25365 + Interview Questions in Mathematics Page 249 InterviewSolution

12401.	Prove that n^{3 }- n is divisible by 6 , for every possible value of n
Answer» Prove that n^{3 }- n is divisible by 6 , for every possible value of n

Discussion

12402.	Simplify the polynomial expression and then write in standard form.(3+5x+7x2+9x3)+(4+2x−3x2−8x3)
Answer» Simplify the polynomial expression and then write in standard form. $(3 + 5 x + 7 x^{2} + 9 x^{3})$ $+ (4 + 2 x - 3 x^{2} - 8 x^{3})$

Discussion

12403.	Kuttan’s mother is 25 years older than Kuttan. When Kuttan is 8, how old will his mother be? How old will Kuttan be when his mother is 40? If we write k for Kuttan’s age and m for mother’s age, in what all ways can we write the relation between them?
Answer» Kuttan’s mother is 25 years older than Kuttan. When Kuttan is 8, how old will his mother be? How old will Kuttan be when his mother is 40? If we write k for Kuttan’s age and m for mother’s age, in what all ways can we write the relation between them?

12403.

Kuttan’s mother is 25 years older than Kuttan. When Kuttan is 8, how old will his mother be? How old will Kuttan be when his mother is 40? If we write k for Kuttan’s age and m for mother’s age, in what all ways can we write the relation between them?

Answer»

Kuttan’s mother is 25 years older than Kuttan. When Kuttan is 8, how old will his mother be? How old will Kuttan be when his mother is 40?

If we write k for Kuttan’s age and m for mother’s age, in what all ways can we write the relation between them?

Discussion

12404.	Question 1(viii) Use a suitable identity to get each of the following products: (−a+c)(−a+c)
Answer» Question 1(viii) Use a suitable identity to get each of the following products: $(- a + c) (- a + c)$

Discussion

12405.	Rationalise: 13 +5 +15
Answer» Rationalise: 13 +5 +15

Discussion

12406.	Evaluate: 176×176−124×124
Answer» Evaluate: $176 \times 176 - 124 \times 124$

Discussion

12407.	Question 4(i)Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of :Getting a number 6.
Answer» Question 4(i) Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of : Getting a number 6.

Discussion

12408.	Given that ABCD is a rectangle as shown in the figure . Here, AC = ___ × OB.
Answer» Given that ABCD is a rectangle as shown in the figure . Here, AC = ___ $\times$ OB.

Discussion

12409.	Factorise: 4y2+20y+25
Answer» Factorise: $4 y^{2} + 20 y + 25$

Discussion

12410.	If 8 oranges cost Rs. 10.40, how many oranges can be bought for Rs. 33.80 ? (a) 13 (b) 18 (c) 26 (d) 24
Answer» If 8 oranges cost Rs. 10.40, how many oranges can be bought for Rs. 33.80 ? (a) 13 (b) 18 (c) 26 (d) 24

12410.

If 8 oranges cost Rs. 10.40, how many oranges can be bought for Rs. 33.80 ? (a) 13 (b) 18 (c) 26 (d) 24

Answer»

If 8 oranges cost Rs. 10.40, how many oranges can be bought for Rs. 33.80 ?

(a) 13 (b) 18 (c) 26 (d) 24

Discussion

12411.	Name the property involved in the following example. 3/7×1=3/7=1×3/7
Answer» Name the property involved in the following example. 3/7×1=3/7=1×3/7

Discussion

12412.	A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in (m2)? [ 1 MARK ]
Answer» A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in (m²)? [ 1 MARK ]

Discussion

12413.	Write the reciprocal of 5+2.
Answer» Write the reciprocal of $5 + \sqrt{2}$ .

Discussion

12414.	Find the square root of: 4a2+9b2+c2−12ab+6bc−4ac
Answer» Find the square root of: $4 a^{2} + 9 b^{2} + c^{2} - 12 a b + 6 b c - 4 a c$

Discussion

12415.	The difference between selling a coat at a profit of 4% and that of 6% is ₹3. Find the two selling price.
Answer» The difference between selling a coat at a profit of $4 %$ and that of $6 %$ is ₹3. Find the two selling price.

