

Question 2 (v) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. −14,14

Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation.(1) x − 4 = 3, x =−1, 7,−7(2) 9m = 81, m = 3, 9, −3(3) 2a + 4 = 0, a = 2, −2, 1(4) 3 − y = 4, y = −1, 1, 2

The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder ?

Two customers A and B are visiting a particular shop in the same week (Monday to Friday). Each of them is equally likely to visit the shop on any of these days. The probability that both will visit the shop on consecutive days is:[1 mark]

Solve the following simultaneous equations:14x+y=11;x+15y=6

13. If (2n)!/3!(2n-3)! and n!/2!(n-2)! are in the ratio 44:3 then n is equal to

What is a control setup ?

There are 40 passengers on a bus. Some have tickets worth Rs 3 and remaining worth Rs 10. The total collection of these passengers is Rs 295. Find how many passengers have tickets worth Rs 3?

The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.

Find area of quadrilateral ABCD

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use π = 3.14)

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by l2−a2k−(l+a), then k =

If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =(a) −1(b) 1(c) 0(d) None of these

6.Find the total number of ways in which a person can buy 6 chocolates,if ther are 3 types of chocolates available. (Chocolate of same type are identical)

A number consists of 2 digits whose sum is 5. If we add 9 with the number, the digits in the number are interchanged. Find the numbers

Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.

Five years hence, a man's age will be three times the age of his son. Five years ago, the man was seven times as old as his son.Find their present ages.

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution: x6+y15=4 x3−y12=434

If -1 and 2 are the zeroes of polynomial 2x³-x²-5x-2 then what are it's other zeroes?

Howto plot y= 3x with step-by -step

The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is(a) 321 π cm2(b) 300 π cm2(c) 260 π cm2(d) 250 π cm2

The product of two expressions is (a4 − 9a2 + 4a + 12) and their H.C.F. is (a − 2) find their L.C.M.

Euclid’s division lemma states “Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r".Which of the following is true for r?

18. If tanθ =1+ 2tanα , prove that sinθ =(1+ sinα )

Question 12Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y - axis, find the area of this triangle?

The minute hand of a clock is 21 cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 143 m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2-2ax-4b2-a2=0 [CBSE 2015]

the angle of elevation of the top of a tower at a point on the ground is 30. if on walkinf 20m towards the tower, the angle of elevation become 60, then the height of the tower is

If the sum of circumference of three circles with radii r1,r2 and r3 is equal to the circumference of a circle of radius R, then which of the following is true?

In the given figure, the tangent from A touches the circle at B. BC is a diameter. The Line AC cuts the circle at P. The tangent at P cuts AB at M. If ∠PCB = x∘ , then ∠BPM = ____.

Find the missing frequencies and the median for the following distribution if the mean is 1.46. No. of accidents: 0 1 2 3 4 5 Total Frequency: 46 ? ? 25 10 5 200

A natural number, when increased by 12, equals 160 times its reciprocal find the number.

24. The perimeters of two similar triangles are 25 cm and 15cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle? Also, derive the formula used.

If A=[543−1],B=[2104] and C=[−3210] then find A + B - C

Gopal has a cumulative deposit account and deposits Rs 900 per month for a period of 4 years. If he gets Rs 52,020 at the time of maturity, find the rate of interest.

Choose the correct answer of the following question:If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2012]

Solve each of the following quadratic equations:x2+6x+5=0

If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 + bx + 1 = 0 having real roots is(a) 10(b) 7(c) 6(d) 12

Mark the number of terms of the polynomial 3a−2a2+3+4a3.4