32581 + Interview Questions in Mathematics Page 103 InterviewSolution

5101.	The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.
Answer» The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.

Discussion

5102.	The 16th term of the AP: 15,252,10,152,5,.... is:
Answer» The $16^{t h}$ term of the AP: $15, \frac{25}{2}, 10, \frac{15}{2}, 5, . . . .$ is:

Discussion

5103.	...it is out of syllabus...........We have got project on various types of cryptarithm Plz send as much as detail is possible..with problems,images,rules everything
Answer» ...it is out of syllabus...........We have got project on various types of cryptarithm Plz send as much as detail is possible..with problems,images,rules everything

5103.

...it is out of syllabus...........We have got project on various types of cryptarithm Plz send as much as detail is possible..with problems,images,rules everything

Answer»

...it is out of syllabus...........We have got project on various types of cryptarithm

Plz send as much as detail is possible..with problems,images,rules everything

Discussion

5104.	A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60∘ with the horizontal. Find the height of the tree.
Answer» A storm broke a tree and the treetop rested $20 m$ from the base of the tree, making an angle of $60^{\circ}$ with the horizontal. Find the height of the tree.

Discussion

5105.	There is a finite AP of n terms such that the difference between the last and first term when divided by (n-1), gives a quotient 12 and leaves no remainder. Find the common difference of this AP.
Answer» There is a finite AP of n terms such that the difference between the last and first term when divided by (n-1), gives a quotient 12 and leaves no remainder. Find the common difference of this AP.

Discussion

5106.	Find all the zeros of 2x4 – 13x3 + 19x2 + 7x – 3 if two of its zeros are 2+3 and 2-3.
Answer» Find all the zeros of 2x⁴– 13x³+ 19x²+ 7x – 3 if two of its zeros are $(2 + \sqrt{3}) and (2 - \sqrt{3})$ .

Discussion

5107.	300 apples are distributed equally among students. Had there been 10more students then each would get one apple less. Find the no. Of students.
Answer» 300 apples are distributed equally among students. Had there been 10more students then each would get one apple less. Find the no. Of students.

Discussion

5108.	In Fig. 13.112, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of shaded region (use π = 3.14).
Answer» In Fig. 13.112, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of shaded region (use π = 3.14).

Discussion

5109.	A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30∘, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60∘. Find the time taken by the car to reach the foot of the tower from this point.
Answer» A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$ , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{\circ}$ . Find the time taken by the car to reach the foot of the tower from this point.

Discussion

5110.	Question 10 The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? why?
Answer» Question 10 The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? why?

Discussion

5111.	If mean of 5 number is 13.6 and on excludingone number , the mean becomes 13 , then the excluded number is Warm regardsHero
Answer» If mean of 5 number is 13.6 and on excludingone number , the mean becomes 13 , then the excluded number is Warm regards Hero

Discussion

5112.	A circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use π=3.14 and √3=1.73]
Answer» A circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use $π = 3.14 a n d \sqrt{3} = 1.73$ ]

Discussion

5113.	If A = {set of whole numbers less than 6} and B = {set of prime natural numbers less than 7}, then _________ .
Answer» If A = {set of whole numbers less than 6} and B = {set of prime natural numbers less than 7}, then _________ .

Discussion

5114.	The equation (xx) raised to x = 2 is satisfied when x is equal to
Answer» The equation (x^x) raised to x = 2 is satisfied when x is equal to

Discussion

5115.	Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.
Answer» Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.

Discussion

5116.	In the given figure, O is the centre of a circle and PT is the tangent to the circle. If PQ is a chord, such that ∠QPT = 50° then ∠POQ = ?(a) 100°(b) 90°(c) 80°(d) 75°
Answer» In the given figure, O is the centre of a circle and PT is the tangent to the circle. If PQ is a chord, such that ∠QPT = 50° then ∠POQ = ? (a) 100° (b) 90° (c) 80° (d) 75°

Discussion

5117.	if s is the circumcentre , o is the orthocentre of triangle ABC, then SA+SB+SC equals
Answer» if s is the circumcentre , o is the orthocentre of triangle ABC, then SA+SB+SC equals

Discussion

5118.	Question 14 (v)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a spade.
Answer» Question 14 (v) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a spade.

Discussion

5119.	The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.
Answer» The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.

5119.

The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.

Answer»

The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.

Discussion

5120.	If 1a and 1b are the zero of f(x), then one of the factor of f(x) can be,
Answer» If $\frac{1}{a}$ and $\frac{1}{b}$ are the zero of f(x), then one of the factor of f(x) can be,

Discussion

5121.	Every straight line can be represented by ___________ equation.
Answer» Every straight line can be represented by ___________ equation.

Discussion

5122.	Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Answer» Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.

Discussion

5123.	Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.
Answer» Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.

