32581 + Interview Questions in Mathematics

1.	Decimal number 14587/400 will terminate after:
Answer» Decimal number 14587/400 will terminate after:

Discussion

2.	5 defective glasses are accidentally mixed with 20 good ones. The good ones and the defective ones look the same from the outside. If a glass is picked at random, what is the probability that the chosen glass is not defective?
Answer» 5 defective glasses are accidentally mixed with 20 good ones. The good ones and the defective ones look the same from the outside. If a glass is picked at random, what is the probability that the chosen glass is not defective?

Discussion

3.	If θ is an acute angle and tanθ=1√7, then the value of cosec2θ−sec2θcosec2θ+sec2θ is
Answer» If $θ$ is an acute angle and $t a n θ = \frac{1}{\sqrt{7}}$ , then the value of $\frac{c o s e c^{2} θ - s e c^{2} θ}{c o s e c^{2} θ + s e c^{2} θ}$ is

Discussion

4.	An infinite number of tangents can be drawn from (1, 2) to the circle x2+y2−2x−4y+λ=0, then λ=
Answer» An infinite number of tangents can be drawn from (1, 2) to the circle $x^{2} + y^{2} - 2 x - 4 y + λ = 0,$ then $λ =$

Discussion

5.	ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that CM=MA=12AB [4 MARKS]
Answer» $A B C$ is a triangle right angled at $C$ . A line through the mid-point $M$ of hypotenuse $A B$ and parallel to $B C$ intersects AC at D. Show that $C M = M A = \frac{1}{2} A B$ [4 MARKS]

Discussion

6.	In ΔABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?
Answer» In $Δ A B C$ , a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

Discussion

7.	ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP=∠BEQ=100∘. What is the value of ∠PRD?
Answer» ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $∠ A D P = ∠ B E Q = 100^{\circ}$ . What is the value of $∠ P R D$ ?

7.

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP=∠BEQ=100∘. What is the value of ∠PRD?

Answer»

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $∠ A D P = ∠ B E Q = 100^{\circ}$ . What is the value of $∠ P R D$ ?

Discussion

8.	The are of △ABC with vertices A(a, 0), O(0, 0) and B(0, b) in square units is (a) ab (b) 12ab (c) 12a2b2 (d) 12b2
Answer» The are of $△ A B C$ with vertices A(a, 0), O(0, 0) and B(0, b) in square units is (a) ab (b) $\frac{1}{2} a b$ (c) $\frac{1}{2} a^{2} b^{2}$ (d) $\frac{1}{2} b^{2}$

8.

The are of △ABC with vertices A(a, 0), O(0, 0) and B(0, b) in square units is (a) ab (b) 12ab (c) 12a2b2 (d) 12b2

Answer»

The are of $△ A B C$ with vertices A(a, 0), O(0, 0) and B(0, b) in square units is

(a) ab (b) $\frac{1}{2} a b$ (c) $\frac{1}{2} a^{2} b^{2}$ (d) $\frac{1}{2} b^{2}$

Discussion

9.	In the given figure, a circle touches the side DF of Δ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of Δ EDF is (a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm
Answer» In the given figure, a circle touches the side DF of $Δ$ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of $Δ$ EDF is (a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm

9.

In the given figure, a circle touches the side DF of Δ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of Δ EDF is (a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm

Answer»

In the given figure, a circle touches the side DF of $Δ$ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of $Δ$ EDF is

(a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm

Discussion

10.	(i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path. (ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.
Answer» (i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path. (ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.

10.

(i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path. (ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.

Answer»

(i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path.

(ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.

Discussion

11.	Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60∘.
Answer» Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of $60^{\circ} .$

Discussion

12.	Find the value for k which each of the following systems of equations has a unique solution: 5x−7y−5=0,2x+ky−1=0.
Answer» Find the value for k which each of the following systems of equations has a unique solution: $5 x - 7 y - 5 = 0, 2 x + k y - 1 = 0.$

12.