Discussion

12416.	The compound interest on a certain sum of money at 5% per annum for two years is Rs.246. Calculate the simple interest on the same sum for three years at 6% per annum.
Answer» The compound interest on a certain sum of money at $5 %$ per annum for two years is Rs.246. Calculate the simple interest on the same sum for three years at $6 %$ per annum.

Discussion

12417.	Question 180(ii)Simplify[(43)−2−(34)2]−2
Answer» Question 180(ii) Simplify ${[{(\frac{4}{3})}^{- 2} - {(\frac{3}{4})}^{2}]}^{- 2}$

12417.

Question 180(ii)Simplify[(43)−2−(34)2]−2

Answer»

Question 180(ii)

Simplify

${[{(\frac{4}{3})}^{- 2} - {(\frac{3}{4})}^{2}]}^{- 2}$

Discussion

12418.	In the parallelogram ABCD, value of ∠D is .
Answer» In the parallelogram ABCD, value of ∠D is .

Discussion

12419.	A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?
Answer» A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Discussion

12420.	The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 ii) 1997
Answer» The population of a city increases each year by $4 %$ of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 ii) 1997

12420.

The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 ii) 1997

Answer»

The population of a city increases each year by $4 %$ of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in

(i) 2001

ii) 1997

Discussion

12421.	A sum of money triple itself in 3 years at compound interest. In how many years will it become 9 times itself?
Answer» A sum of money triple itself in 3 years at compound interest. In how many years will it become 9 times itself?

Discussion

12422.	Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.
Answer» Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.

Discussion

12423.	On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/-. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.
Answer» On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/-. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

Discussion

12424.	Question 1 (b) Calculate the amount and compound interest on: b) ₹18,000 for 212% years at 10% per annum compounded annually.
Answer» Question 1 (b) Calculate the amount and compound interest on: b) ₹18,000 for $2 \frac{1}{2} %$ years at 10% per annum compounded annually.

Discussion

12425.	How many significant figures are there in the product: (2.156×101)×(4.567891×102)×(5.1102×103)
Answer» How many significant figures are there in the product: $(2.156 \times 10^{1}) \times (4.567891 \times 10^{2}) \times (5.1102 \times 10^{3})$

12425.

How many significant figures are there in the product: (2.156×101)×(4.567891×102)×(5.1102×103)

Answer»

How many significant figures are there in the product:

$(2.156 \times 10^{1}) \times (4.567891 \times 10^{2}) \times (5.1102 \times 10^{3})$

Discussion

12426.	Factorise by grouping method: a2+b−ab−a
Answer» Factorise by grouping method: $a^{2} + b - a b - a$

12426.

Factorise by grouping method: a2+b−ab−a

Answer»

Factorise by grouping method:

$a^{2} + b - a b - a$

Discussion

12427.	PROVE THAT:(1/1+a+b^-1)+(1/1+b+c^-1)+(1/1+c+a^-1)=abc
Answer» PROVE THAT: (1/1+a+b^-1)+(1/1+b+c^-1)+(1/1+c+a^-1)=abc

Discussion

12428.	Formula to find the total surface area of cylinder is:
Answer» Formula to find the total surface area of cylinder is:

Discussion

12429.	Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an 'inclusive or' or 'exclusive or' is used. (i) The sum of 3 and 7 is 10 or 11. (ii) (1+i) is a real or a complex number. (iii) Every quadratic equation has one or two real roots. (iv) You are wet when it rains or you are in a river. (v) 24 is a multiple of 5 or 8. (vi) Every integer is rational or irrational. (vii) For getting a driving licence you should have a ration card or a passport. (viii) 100 is a multiple of 6 or 8. (ix) Square of an integer is positive or negative. (x) Sun rises or Moon sets.
Answer» Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an 'inclusive or' or 'exclusive or' is used. (i) The sum of 3 and 7 is 10 or 11. (ii) (1+i) is a real or a complex number. (iii) Every quadratic equation has one or two real roots. (iv) You are wet when it rains or you are in a river. (v) 24 is a multiple of 5 or 8. (vi) Every integer is rational or irrational. (vii) For getting a driving licence you should have a ration card or a passport. (viii) 100 is a multiple of 6 or 8. (ix) Square of an integer is positive or negative. (x) Sun rises or Moon sets.

