32581 + Interview Questions in Mathematics

1.	Find the values of k for which the given equation has real and equal roots: [3 MARKS] x2−2x(1+3k)+7(3+2k)=0
Answer» Find the values of k for which the given equation has real and equal roots: [3 MARKS] $x^{2} - 2 x (1 + 3 k) + 7 (3 + 2 k) = 0$

Discussion

2.	Sides of two similar triangles are in the ratio of 8 : 9. Areas of these triangles are in the ratio.
Answer» Sides of two similar triangles are in the ratio of 8 : 9. Areas of these triangles are in the ratio.

Discussion

3.	Which of the following terms of the AP 3, 15, 27, 39, .... will be 132 more than its 54th term?
Answer» Which of the following terms of the AP 3, 15, 27, 39, .... will be 132 more than its $54^{t h}$ term?

Discussion

4.	If you randomly pick a day of the week twice, find the probability of picking (i) the same day twice (ii) adjacent days. [3 MARKS]
Answer» If you randomly pick a day of the week twice, find the probability of picking (i) the same day twice (ii) adjacent days. [3 MARKS]

Discussion

5.	A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a card bearing a number greater than 2 but less than 9.
Answer» A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a card bearing a number greater than 2 but less than 9.

Discussion

6.	Question 3 Prove that one of any three consecutive positive integers must be divisible by 3.
Answer» Question 3 Prove that one of any three consecutive positive integers must be divisible by 3.

Discussion

7.	Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and ∠BOD = 160∘, then find the measure of ∠BPD.
Answer» Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $∠$ BOD = $160^{\circ}$ , then find the measure of $∠$ BPD.

7.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and ∠BOD = 160∘, then find the measure of ∠BPD.

Answer»

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $∠$ BOD = $160^{\circ}$ , then find the measure of $∠$ BPD.

Discussion

8.	If x a set of all real numbers R the find the solution set for (x−3)(x+5)<0
Answer» If x a set of all real numbers R the find the solution set for $(x - 3) (x + 5) < 0$

Discussion

9.	Match the following objects to their volume.
Answer» Match the following objects to their volume.

Discussion

10.	Match the terms having same value.
Answer» Match the terms having same value.

Discussion

11.	Assertion (A)Reason (R)At a point P of a circle with centreThe tangent at any point of a circle isO and radius 12 cm, a tangent PQPerpendicular to the radius throughof length 16 cm is drawn. Then,the point of contact.OQ=20 cm The correct answer is (a)/(b)/(c)/(d).
Answer» $\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) A t a p o i n t P o f a c i r c l e w i t h c e n t r e & T h e t a n g e n t a t a n y p o i n t o f a c i r c l e i s O a n d r a d i u s 12 c m, a t a n g e n t P Q & P e r p e n d i c u l a r t o t h e r a d i u s t h r o u g h o f l e n g t h 16 c m i s d r a w n . T h e n, & t h e p o i n t o f c o n t a c t . O Q = 20 c m \end{matrix}$ The correct answer is (a)/(b)/(c)/(d).

11.

Assertion (A)Reason (R)At a point P of a circle with centreThe tangent at any point of a circle isO and radius 12 cm, a tangent PQPerpendicular to the radius throughof length 16 cm is drawn. Then,the point of contact.OQ=20 cm The correct answer is (a)/(b)/(c)/(d).

Answer»

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) A t a p o i n t P o f a c i r c l e w i t h c e n t r e & T h e t a n g e n t a t a n y p o i n t o f a c i r c l e i s O a n d r a d i u s 12 c m, a t a n g e n t P Q & P e r p e n d i c u l a r t o t h e r a d i u s t h r o u g h o f l e n g t h 16 c m i s d r a w n . T h e n, & t h e p o i n t o f c o n t a c t . O Q = 20 c m \end{matrix}$

The correct answer is (a)/(b)/(c)/(d).

Discussion

12.	Ram asked Kiran to find the ‘surface area’ of a flower vase. What does Kiran need to do?
Answer» Ram asked Kiran to find the ‘surface area’ of a flower vase. What does Kiran need to do?

Discussion

13.	The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 14 . The probability of selecting a blue ball at random from the same jar is 13. If the jar contains 10 orange balls, find the total number of balls in the jar.
Answer» The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is $\frac{1}{4}$ . The probability of selecting a blue ball at random from the same jar is $\frac{1}{3}$ . If the jar contains 10 orange balls, find the total number of balls in the jar.

Discussion

14.	In Fig. OC = 20 cm. In sector OQBP, square OABC is inscribed. Find the area of the shaded region.
Answer» In Fig. OC = 20 cm. In sector OQBP, square OABC is inscribed. Find the area of the shaded region.