Find the value for k which each of the following systems of equations has a unique solution: 5x−7y−5=0,2x+ky−1=0.

Answer»

Find the value for k which each of the following systems of equations has a unique solution:

$5 x - 7 y - 5 = 0, 2 x + k y - 1 = 0.$

Discussion

13.	If teh zeros of the polynomial f(x)=ax3+3bx2+3cx+d are in A.P., prove that 2b3−3abc+a2d=0
Answer» If teh zeros of the polynomial $f (x) = a x^{3} + 3 b x^{2} + 3 c x + d$ are in A.P., prove that $2 b^{3} - 3 a b c + a^{2} d = 0$

Discussion

14.	The value of the variable for which the polynomial becomes 0 is called __ of the polynomial.
Answer» The value of the variable for which the polynomial becomes 0 is called __ of the polynomial.

Discussion

15.	The square of an odd integer must be of the form:
Answer» The square of an odd integer must be of the form:

Discussion

16.	What is the probability of getting a sum of 7 on a roll of two dice?
Answer» What is the probability of getting a sum of 7 on a roll of two dice?

Discussion

17.	A statue 2 m tall, stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.
Answer» A statue 2 m tall, stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$ . Find the height of the pedestal.

Discussion

18.	A steel box has dimensions of 2 m, 3 m and 0.5 m. It has to be gold plated using electrolysis. If each square metre of gold plating costs Rs.100, then find the cost of gold plating the outer surface of the box.
Answer» A steel box has dimensions of 2 m, 3 m and 0.5 m. It has to be gold plated using electrolysis. If each square metre of gold plating costs Rs.100, then find the cost of gold plating the outer surface of the box.

Discussion

19.	Question 119 State whether the statements are True or False. Every square is a parallelogram.
Answer» Question 119 State whether the statements are True or False. Every square is a parallelogram.

Discussion

20.	If the distance between points P (x, 2) and Q (3, 6) is 10 units, then x =
Answer» If the distance between points P (x, 2) and Q (3, 6) is 10 units, then x =

Discussion

21.	If a polynomial has more than 3 terms, which polynomial which polynomial we can call it as ?
Answer» If a polynomial has more than 3 terms, which polynomial which polynomial we can call it as ?

Discussion

22.	If x+y=2+(3to the power 0.5), then x and y are irrational or not?
Answer» If x+y=2+(3to the power 0.5), then x and y are irrational or not?

Discussion

23.	Which term of the A. P. 1 + 4 + 7 + 10 + ............. is 52 ?
Answer» Which term of the A. P. 1 + 4 + 7 + 10 + ............. is 52 ?

Discussion

24.	A tower subtends an angle of 30∘ at a point, C, on the same level as its foot, A. At a second point, D, 'h' meters above C, the angle of depression of the foot of the tower is 60∘. What is the height of the tower?
Answer» A tower subtends an angle of $30^{\circ}$ at a point, C, on the same level as its foot, A. At a second point, D, 'h' meters above C, the angle of depression of the foot of the tower is $60^{\circ}$ . What is the height of the tower?

Discussion

25.	In a seminar, the number of participants in hindi, English and mathematics are 60,84 and 108 respectively.find the maximum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same sunject
Answer» In a seminar, the number of participants in hindi, English and mathematics are 60,84 and 108 respectively.find the maximum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same sunject

Discussion

26.	If the t-th term of an AP is s and s-th term of the same AP is t, then an is
Answer» If the t-th term of an AP is s and s-th term of the same AP is t, then $a_{n}$ is

Discussion

27.	Question 87 A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?
Answer» Question 87 A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

27.

Question 87 A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

Answer»

Question 87

A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

Discussion

28.	Can two numbers have 16 as their HCF and 380 LCM ? Give reasons
Answer» Can two numbers have 16 as their HCF and 380 LCM ? Give reasons

Discussion

29.	The constant term of the quadratic equation whose roots are 3+2√2 and 3−2√2.
Answer» The constant term of the quadratic equation whose roots are $3 + 2 \sqrt{2}$ and $3 - 2 \sqrt{2}$ .