Discussion

5124.	General solution of the equation 7cos^2theta+3sin^2theta=4.
Answer» General solution of the equation 7cos^2theta+3sin^2theta=4.

Discussion

5125.	If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
Answer» If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.

Discussion

5126.	In an equilateral triangle ABC of side 'a', AD is the perpendicular drawn onto side BC. Find AD cot θ in terms of a.
Answer» In an equilateral triangle ABC of side 'a', AD is the perpendicular drawn onto side BC. Find $A D c o t θ$ in terms of a.

Discussion

5127.	Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB - 5 cm, BC = 7 cm and ∠ABC = 50°.
Answer» Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)^th of the corresponding sides of Δ ABC. It is given that AB - 5 cm, BC = 7 cm and ∠ABC = 50°.

Discussion

5128.	If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k.
Answer» If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k.

Discussion

5129.	Solve for x : 2x2+x–6=0
Answer» Solve for $x$ : $2 x^{2} + x - 6 = 0$

Discussion

5130.	Question 1If a hexagon ABCDEF circumscribe a circle. Prove thatAB+CD+EF = BC+DE+FA
Answer» Question 1 If a hexagon ABCDEF circumscribe a circle. Prove that AB+CD+EF = BC+DE+FA

Discussion

5131.	Solve the following quadratic equations by factorization:x-1x=3, x≠0
Answer» Solve the following quadratic equations by factorization: $x - \frac{1}{x} = 3, x \neq 0$

Discussion

5132.	In the given figure, PQ \|\| BC and AP : PB = 1 : 2. Find area ∆APQarea ∆ABC.
Answer» In the given figure, PQ \|\| BC and AP : PB = 1 : 2. Find $\frac{area (∆ APQ)}{area (∆ ABC)}$ .

Discussion

5133.	Which of the following can be an alternate representation of variance, where xi being the midpoint of class intervals, fi being frequency of class interval and ¯x the mean,N = ∑ni=1fi
Answer» Which of the following can be an alternate representation of variance, where $x_{i}$ being the midpoint of class intervals, $f_{i}$ being frequency of class interval and $¯ x$ the mean,N = $\sum_{i = 1}^{n} f_{i}$

Discussion

5134.	The number of distinct prime divisors of the number 512^3-253^3-259^3 is
Answer» The number of distinct prime divisors of the number 512^3-253^3-259^3 is

Discussion

5135.	Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.
Answer» Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.

Discussion

5136.	For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.(1) (2) (3) (4)
Answer» For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary. (1) (2) (3) (4)

5136.

For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.(1) (2) (3) (4)

Answer»

For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.

(1)

(2)

(3)

(4)

Discussion

5137.	18. A villager has a plot of the land of the shape of the quadrilateral. The gram panchayat of the village decided to take over some portion of his plot from one corner to construct a health center. He agrees with the condition that he should be given equal amount of land in return of the adjacent plot so as to form a triangular plot. Explain how this proposal be implemented
Answer» 18. A villager has a plot of the land of the shape of the quadrilateral. The gram panchayat of the village decided to take over some portion of his plot from one corner to construct a health center. He agrees with the condition that he should be given equal amount of land in return of the adjacent plot so as to form a triangular plot. Explain how this proposal be implemented

Discussion

5138.	If the sum of first p terms of an AP is q and the sum of first q terms is p. Then find the sum of first (p+q) terms.
Answer» If the sum of first p terms of an AP is q and the sum of first q terms is p. Then find the sum of first (p+q) terms.

Discussion

5139.	26. A cube and a sphere are of the same height. Find the ratio of their volume
Answer» 26. A cube and a sphere are of the same height. Find the ratio of their volume

Discussion

5140.	Question 4 (iv)Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.
Answer» Question 4 (iv) Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Discussion

5141.	The value of the determinant ∆=1234563x6x9x is ____________.
Answer» The value of the determinant $∆ = \|\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x \end{matrix}\|$ is ____________.

Discussion

5142.	Construct incircle and circumcircle of an equilateral ∆DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.
Answer» Construct incircle and circumcircle of an equilateral $∆$ DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

Discussion

5143.	If the coordinates of the mid-points of the sides of a triangle are (3, 4) (4, 6) and (5, 7), find its vertices.
Answer» If the coordinates of the mid-points of the sides of a triangle are (3, 4) (4, 6) and (5, 7), find its vertices.

Discussion

5144.

Consider the following distribution of daily wages of 50 workers of a factory. Daily wages (in Rs.) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer» Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs.)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Discussion

5145.	Prove the following trigonometric identities.1+cot2 θ1+cosec θ=cosec θ
Answer» Prove the following trigonometric identities. $1 + \frac{\cot^{2} θ}{1 + cosec θ} = cosec θ$

Discussion

5146.	The dimensions of a brick are 20cm x 10 cm x 6 cm.How many bricks are required to be put in a line to make a wall 4 m long?
Answer» The dimensions of a brick are 20cm x 10 cm x 6 cm.How many bricks are required to be put in a line to make a wall 4 m long?

