24740 + Interview Questions in Mathematics Page 192 InterviewSolution

9551.	Number of integer(s) in the domain of the function f(x)=cos−1(x2−4) is
Answer» Number of integer(s) in the domain of the function $f (x) = {cos}^{- 1} (x^{2} - 4)$ is

Discussion

9552.	Which one of the following numbers lies between 57 and 49?
Answer» Which one of the following numbers lies between $\frac{5}{7}$ and $\frac{4}{9}$ ?

Discussion

9553.	57. An agricultural field is in form of a rectangle of length 20m and width14m.A pit 6m long 3m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field.Find the extent to which the level of the field has
Answer» 57. An agricultural field is in form of a rectangle of length 20m and width14m.A pit 6m long 3m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field.Find the extent to which the level of the field has

Discussion

9554.

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below: Monthly income: (in Rs) Vehicles per family 0 1 2 Above 2 Less than 7000 7000-10000 10000-13000 13000-16000 16000 or more 10 0 1 2 1 160 305 535 469 579 25 27 29 29 82 0 2 1 25 88 If a family is chosen, find the probability that family is:(i) earning Rs10000-13000 per month and owning exactly 2 vehicles.(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.(iii) earning less than Rs 7000 per month and does not own any vehicle.(iv) earning Rs 13000-16000 per month and owning more than 2 vehicle.(v) owning not more than 1 vehicle(vi) owning at least one vehicle.

Answer» A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below:

Monthly income: (in Rs)	Vehicles per family
Monthly income: (in Rs)	0	1	2	Above 2
Less than 7000 7000-10000 10000-13000 13000-16000 16000 or more	10 0 1 2 1	160 305 535 469 579	25 27 29 29 82	0 2 1 25 88

If a family is chosen, find the probability that family is:

(i) earning Rs10000-13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000-16000 per month and owning more than 2 vehicle.

(v) owning not more than 1 vehicle

(vi) owning at least one vehicle.

Discussion

9555.	{ If }(x+1) is factor of }f(x)=a_0x^n+a_1x^{n-1}...+a_{n^'}} then
Answer» { If }(x+1) is factor of }f(x)=a_0x^n+a_1x^{n-1}...+a_{n^'}} then

Discussion

9556.	In the given figure, what is the measure of angle ADC?
Answer» In the given figure, what is the measure of angle ADC?

Discussion

9557.	Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.
Answer» Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Discussion

9558.	Question 1 (iii)Classify 2√77√7 as rational or irrational.
Answer» Question 1 (iii) Classify $\frac{2 \sqrt{7}}{7 \sqrt{7}}$ as rational or irrational.

Discussion

9559.	Match the following with respect to the polynomial 4x−3y2+7.
Answer» Match the following with respect to the polynomial $4 x - 3 y^{2} + 7$ .

Discussion

9560.

The following table gives the life times of neon lamps: Length (in hours) Number of lamps 300 − 400 400 − 500 500 − 600 600 − 700 700 − 800 800 − 900 900 − 1000 14 56 60 86 74 62 48 (i) Represent the given information with the help of a histogram.(ii) How many lamps have a lifetime of more than 700 hours?

Answer»

The following table gives the life times of neon lamps:

Length (in hours)

Number of lamps

300 − 400

400 − 500

500 − 600

600 − 700

700 − 800

800 − 900

900 − 1000

14

56

60

86

74

62

48

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

Discussion

9561.	ABCD is a quadrilateral in which AD = BC. If P, Q, R , S be the mid points of AB, AC, CD and BD respectively, show that PQRS is a rhombus.
Answer» ABCD is a quadrilateral in which AD = BC. If P, Q, R , S be the mid points of AB, AC, CD and BD respectively, show that PQRS is a rhombus.

Discussion

9562.	tan2θ1+tan2θ + cot2θ1+cot2θ =
Answer» $\frac{t a n^{2} θ}{1 + t a n^{2} θ}$ + $\frac{c o t^{2} θ}{1 + c o t^{2} θ}$ =

Discussion

9563.	Two fair dice are thrown simultaneously. The probability of getting the sum of numbers shown on the dice is either divisible by 2 or divisible by 5, is
Answer» Two fair dice are thrown simultaneously. The probability of getting the sum of numbers shown on the dice is either divisible by 2 or divisible by 5, is

Discussion

9564.	If a+b+c=8 and ab+ bc+ca=20, find the value for a3+b3+c3 -3abc the options are :- 16 32 48 64 please solve this question with explanation
Answer» If a+b+c=8 and ab+ bc+ca=20, find the value for a³+b³+c³-3abc the options are :- 16 32 48 64 please solve this question with explanation

9564.