Discussion

30.	If alpha and ß are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -alpha, -ß.
Answer» If alpha and ß are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -alpha, -ß.

Discussion

31.	Find out which of the following equations have x=1, y=2 as solution. x + 2y = 5 2y - 3x + 3 = 0 3x + 4y - 8 = 0 [4 MARKS]
Answer» Find out which of the following equations have x=1, y=2 as solution. x + 2y = 5 2y - 3x + 3 = 0 3x + 4y - 8 = 0 [4 MARKS]

Discussion

32.	In the following series, find the next term. 0,1,1,2,3,5,8,13, __
Answer» In the following series, find the next term. $0, 1, 1, 2, 3, 5, 8, 13,$ __

Discussion

33.	If numbers n-2 , 4n-1 and 5n+2 are in AP. Find the value of n and its next two terms.
Answer» If numbers n-2 , 4n-1 and 5n+2 are in AP. Find the value of n and its next two terms.

Discussion

34.	An Incircle touches the ___ of a polygon.
Answer» An Incircle touches the ___ of a polygon.

Discussion

35.	D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CBCA = CADC or CA2= CB×CD. [2 MARKS]
Answer» D is a point on the side BC of $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Prove that $\frac{C B}{C A}$ = $\frac{C A}{D C}$ or $C A^{2}$ = $C B \times C D$ . [2 MARKS]

35.

D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CBCA = CADC or CA2= CB×CD. [2 MARKS]

Answer»

D is a point on the side BC of $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Prove that $\frac{C B}{C A}$ = $\frac{C A}{D C}$ or $C A^{2}$ = $C B \times C D$ .

[2 MARKS]

Discussion

36.	₹ 9800 is invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
Answer» ₹ 9800 is invested partly in $9 %$ stock at 75 and $10 %$ stock at 80 to have equal amount of incomes. The investment in $9 %$ stock is:

Discussion

37.	a) Two coins are tossed once. Find the probability of getting: i) 2 heads ii) at least 1 tail. b) From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is: (i) a face card (King, Jack or Queen) (ii) an even-numbered red card? [6 MARKS]
Answer» a) Two coins are tossed once. Find the probability of getting: i) 2 heads ii) at least 1 tail. b) From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is: (i) a face card (King, Jack or Queen) (ii) an even-numbered red card? [6 MARKS]

Discussion

38.	If roots of the equation differ by 2 , then the product of sum of roots and product of roots is divisible by(i) 2 (ii) 3 (iii) 6 (iv) 12
Answer» If roots of the equation differ by 2 , then the product of sum of roots and product of roots is divisible by(i) 2 (ii) 3 (iii) 6 (iv) 12

Discussion

39.	The salary per month of the workers in a factory were as follows: Salary(in Rs)No. of workers300−40052400−50043500−60084600−700142700−80093800−90062 i) Find the modal class of this grouped data ii) Draw the histogram and locate the mode. [6 MARKS]
Answer» The salary per month of the workers in a factory were as follows: $\begin{matrix} S a l a r y (i n R s) & N o . o f w o r k e r s 300 - 400 & 52 400 - 500 & 43 500 - 600 & 84 600 - 700 & 142 700 - 800 & 93 800 - 900 & 62 \end{matrix}$ i) Find the modal class of this grouped data ii) Draw the histogram and locate the mode. [6 MARKS]

Discussion

40.	If the radius of a cylinder is reduced by 50%, then find the percentage by which volume of the cylinder will be reduced.75
Answer» If the radius of a cylinder is reduced by 50%, then find the percentage by which volume of the cylinder will be reduced. 75

Discussion

41.	An aeroplane travelled a distance of 400km at an average speed of x km/hr . On return journey the speed was increased by 40km/hr . If it takes 30 minutes less in return journey , find the value of x .
Answer» An aeroplane travelled a distance of 400km at an average speed of x km/hr . On return journey the speed was increased by 40km/hr . If it takes 30 minutes less in return journey , find the value of x .