Discussion

15.	A boiler is in the form of a cylinder 2 m long with hemispherical ends of 2 metre diameter.Find the volume of the boiler.
Answer» A boiler is in the form of a cylinder 2 m long with hemispherical ends of 2 metre diameter.Find the volume of the boiler.

Discussion

16.	The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.
Answer» The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.

Discussion

17.	An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45∘ with the horizontal through the foot of the pole, find the length of the wire.
Answer» An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of $45^{\circ}$ with the horizontal through the foot of the pole, find the length of the wire.

Discussion

18.	A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)
Answer» A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of $π$ as found appropriate)

Discussion

19.	Find out which part of the sentence has an error: The teacher tolda the students thatb the earth movedc around the sund
Answer» Find out which part of the sentence has an error: $\frac{T h e t e a c h e r t o l d}{a} \frac{t h e s t u d e n t s t h a t}{b} \frac{t h e e a r t h m o v e d}{c} \frac{a r o u n d t h e s u n}{d}$

19.

Find out which part of the sentence has an error: The teacher tolda the students thatb the earth movedc around the sund

Answer»

Find out which part of the sentence has an error:

$\frac{T h e t e a c h e r t o l d}{a} \frac{t h e s t u d e n t s t h a t}{b} \frac{t h e e a r t h m o v e d}{c} \frac{a r o u n d t h e s u n}{d}$

Discussion

20.	In Krishna’s family there are 4 members. The daily rice consumption of the 4 family members are - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the rice consumption per family member. What is the quantity that will come into use now?
Answer» In Krishna’s family there are 4 members. The daily rice consumption of the 4 family members are - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the rice consumption per family member. What is the quantity that will come into use now?

Discussion

21.	A shopkeeper sells lemon juice. He fills glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges Rs. 10 for each glass of height 10cm and 4cm radius. Find the amount of money he earns by selling juice. (Take π= 227)
Answer» A shopkeeper sells lemon juice. He fills glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges Rs. 10 for each glass of height 10cm and 4cm radius. Find the amount of money he earns by selling juice. (Take $π$ = $\frac{22}{7}$ )

Discussion

22.	Solve the matrix equation [41]*X=[(-4)8(-1)2]
Answer» Solve the matrix equation [41]*X=[(-4)8(-1)2]

Discussion

23.	If set A has 10 elements and set B has 4 elements, number of elements in set A × B is _____.
Answer» If set A has 10 elements and set B has 4 elements, number of elements in set A $\times$ B is _____.

Discussion

24.	Draw a histogram from the following frequency distribution and find the mode from the graph: [4 MARKS] ClassFrequency0−525−10510−151815−201420−25825−305
Answer» Draw a histogram from the following frequency distribution and find the mode from the graph: [4 MARKS] $\begin{matrix} C l a s s & F r e q u e n c y 0 - 5 & 2 5 - 10 & 5 10 - 15 & 18 15 - 20 & 14 20 - 25 & 8 25 - 30 & 5 \end{matrix}$

Discussion

25.	ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its in circle is
Answer» ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its in circle is

25.

ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its in circle is

Answer»

ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its in circle is

Discussion

26.	Which of the following is the inverse ratio of 23:15
Answer» Which of the following is the inverse ratio of 23:15

Discussion

27.	For any arithmatic progression the. Expiration for. The nth. Team is always a. ........... Expiration in. n.?
Answer» For any arithmatic progression the. Expiration for. The nth. Team is always a. ........... Expiration in. n.?

Discussion

28.	The given image is equal to (x+y+z)2, which parts are equal to x2 and yz?
Answer» The given image is equal to $(x + y + z)^{2}$ , which parts are equal to $x^{2}$ and yz?

Discussion

29.	If α,β are zeros of x²-(k-6)x+(2x+1) . Find k if α+β=αβ
Answer» If α,β are zeros of x²-(k-6)x+(2x+1) . Find k if α+β=αβ

Discussion

30.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

31.	If ABC=1 , show that 1/1+a+b^-1 + 1/1+b+c^-1 + 1/1+c+a^-1=1
Answer» If ABC=1 , show that 1/1+a+b^-1 + 1/1+b+c^-1 + 1/1+c+a^-1=1

Discussion

32.	Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x)=2x3+x2−2x−1,g(x)=x+1 (ii) p(x)=x3+3x2+3x+1,g(x)=x+2 (iii) p(x)=x3−4x2+x+6,g(x)=x−3
Answer» Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x)=2 $x^{3}$ + $x^{2}$ −2x−1,g(x)=x+1 (ii) p(x)= $x^{3}$ +3 $x^{2}$ +3x+1,g(x)=x+2 (iii) p(x)= $x^{3}$ −4 $x^{2}$ +x+6,g(x)=x−3

Discussion

33.	Sum of four consecutive number in an AP is 32 and the ratio of products of first and last term to the product of middle term is 7:15. Find the no.
Answer» Sum of four consecutive number in an AP is 32 and the ratio of products of first and last term to the product of middle term is 7:15. Find the no.