Discussion

5147.	Find the value of k for which the system 3x + 5y = 0 and kx + 10y = 0 has a nonzero solution.
Answer» Find the value of k for which the system 3x + 5y = 0 and kx + 10y = 0 has a nonzero solution.

Discussion

5148.	Construct ∆PQR, in which QR = 4.2cm m∠Q = 40° and PQ + PR = 8.5cm
Answer» Construct $∆$ PQR, in which QR = 4.2cm $m ∠$ Q = $40^{°}$ and PQ + PR = 8.5cm

Discussion

5149.	If cotA = 125, then the value of (sinA+cosA) × cosecA is:
Answer» If cotA = $\frac{12}{5}$ , then the value of (sinA+cosA) $\times$ cosecA is:

Discussion

5150.	A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?
Answer» A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?

Discussion

Explore topic-wise InterviewSolutions in .

The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.

The 16th term of the AP: 15,252,10,152,5,.... is:

...it is out of syllabus...........We have got project on various types of cryptarithm Plz send as much as detail is possible..with problems,images,rules everything

A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60∘ with the horizontal. Find the height of the tree.

There is a finite AP of n terms such that the difference between the last and first term when divided by (n-1), gives a quotient 12 and leaves no remainder. Find the common difference of this AP.

Find all the zeros of 2x4 – 13x3 + 19x2 + 7x – 3 if two of its zeros are 2+3 and 2-3.

300 apples are distributed equally among students. Had there been 10more students then each would get one apple less. Find the no. Of students.

In Fig. 13.112, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of shaded region (use π = 3.14).

Question 10 The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? why?

If mean of 5 number is 13.6 and on excludingone number , the mean becomes 13 , then the excluded number is Warm regardsHero

A circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use π=3.14 and √3=1.73]

If A = {set of whole numbers less than 6} and B = {set of prime natural numbers less than 7}, then _________ .

The equation (x​​​​​​x) raised to x = 2 is satisfied when x is equal to

Apurva deposited ₹200 per month for 36 months in a bank’s recurring deposit account. The bank pays interest rate of 11% per annum. Calculate the amount that she will receive on the maturity.

In the given figure, O is the centre of a circle and PT is the tangent to the circle. If PQ is a chord, such that ∠QPT = 50° then ∠POQ = ?(a) 100°(b) 90°(c) 80°(d) 75°

if s is the circumcentre , o is the orthocentre of triangle ABC, then SA+SB+SC equals

Question 14 (v)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a spade.

The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.

If 1a and 1b are the zero of f(x), then one of the factor of f(x) can be,

Every straight line can be represented by ___________ equation.

Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.

Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.

General solution of the equation 7cos^2theta+3sin^2theta=4.

If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.

In an equilateral triangle ABC of side 'a', AD is the perpendicular drawn onto side BC. Find AD cot θ in terms of a.

Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB - 5 cm, BC = 7 cm and ∠ABC = 50°.

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k.

Solve for x : 2x2+x–6=0

Question 1If a hexagon ABCDEF circumscribe a circle. Prove thatAB+CD+EF = BC+DE+FA

Solve the following quadratic equations by factorization:x-1x=3, x≠0

In the given figure, PQ || BC and AP : PB = 1 : 2. Find area ∆APQarea ∆ABC.

Which of the following can be an alternate representation of variance, where xi being the midpoint of class intervals, fi being frequency of class interval and ¯x the mean,N = ∑ni=1fi

The number of distinct prime divisors of the number 512^3-253^3-259^3 is

Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.

For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.(1) (2) (3) (4)

If the sum of first p terms of an AP is q and the sum of first q terms is p. Then find the sum of first (p+q) terms.

26. A cube and a sphere are of the same height. Find the ratio of their volume

Question 4 (iv)Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

The value of the determinant ∆=1234563x6x9x is ____________.

Construct incircle and circumcircle of an equilateral ∆DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

If the coordinates of the mid-points of the sides of a triangle are (3, 4) (4, 6) and (5, 7), find its vertices.

Consider the following distribution of daily wages of 50 workers of a factory. Daily wages (in Rs.) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Find the mean daily wages of the workers of the factory by using an appropriate method.

Prove the following trigonometric identities.1+cot2 θ1+cosec θ=cosec θ

The dimensions of a brick are 20cm x 10 cm x 6 cm.How many bricks are required to be put in a line to make a wall 4 m long?

Find the value of k for which the system 3x + 5y = 0 and kx + 10y = 0 has a nonzero solution.

Construct ∆PQR, in which QR = 4.2cm m∠Q = 40° and PQ + PR = 8.5cm

If cotA = 125, then the value of (sinA+cosA) × cosecA is:

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?

The equation (xx) raised to x = 2 is satisfied when x is equal to