12429.

Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an 'inclusive or' or 'exclusive or' is used. (i) The sum of 3 and 7 is 10 or 11. (ii) (1+i) is a real or a complex number. (iii) Every quadratic equation has one or two real roots. (iv) You are wet when it rains or you are in a river. (v) 24 is a multiple of 5 or 8. (vi) Every integer is rational or irrational. (vii) For getting a driving licence you should have a ration card or a passport. (viii) 100 is a multiple of 6 or 8. (ix) Square of an integer is positive or negative. (x) Sun rises or Moon sets.

Answer»

Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an 'inclusive or' or 'exclusive or' is used.

(i) The sum of 3 and 7 is 10 or 11.

(ii) (1+i) is a real or a complex number.

(iii) Every quadratic equation has one or two real roots.

(iv) You are wet when it rains or you are in a river.

(v) 24 is a multiple of 5 or 8.

(vi) Every integer is rational or irrational.

(vii) For getting a driving licence you should have a ration card or a passport.

(viii) 100 is a multiple of 6 or 8.

(ix) Square of an integer is positive or negative.

(x) Sun rises or Moon sets.

Discussion

12430.	Question 48Discount is a reduction given on cost price of an article.
Answer» Question 48 Discount is a reduction given on cost price of an article.

12430.

Question 48Discount is a reduction given on cost price of an article.

Answer»

Question 48

Discount is a reduction given on cost price of an article.

Discussion

12431.	Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. Then, the probability that the ticket has a number which is a multiple of 3 or 7 is _____.
Answer» Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. Then, the probability that the ticket has a number which is a multiple of 3 or 7 is _____.

Discussion

12432.	Find the value of 27x3 + 8y3, if(i) 3x + 2y = 14 and xy = 8(ii) 3x + 2y = 20 and xy = 149
Answer» Find the value of 27x³ + 8y³, if (i) 3x + 2y = 14 and xy = 8 (ii) 3x + 2y = 20 and xy = $\frac{14}{9}$

Discussion

12433.	Write down the number of faces of each of the following figures : (i) Cuboid (ii) Cube (iii) Triangular prism (iv) Square pyramid (v) Tetrahedron
Answer» Write down the number of faces of each of the following figures : (i) Cuboid (ii) Cube (iii) Triangular prism (iv) Square pyramid (v) Tetrahedron

Discussion

12434.	Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15% on the third day. If the number of pages remaining to be read is 30, find the total number of pages in the book.
Answer» Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15% on the third day. If the number of pages remaining to be read is 30, find the total number of pages in the book.

Discussion

12435.	Factorise : 16a2−225b2
Answer» Factorise : $16 a^{2} - 225 b^{2}$

12435.

Factorise : 16a2−225b2

Answer»

Factorise :

$16 a^{2} - 225 b^{2}$

Discussion

12436.	(a) Find the value of x in the below diagram given that, ∠ACB = 25o, ∠CBA = 15o and CD is the height of C from the extended line segment BA: (b) The lengths of two sides of a triangle are 13 cm and 16 cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. Find the value of a + b? [4 MARKS]
Answer» (a) Find the value of x in the below diagram given that, $∠ A C B$ = 25 $^{o}$ , $∠ C B A$ = 15 $^{o}$ and CD is the height of C from the extended line segment BA: (b) The lengths of two sides of a triangle are 13 cm and 16 cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. Find the value of a + b? [4 MARKS]

Discussion

12437.	ABCD is a quadrilateral and the measure of AB, BC , CD and ∠ABC are known. Which of the following parameter required for the construction of a unique quadrilateral ABCD ?
Answer» ABCD is a quadrilateral and the measure of AB, BC , CD and $∠ A B C$ are known. Which of the following parameter required for the construction of a unique quadrilateral ABCD ?