Discussion

42.	The positive value of K for which the equation x2 + kx + 64 = 0 has equal roots is :
Answer» The positive value of K for which the equation x² + kx + 64 = 0 has equal roots is :

Discussion

43.	a company is producing a one page flysheet 24cm high by18 cm wide. It will have a text area in the centre which has a margin of the same width all the way around. The text must occupy exactly half of the total area: What is the width of the margin??? A 3.00cm B 4.50cm C 5.25cm D 6.00cm E 12.00 cm
Answer» a company is producing a one page flysheet 24cm high by18 cm wide. It will have a text area in the centre which has a margin of the same width all the way around. The text must occupy exactly half of the total area: What is the width of the margin??? A 3.00cm B 4.50cm C 5.25cm D 6.00cm E 12.00 cm

Discussion

44.	Show that any positive integer is of the form 3q or, 3q +1 or 3q + 2 for some integers q
Answer» Show that any positive integer is of the form 3q or, 3q +1 or 3q + 2 for some integers q

Discussion

45.	Solve:- 8x2 + 10x +3 = 0
Answer» Solve:- 8 $x^{2}$ + 10x +3 = 0

Discussion

46.	What is the difference in the ages of P and K? I. P is 20 yr older than M. II. M is 2 yr younger than Z.
Answer» What is the difference in the ages of P and K? I. P is 20 yr older than M. II. M is 2 yr younger than Z.

Discussion

47.	Solve : 15−2(2x−1)<15,x ϵ Z
Answer» Solve : $15 - 2 (2 x - 1) < 15, x ϵ Z$

Discussion

48.	Find the equation of the line through the intersection of 2x+y=8,3x–7=y and parallel to 4x+y=11.
Answer» Find the equation of the line through the intersection of $2 x + y = 8, 3 x - 7 = y$ and parallel to $4 x + y = 11$ .

Discussion

49.	Solve the following systems of equations: 7(y+3)−2(x+2)=14 4(y−2)+3(x−3)=2
Answer» Solve the following systems of equations: $7 (y + 3) - 2 (x + 2) = 14$ $4 (y - 2) + 3 (x - 3) = 2$

49.

Solve the following systems of equations: 7(y+3)−2(x+2)=14 4(y−2)+3(x−3)=2

Answer»

Solve the following systems of equations:

$7 (y + 3) - 2 (x + 2) = 14$

$4 (y - 2) + 3 (x - 3) = 2$

Discussion

50.	The height of a triangle is 3 m more than its base. If the area of the triangle is 35 sq.m. , then find its height.
Answer» The height of a triangle is 3 m more than its base. If the area of the triangle is 35 sq.m. , then find its height.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Decimal number 14587/400 will terminate after:

5 defective glasses are accidentally mixed with 20 good ones. The good ones and the defective ones look the same from the outside. If a glass is picked at random, what is the probability that the chosen glass is not defective?

If θ is an acute angle and tanθ=1√7, then the value of cosec2θ−sec2θcosec2θ+sec2θ is

An infinite number of tangents can be drawn from (1, 2) to the circle x2+y2−2x−4y+λ=0, then λ=

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that CM=MA=12AB [4 MARKS]

In ΔABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP=∠BEQ=100∘. What is the value of ∠PRD?

The are of △ABC with vertices A(a, 0), O(0, 0) and B(0, b) in square units is (a) ab (b) 12ab (c) 12a2b2 (d) 12b2

In the given figure, a circle touches the side DF of Δ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of Δ EDF is (a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm

(i) A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path. (ii) A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of the width of 0.7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq m.

Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60∘.

Find the value for k which each of the following systems of equations has a unique solution: 5x−7y−5=0,2x+ky−1=0.