Discussion

34.	A man wants to buy 62 shares available at Rs 132 (par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5%, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy? [4 MARKS]
Answer» A man wants to buy 62 shares available at Rs 132 (par value of Rs 100) (i) How much should he invest? (ii) If the dividend is $7.5 %$ , what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy? [4 MARKS]

Discussion

35.	A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the surface area tin is
Answer» A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the surface area tin is

Discussion

36.	A big iron boiler tank opened on top is cylindrical in shape. It's height is 10 m and radius is 7 m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it totally gets corroded is (Take π=227)
Answer» A big iron boiler tank opened on top is cylindrical in shape. It's height is $10$ m and radius is $7$ m. It gets corroded at a rate of $3$ sq. meter/day. The number of days in which it totally gets corroded is $(Take π = \frac{22}{7})$

Discussion

37.	If cos (40o + A) = sin 30o, the value of A is:
Answer» If cos (40^o + A) = sin 30^o, the value of A is:

Discussion

38.	In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB=100∘, then ∠BAT is equal to
Answer» In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If $∠ A O B = 100^{\circ}$ , then $∠ B A T$ is equal to

38.

In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB=100∘, then ∠BAT is equal to

Answer»

In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If $∠ A O B = 100^{\circ}$ , then $∠ B A T$ is equal to

Discussion

39.	In the given figure what is the relation between PA and PB.
Answer» In the given figure what is the relation between PA and PB.

39.

In the given figure what is the relation between PA and PB.

Answer»

In the given figure what is the relation between PA and PB.

Discussion

40.	Mention the procedures to draw the quadratic graph y=ax2+bx+c
Answer» Mention the procedures to draw the quadratic graph $y = a x^{2} + b x + c$

Discussion

41.	How many balls, each of radii 0.5 cm, can be made from a solid sphere of metal of radius 10 cm by melting it?
Answer» How many balls, each of radii 0.5 cm, can be made from a solid sphere of metal of radius 10 cm by melting it?

Discussion

42.	Taxes which are really paid by those on whom they are legally imposed are known as
Answer» Taxes which are really paid by those on whom they are legally imposed are known as

Discussion

43.	A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q. If AQ and BP intersect at R, the locus of R is
Answer» A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q. If AQ and BP intersect at R, the locus of R is

Discussion

44.	If the perimeter and area of a circle are numerically equal, then the radius of the circle is
Answer» If the perimeter and area of a circle are numerically equal, then the radius of the circle is

Discussion

45.	OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region. ___ cm2 .
Answer» OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region. ___ $c m^{2}$ .

45.

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region. ___ cm2 .

Answer»

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.

___

c m^{2}

.

Discussion

46.	Two radii of a circle are inclined at 130∘. Tangents are drawn at the end points of the diameters formed from the radii to form a quadrilateral. Explain the special quadrilateral formed.
Answer» Two radii of a circle are inclined at $130^{\circ}$ . Tangents are drawn at the end points of the diameters formed from the radii to form a quadrilateral. Explain the special quadrilateral formed.

Discussion

47.	When divided by x - 3 the polynomials x3−px2+x+6 and 2x3−x2−(p+3)x−6 leave the same remainder. Find the value of 'p'.
Answer» When divided by x - 3 the polynomials $x^{3} - p x^{2} + x + 6$ and $2 x^{3} - x^{2} - (p + 3) x - 6$ leave the same remainder. Find the value of 'p'.

Discussion

48.	What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?
Answer» What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?

Discussion

49.	In triangle ABC, write Cos in terms of [B+C/2] in terms of angle A
Answer» In triangle ABC, write Cos in terms of [B+C/2] in terms of angle A

Discussion

50.	What is the probability that a leap year selected at random will contain 53 Sundays?
Answer» What is the probability that a leap year selected at random will contain 53 Sundays?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the values of k for which the given equation has real and equal roots: [3 MARKS] x2−2x(1+3k)+7(3+2k)=0

Sides of two similar triangles are in the ratio of 8 : 9. Areas of these triangles are in the ratio.