If a+b+c=8 and ab+ bc+ca=20, find the value for a3+b3+c3 -3abc the options are :- 16 32 48 64 please solve this question with explanation

Answer»

If a+b+c=8 and ab+ bc+ca=20, find the value for a³+b³+c³-3abc

the options are :-

16

32

48

64

please solve this question with explanation

Discussion

9565.	If y = x + ex, then d2ydx2 = _____________________.
Answer» If y = x + e^x, then $\frac{d^{2} y}{d x^{2}}$ = _____________________.

Discussion

9566.	The sum of a number and its square root.
Answer» The sum of a number and its square root.

9566.

The sum of a number and its square root.

Answer»

The sum of a number and its square root.

Discussion

9567.	Question 86 (x)Using suitable identities, evaluate the following:104×97
Answer» Question 86 (x) Using suitable identities, evaluate the following: $104 \times 97$

9567.

Question 86 (x)Using suitable identities, evaluate the following:104×97

Answer»

Question 86 (x)

Using suitable identities, evaluate the following:

$104 \times 97$

Discussion

9568.	Question 1The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of Rs 50 per m.
Answer» Question 1 The area of a circular playground is $22176 m^{2}$ . Find the cost of fencing this ground at the rate of Rs 50 per m.

Discussion

9569.	If x+1x=2, then x3+1x3=
Answer» $I f x + \frac{1}{x} = 2, t h e n x^{3} + \frac{1}{x^{3}} =$

Discussion

9570.	ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that(i) ΔAPB ≅ ΔCQD(ii) AP = CQ
Answer» ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ

9570.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that(i) ΔAPB ≅ ΔCQD(ii) AP = CQ

Answer»

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

(i) ΔAPB ≅ ΔCQD

(ii) AP = CQ

Discussion

9571.	Question 10 Verify whether the following are true or false. (i) -3 is a zero of x - 3 (ii) −13 is a zero of 3x + 1 (iii) −45 is a zero of 4 - 5y (iv) 0 and 2 are the zeroes of t2–t (v) -3 is a zero of y2+y–6
Answer» Question 10 Verify whether the following are true or false. (i) -3 is a zero of x - 3 (ii) $- \frac{1}{3}$ is a zero of 3x + 1 (iii) $- \frac{4}{5}$ is a zero of 4 - 5y (iv) 0 and 2 are the zeroes of $t^{2} - t$ (v) -3 is a zero of $y^{2} + y - 6$

Discussion

9572.	The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Answer» The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Discussion

9573.	The following graph shows the quantity of wheat and jowar produced in 2010-2012.In which year the production of jower is the same?
Answer» The following graph shows the quantity of wheat and jowar produced in 2010-2012. In which year the production of jower is the same?

Discussion

9574.	What is the ratio between length of perpendicular AO and the perimeter of the △ABC?
Answer» What is the ratio between length of perpendicular AO and the perimeter of the $△$ ABC?

9574.

What is the ratio between length of perpendicular AO and the perimeter of the △ABC?

Answer»

What is the ratio between length of perpendicular AO and the perimeter of the $△$ ABC?

Discussion

9575.	O is the centre of the circle. ∠OAB=20∘,∠OCB=55∘. Find ∠BOC and ∠AOC.
Answer» O is the centre of the circle. $∠ O A B = 20^{\circ}, ∠ O C B = 55^{\circ}$ . Find $∠ B O C$ and $∠ A O C$ .

Discussion

9576.	If A={2,4,6,8,10,12},B={4,6,8} and C={4,6}, then which of the following statements are correct?
Answer» If $A = {2, 4, 6, 8, 10, 12}, B = {4, 6, 8}$ and $C = {4, 6}$ , then which of the following statements are correct?

Discussion

9577.	What is ratio actually of two things
Answer» What is ratio actually of two things

Discussion

9578.	32. Prove that a cyclic rhombus is a square
Answer» 32. Prove that a cyclic rhombus is a square

Discussion

9579.	18. Does complex [Ma3b3] possess any element of symmetry in facial form?
Answer» 18. Does complex [Ma3b3] possess any element of symmetry in facial form?

Discussion

9580.	Question 5 (ii)D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:(ii) area(DEF)=14area(ABC)
Answer» Question 5 (ii) D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that: (ii) $a r e a (D E F) = \frac{1}{4} a r e a (A B C)$

Discussion

9581.	Define Area?
Answer» Define Area?

Discussion

9582.	Question 1 (ii)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.4s2−4s+1
Answer» Question 1 (ii) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. $4 s^{2} - 4 s + 1$

9582.