If teh zeros of the polynomial f(x)=ax3+3bx2+3cx+d are in A.P., prove that 2b3−3abc+a2d=0

The value of the variable for which the polynomial becomes 0 is called __ of the polynomial.

The square of an odd integer must be of the form:

What is the probability of getting a sum of 7 on a roll of two dice?

A statue 2 m tall, stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.

A steel box has dimensions of 2 m, 3 m and 0.5 m. It has to be gold plated using electrolysis. If each square metre of gold plating costs Rs.100, then find the cost of gold plating the outer surface of the box.

Question 119 State whether the statements are True or False. Every square is a parallelogram.

If the distance between points P (x, 2) and Q (3, ­6) is 10 units, then x =

If a polynomial has more than 3 terms, which polynomial which polynomial we can call it as ?

If x+y=2+(3to the power 0.5), then x and y are irrational or not?

Which term of the A. P. 1 + 4 + 7 + 10 + ............. is 52 ?

A tower subtends an angle of 30∘ at a point, C, on the same level as its foot, A. At a second point, D, 'h' meters above C, the angle of depression of the foot of the tower is 60∘. What is the height of the tower?

In a seminar, the number of participants in hindi, English and mathematics are 60,84 and 108 respectively.find the maximum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same sunject

If the t-th term of an AP is s and s-th term of the same AP is t, then an is

Question 87 A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

Can two numbers have 16 as their HCF and 380 LCM ? Give reasons

The constant term of the quadratic equation whose roots are 3+2√2 and 3−2√2.

If alpha and ß are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -alpha, -ß.

Find out which of the following equations have x=1, y=2 as solution. x + 2y = 5 2y - 3x + 3 = 0 3x + 4y - 8 = 0 [4 MARKS]

In the following series, find the next term. 0,1,1,2,3,5,8,13, __

If numbers n-2 , 4n-1 and 5n+2 are in AP. Find the value of n and its next two terms.

An Incircle touches the ___ of a polygon.

D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CBCA = CADC or CA2= CB×CD. [2 MARKS]

₹ 9800 is invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:

If roots of the equation differ by 2 , then the product of sum of roots and product of roots is divisible by(i) 2 (ii) 3 (iii) 6 (iv) 12

The salary per month of the workers in a factory were as follows: Salary(in Rs)No. of workers300−40052400−50043500−60084600−700142700−80093800−90062 i) Find the modal class of this grouped data ii) Draw the histogram and locate the mode. [6 MARKS]

If the radius of a cylinder is reduced by 50%, then find the percentage by which volume of the cylinder will be reduced.75

An aeroplane travelled a distance of 400km at an average speed of x km/hr . On return journey the speed was increased by 40km/hr . If it takes 30 minutes less in return journey , find the value of x .

The positive value of K for which the equation x2 + kx + 64 = 0 has equal roots is :

a company is producing a one page flysheet 24cm high by18 cm wide. It will have a text area in the centre which has a margin of the same width all the way around. The text must occupy exactly half of the total area: What is the width of the margin??? A 3.00cm B 4.50cm C 5.25cm D 6.00cm E 12.00 cm

Show that any positive integer is of the form 3q or, 3q +1 or 3q + 2 for some integers q

Solve:- 8x2 + 10x +3 = 0

What is the difference in the ages of P and K? I. P is 20 yr older than M. II. M is 2 yr younger than Z.

Solve : 15−2(2x−1)&lt;15,x ϵ Z

Find the equation of the line through the intersection of 2x+y=8,3x–7=y and parallel to 4x+y=11.

Solve the following systems of equations: 7(y+3)−2(x+2)=14 4(y−2)+3(x−3)=2

The height of a triangle is 3 m more than its base. If the area of the triangle is 35 sq.m. , then find its height.

If the distance between points P (x, 2) and Q (3, 6) is 10 units, then x =

Solve : 15−2(2x−1)<15,x ϵ Z