Discussion

12438.	It is known that a box of 100 electric bulbs contains 8 defeective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective ? (ii) non-defective?
Answer» It is known that a box of 100 electric bulbs contains 8 defeective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective ? (ii) non-defective?

Discussion

12439.	11. Compound interest on 13200 for 3/2 year at 10% per annum compounded half yearly will be
Answer» 11. Compound interest on 13200 for 3/2 year at 10% per annum compounded half yearly will be

Discussion

12440.

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers. Daily Income (in Rs) 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 Number of workers 5 10 15 20 10 5 (Hint: Compute median, lower quartile and upper quartile)

Answer»

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.

Daily Income (in Rs)	10 – 14	15 – 19	20 – 24	25 – 29	30 – 34	35 – 39
Number of workers	5	10	15	20	10	5

(Hint: Compute median, lower quartile and upper quartile)

Discussion

12441.	√3×√12+4÷√2−√8=
Answer» $\sqrt{3} \times \sqrt{12} + 4 \div \sqrt{2} - \sqrt{8} =$

Discussion

12442.	Find the volume of a cone given in the figure.
Answer» Find the volume of a cone given in the figure.

Discussion

12443.	Find the C.I paid when a sum of ₹ 40,000 is taken for one year and six months at 5% per annum compounded annually.
Answer» Find the C.I paid when a sum of ₹ 40,000 is taken for one year and six months at $5 %$ per annum compounded annually.

Discussion

12444.	Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Answer» Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

12444.

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Answer»

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Discussion

12445.	Samira sells newspapers at Janpath crossing daily. On a particular day, she had 312 newspapers out of which 216 were in English and remaining in Hindi. Find the ratio ofa) The number of English newspapers to the number of Hindi newspapers.b) The number of Hindi newspapers to the total number of newspapers.
Answer» Samira sells newspapers at Janpath crossing daily. On a particular day, she had 312 newspapers out of which 216 were in English and remaining in Hindi. Find the ratio of a) The number of English newspapers to the number of Hindi newspapers. b) The number of Hindi newspapers to the total number of newspapers.

12445.

Samira sells newspapers at Janpath crossing daily. On a particular day, she had 312 newspapers out of which 216 were in English and remaining in Hindi. Find the ratio ofa) The number of English newspapers to the number of Hindi newspapers.b) The number of Hindi newspapers to the total number of newspapers.

Answer»

Samira sells newspapers at Janpath crossing daily. On a particular day, she had 312 newspapers out of which 216 were in English and remaining in Hindi. Find the ratio of

a) The number of English newspapers to the number of Hindi newspapers.

b) The number of Hindi newspapers to the total number of newspapers.

Discussion

12446.	Anita and her friends bought some pens. For a packet of five pens, they got two rupees reduction in price. They had to pay only 18 rupees. Had they bought the pens separately, how much would have been the price for each pen?
Answer» Anita and her friends bought some pens. For a packet of five pens, they got two rupees reduction in price. They had to pay only 18 rupees. Had they bought the pens separately, how much would have been the price for each pen?

12446.

Anita and her friends bought some pens. For a packet of five pens, they got two rupees reduction in price. They had to pay only 18 rupees. Had they bought the pens separately, how much would have been the price for each pen?

Answer»

Anita and her friends bought some pens. For a packet of five pens, they got two rupees reduction in price. They had to pay only 18 rupees. Had they bought the pens separately, how much would have been the price for each pen?

Discussion

12447.	The given pictures are different varieties of:
Answer» The given pictures are different varieties of:

Discussion

12448.	If a triangle having a point O inside it then prove that the sides of the triangle is greater than the line segment joining O to the vertices of that triangle?
Answer» If a triangle having a point O inside it then prove that the sides of the triangle is greater than the line segment joining O to the vertices of that triangle?