Question 1 (ii)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.4s2−4s+1

Answer»

Question 1 (ii)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$4 s^{2} - 4 s + 1$

Discussion

9583.	What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assum that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm.(Use π=3.14)
Answer» What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assum that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm.(Use $π = 3.14)$

Discussion

9584.	Point P (x, y) is a point in the first quadrant of the Cartesian plane. Then
Answer» Point P (x, y) is a point in the first quadrant of the Cartesian plane. Then

Discussion

9585.	The projection of point P(−1,−2,−3) on x−axis is
Answer» The projection of point $P (- 1, - 2, - 3)$ on $x -$ axis is

Discussion

9586.	Polygon among the following is
Answer» Polygon among the following is

Discussion

9587.	How many digits are there in the repeating block of digits in the decimal expansion of 177?(a) 16(b) 6(c) 26(d) 7
Answer» How many digits are there in the repeating block of digits in the decimal expansion of $\frac{17}{7}$ ? (a) 16 (b) 6 (c) 26 (d) 7

Discussion

9588.	If a=π3e,b=3πe and c=e3π, then
Answer» If $a = π^{3 e}, b = 3^{π e} a n d c = e^{3 π},$ then

Discussion

9589.	Zero of the polynomial p(x)=x2+x−6 are (a) 2,3 (b) -2,3 (c) 2,-3 (d) -2,-3
Answer» Zero of the polynomial $p (x) = x^{2} + x - 6$ are (a) 2,3 (b) -2,3 (c) 2,-3 (d) -2,-3

Discussion

9590.	The system of equation ax+y+z=0,x+by+z=0;x+y+cz=0 has a non-trivial solution then 11−a+11−b+11−c=
Answer» The system of equation $a x + y + z = 0, x + b y + z = 0; x + y + c z = 0$ has a non-trivial solution then $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =$

Discussion

9591.	If one of the zeroes of the quadratic polynomial (k–1)x2+kx+1 is –3, then the value of k is:
Answer» If one of the zeroes of the quadratic polynomial $(k - 1) x^{2} + k x + 1$ is –3, then the value of k is:

Discussion

9592.	Which of the following statements are true (T) and which are false (F)? Give reasons.(i) If two lines are intersected by a transversal, then corresponding angles are equal.(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.(iii) Two lines perpendicular to the same line are perpendicular to each other.(iv) Two line parallel to the same line are parallel to each other.(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.
Answer» Which of the following statements are true (T) and which are false (F)? Give reasons. (i) If two lines are intersected by a transversal, then corresponding angles are equal. (ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal. (iii) Two lines perpendicular to the same line are perpendicular to each other. (iv) Two line parallel to the same line are parallel to each other. (v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Discussion

9593.	In a school all the students have to learn drawing or painting. If 36% of the students learn drawing and painting and 40% of those who learn drawing do not learn painting, then what % of the students learn painting?
Answer» In a school all the students have to learn drawing or painting. If 36% of the students learn drawing and painting and 40% of those who learn drawing do not learn painting, then what % of the students learn painting?

Discussion

9594.	If radius have a error of 3% then find the error in volume of sphere
Answer» If radius have a error of 3% then find the error in volume of sphere

Discussion

9595.	Let f(x) be cubic polynomial such that f(1)=1, f(2)=2, f(3)=3 and f(4)=16. Find the value of f(5).
Answer» Let f(x) be cubic polynomial such that f(1)=1, f(2)=2, f(3)=3 and f(4)=16. Find the value of f(5).

Discussion

9596.	External dimensions of a wooden cuboid are 30 cm, 25 cm and 20 cm. If the thickness of the wood is 2 cm all around, find the volume of the wood contained in the cuboid formed.
Answer» External dimensions of a wooden cuboid are 30 cm, 25 cm and 20 cm. If the thickness of the wood is 2 cm all around, find the volume of the wood contained in the cuboid formed.

Discussion

9597.	34. Which of the folowing numbers is the fourth power of a natural number ? i) 6765201 ii) 6765206 iii) 6765207 iv) 6765209
Answer» 34. Which of the folowing numbers is the fourth power of a natural number ? i) 6765201 ii) 6765206 iii) 6765207 iv) 6765209

Discussion

9598.	A point is at a distance of 3 Units from the x-axis and 5 units from y-axis. Which of the following are the coordinates of the point?
Answer» A point is at a distance of 3 Units from the x-axis and 5 units from y-axis. Which of the following are the coordinates of the point?