Which of the following terms of the AP 3, 15, 27, 39, .... will be 132 more than its ​54th term?

If you randomly pick a day of the week twice, find the probability of picking (i) the same day twice (ii) adjacent days. [3 MARKS]

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a card bearing a number greater than 2 but less than 9.

Question 3 Prove that one of any three consecutive positive integers must be divisible by 3.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and ∠BOD = 160∘, then find the measure of ∠BPD.

If x a set of all real numbers R the find the solution set for (x−3)(x+5)&lt;0

Match the following objects to their volume.

Match the terms having same value.

Assertion (A)Reason (R)At a point P of a circle with centreThe tangent at any point of a circle isO and radius 12 cm, a tangent PQPerpendicular to the radius throughof length 16 cm is drawn. Then,the point of contact.OQ=20 cm The correct answer is (a)/(b)/(c)/(d).

Ram asked Kiran to find the ‘surface area’ of a flower vase. What does Kiran need to do?

The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 14 . The probability of selecting a blue ball at random from the same jar is 13. If the jar contains 10 orange balls, find the total number of balls in the jar.

In Fig. OC = 20 cm. In sector OQBP, square OABC is inscribed. Find the area of the shaded region.

A boiler is in the form of a cylinder 2 m long with hemispherical ends of 2 metre diameter.Find the volume of the boiler.

The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.

An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45∘ with the horizontal through the foot of the pole, find the length of the wire.

A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)

Find out which part of the sentence has an error: The teacher tolda the students thatb the earth movedc around the sund

In Krishna’s family there are 4 members. The daily rice consumption of the 4 family members are - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the rice consumption per family member. What is the quantity that will come into use now?

A shopkeeper sells lemon juice. He fills glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges Rs. 10 for each glass of height 10cm and 4cm radius. Find the amount of money he earns by selling juice. (Take π= 227)

Solve the matrix equation [41]*X=[(-4)8(-1)2]

If set A has 10 elements and set B has 4 elements, number of elements in set A × B is _____.

Draw a histogram from the following frequency distribution and find the mode from the graph: [4 MARKS] ClassFrequency0−525−10510−151815−201420−25825−305

ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its in circle is

Which of the following is the inverse ratio of 23:15

For any arithmatic progression the. Expiration for. The nth. Team is always a. ........... Expiration in. n.?

The given image is equal to (x+y+z)2, which parts are equal to x2 and yz?

If α,β are zeros of x²-(k-6)x+(2x+1) . Find k if α+β=αβ

Which of the following should be the LAST sentence after rearrangement?

If ABC=1 , show that 1/1+a+b^-1 + 1/1+b+c^-1 + 1/1+c+a^-1=1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x)=2x3+x2−2x−1,g(x)=x+1 (ii) p(x)=x3+3x2+3x+1,g(x)=x+2 (iii) p(x)=x3−4x2+x+6,g(x)=x−3

Sum of four consecutive number in an AP is 32 and the ratio of products of first and last term to the product of middle term is 7:15. Find the no.

A man wants to buy 62 shares available at Rs 132 (par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5%, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy? [4 MARKS]

A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the surface area tin is

A big iron boiler tank opened on top is cylindrical in shape. It's height is 10 m and radius is 7 m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it totally gets corroded is (Take π=227)

If cos (40o + A) = sin 30o, the value of A is:

In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB=100∘, then ∠BAT is equal to

In the given figure what is the relation between PA and PB.

Mention the procedures to draw the quadratic graph y=ax2+bx+c

How many balls, each of radii 0.5 cm, can be made from a solid sphere of metal of radius 10 cm by melting it?

Taxes which are really paid by those on whom they are legally imposed are known as

A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q. If AQ and BP intersect at R, the locus of R is

If the perimeter and area of a circle are numerically equal, then the radius of the circle is

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region. ___ cm2 .

Two radii of a circle are inclined at 130∘. Tangents are drawn at the end points of the diameters formed from the radii to form a quadrilateral. Explain the special quadrilateral formed.

When divided by x - 3 the polynomials x3−px2+x+6 and 2x3−x2−(p+3)x−6 leave the same remainder. Find the value of 'p'.

What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?

In triangle ABC, write Cos in terms of [B+C/2] in terms of angle A ​

What is the probability that a leap year selected at random will contain 53 Sundays?

Which of the following terms of the AP 3, 15, 27, 39, .... will be 132 more than its 54th term?

If x a set of all real numbers R the find the solution set for (x−3)(x+5)<0

In triangle ABC, write Cos in terms of [B+C/2] in terms of angle A