Discussion

12449.	Select the pair of disjoint sets.
Answer» Select the pair of disjoint sets.

Discussion

12450.	Solve :4-2(z-4)/3=1/2(2z+5)
Answer» Solve :4-2(z-4)/3=1/2(2z+5)

Discussion

Explore topic-wise InterviewSolutions in .

Prove that n^{3 }- n is divisible by 6 , for every possible value of n

Simplify the polynomial expression and then write in standard form.(3+5x+7x2+9x3)+(4+2x−3x2−8x3)

Kuttan’s mother is 25 years older than Kuttan. When Kuttan is 8, how old will his mother be? How old will Kuttan be when his mother is 40? If we write k for Kuttan’s age and m for mother’s age, in what all ways can we write the relation between them?

Question 1(viii) Use a suitable identity to get each of the following products: (−a+c)(−a+c)

Rationalise: 13 +5 +15

Evaluate: 176×176−124×124

Question 4(i)Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of :Getting a number 6.

Given that ABCD is a rectangle as shown in the figure . Here, AC = ___ × OB.

Factorise: 4y2+20y+25

If 8 oranges cost Rs. 10.40, how many oranges can be bought for Rs. 33.80 ? (a) 13 (b) 18 (c) 26 (d) 24

Name the property involved in the following example. 3/7×1=3/7=1×3/7

A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in (m2)? [ 1 MARK ]

Write the reciprocal of 5+2.

Find the square root of: 4a2+9b2+c2−12ab+6bc−4ac

The difference between selling a coat at a profit of 4% and that of 6% is ₹3. Find the two selling price.

The compound interest on a certain sum of money at 5% per annum for two years is Rs.246. Calculate the simple interest on the same sum for three years at 6% per annum.

Question 180(ii)Simplify[(43)−2−(34)2]−2

In the parallelogram ABCD, value of ∠D is .

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 ii) 1997

A sum of money triple itself in 3 years at compound interest. In how many years will it become 9 times itself?

Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.

On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/-. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

Question 1 (b) Calculate the amount and compound interest on: b) ₹18,000 for 212% years at 10% per annum compounded annually.

How many significant figures are there in the product: (2.156×101)×(4.567891×102)×(5.1102×103)

Factorise by grouping method: a2+b−ab−a

PROVE THAT:(1/1+a+b^-1)+(1/1+b+c^-1)+(1/1+c+a^-1)=abc

Formula to find the total surface area of cylinder is:

Question 48Discount is a reduction given on cost price of an article.

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. Then, the probability that the ticket has a number which is a multiple of 3 or 7 is _____.

Find the value of 27x3 + 8y3, if(i) 3x + 2y = 14 and xy = 8(ii) 3x + 2y = 20 and xy = 149

Write down the number of faces of each of the following figures : (i) Cuboid (ii) Cube (iii) Triangular prism (iv) Square pyramid (v) Tetrahedron

Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15% on the third day. If the number of pages remaining to be read is 30, find the total number of pages in the book.

Factorise : 16a2−225b2

ABCD is a quadrilateral and the measure of AB, BC , CD and ∠ABC are known. Which of the following parameter required for the construction of a unique quadrilateral ABCD ?

It is known that a box of 100 electric bulbs contains 8 defeective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective ? (ii) non-defective?

11. Compound interest on 13200 for 3/2 year at 10% per annum compounded half yearly will be

√3×√12+4÷√2−√8=

Find the volume of a cone given in the figure.

Find the C.I paid when a sum of ₹ 40,000 is taken for one year and six months at 5% per annum compounded annually.

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Anita and her friends bought some pens. For a packet of five pens, they got two rupees reduction in price. They had to pay only 18 rupees. Had they bought the pens separately, how much would have been the price for each pen?

The given pictures are different varieties of:

If a triangle having a point O inside it then prove that the sides of the triangle is greater than the line segment joining O to the vertices of that triangle?

Select the pair of disjoint sets.

Solve :4-2(z-4)/3=1/2(2z+5)