Discussion

9599.	If one card is drawn from a well-shuffled deck of 52 cards, then which of the following is true?
Answer» If one card is drawn from a well-shuffled deck of 52 cards, then which of the following is true?

Discussion

9600.	Sin75 =? With proof
Answer» Sin75 =? With proof

Discussion

Explore topic-wise InterviewSolutions in .

Number of integer(s) in the domain of the function f(x)=cos−1(x2−4) is

Which one of the following numbers lies between 57 and 49?

57. An agricultural field is in form of a rectangle of length 20m and width14m.A pit 6m long 3m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field.Find the extent to which the level of the field has

{ If }(x+1) is factor of }f(x)=a_0x^n+a_1x^{n-1}...+a_{n^'}} then

In the given figure, what is the measure of angle ADC?

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Question 1 (iii)Classify 2√77√7 as rational or irrational.

Match the following with respect to the polynomial 4x−3y2+7.

ABCD is a quadrilateral in which AD = BC. If P, Q, R , S be the mid points of AB, AC, CD and BD respectively, show that PQRS is a rhombus.

tan2θ1+tan2θ + cot2θ1+cot2θ =

Two fair dice are thrown simultaneously. The probability of getting the sum of numbers shown on the dice is either divisible by 2 or divisible by 5, is

If a+b+c=8 and ab+ bc+ca=20, find the value for a​​​​​​3+b​​​​​​3+c​​​​3 -3abc the options are :- 16 32 48 64 please solve this question with explanation ​​​​

If y = x + ex, then d2ydx2 = _____________________.

The sum of a number and its square root.

Question 86 (x)Using suitable identities, evaluate the following:104×97

Question 1The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of Rs 50 per m.

If x+1x=2, then x3+1x3=

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that(i) ΔAPB ≅ ΔCQD(ii) AP = CQ

Question 10 Verify whether the following are true or false. (i) -3 is a zero of x - 3 (ii) −13 is a zero of 3x + 1 (iii) −45 is a zero of 4 - 5y (iv) 0 and 2 are the zeroes of t2–t (v) -3 is a zero of y2+y–6

The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

The following graph shows the quantity of wheat and jowar produced in 2010-2012.In which year the production of jower is the same?

What is the ratio between length of perpendicular AO and the perimeter of the △ABC?

O is the centre of the circle. ∠OAB=20∘,∠OCB=55∘. Find ∠BOC and ∠AOC.

If A={2,4,6,8,10,12},B={4,6,8} and C={4,6}, then which of the following statements are correct?

What is ratio actually of two things

32. Prove that a cyclic rhombus is a square

18. Does complex [Ma3b3] possess any element of symmetry in facial form?

Question 5 (ii)D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:(ii) area(DEF)=14area(ABC)

Define Area?

Question 1 (ii)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.4s2−4s+1

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assum that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm.(Use π=3.14)

Point P (x, y) is a point in the first quadrant of the Cartesian plane. Then

The projection of point P(−1,−2,−3) on x−axis is

Polygon among the following is

How many digits are there in the repeating block of digits in the decimal expansion of 177?(a) 16(b) 6(c) 26(d) 7

If a=π3e,b=3πe and c=e3π, then

Zero of the polynomial p(x)=x2+x−6 are (a) 2,3 (b) -2,3 (c) 2,-3 (d) -2,-3

The system of equation ax+y+z=0,x+by+z=0;x+y+cz=0 has a non-trivial solution then 11−a+11−b+11−c=

If one of the zeroes of the quadratic polynomial (k–1)x2+kx+1 is –3, then the value of k is:

In a school all the students have to learn drawing or painting. If 36% of the students learn drawing and painting and 40% of those who learn drawing do not learn painting, then what % of the students learn painting?

If radius have a error of 3% then find the error in volume of sphere

Let f(x) be cubic polynomial such that f(1)=1, f(2)=2, f(3)=3 and f(4)=16. Find the value of f(5).

External dimensions of a wooden cuboid are 30 cm, 25 cm and 20 cm. If the thickness of the wood is 2 cm all around, find the volume of the wood contained in the cuboid formed.

34. Which of the folowing numbers is the fourth power of a natural number ? i) 6765201 ii) 6765206 iii) 6765207 iv) 6765209

A point is at a distance of 3 Units from the x-axis and 5 units from y-axis. Which of the following are the coordinates of the point?

If one card is drawn from a well-shuffled deck of 52 cards, then which of the following is true?

Sin75 =? With proof

If a+b+c=8 and ab+ bc+ca=20, find the value for a3+b3+c3 -3abc the options are :- 16 32 48 64 please solve this question with explanation