32581 + Interview Questions in Mathematics Page 192 InterviewSolution

9551.	Question 32 How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?
Answer» Question 32 How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?

Discussion

9552.	If one root of the equation 2x2+ax+6=0 is 3, then the value of a is ___________.
Answer» If one root of the equation $2 x^{2} + a x + 6 = 0$ is 3, then the value of a is ___________.

Discussion

9553.	There is a natural number x. What is the next natural number from x?
Answer» There is a natural number $x$ . What is the next natural number from $x$ ?

Discussion

9554.	Mark the correct alternative in the following question:Two-third of a number is greater than one-third of the number by 5. The number is(a) 10 (b) 5 (c) 15 (d) 12
Answer» Mark the correct alternative in the following question: Two-third of a number is greater than one-third of the number by 5. The number is (a) 10 (b) 5 (c) 15 (d) 12

Discussion

9555.	Solve each of the following systems of equations graphically: 2x−5y+4=0,2x+y−8=0.
Answer» Solve each of the following systems of equations graphically: $2 x - 5 y + 4 = 0, 2 x + y - 8 = 0.$

9555.

Solve each of the following systems of equations graphically: 2x−5y+4=0,2x+y−8=0.

Answer»

Solve each of the following systems of equations graphically:

$2 x - 5 y + 4 = 0, 2 x + y - 8 = 0.$

Discussion

9556.	A vector A points towards north and vector B points upwards then A×B point toward
Answer» A vector A points towards north and vector B points upwards then A×B point toward

Discussion

9557.	(sin2 A cos2 B−cos2 A sin2 B)=
Answer» $(s i n^{2} A c o s^{2} B - c o s^{2} A s i n^{2} B) =$

Discussion

9558.	From a set of 18 cards, numbered 1, 2, 3, .....,17, 18 one card is drawn. What is the probability that the number on the card is multiple of 3 or 7?
Answer» From a set of 18 cards, numbered 1, 2, 3, .....,17, 18 one card is drawn. What is the probability that the number on the card is multiple of 3 or 7?

Discussion

9559.	List price of a pair of shoes is Rs. 540. If Amit paid Rs. 45 as sales tax for it, find the rate of sales tax.
Answer» List price of a pair of shoes is Rs. 540. If Amit paid Rs. 45 as sales tax for it, find the rate of sales tax.

Discussion

9560.	In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠PAO = 30∘ then ∠CPB + ∠ACP is equal to(a) 60∘(b) 90∘(c) 120∘(d) 150∘
Answer» In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠PAO = 30^∘ then ∠CPB + ∠ACP is equal to (a) 60^∘ (b) 90^∘ (c) 120^∘ (d) 150^∘

Discussion

9561.	Find the roots by method of completing the square :3x2−7x−20=0
Answer» Find the roots by method of completing the square : $3 x^{2} - 7 x - 20 = 0$

Discussion

9562.	The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30∘. On advancing 150 m towards the foot of the tower, the angle of elevation becomes 60∘. Show that the height of the tower is 129.9 metres. [Take √3=1.732.]
Answer» The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is $30^{\circ}$ . On advancing 150 m towards the foot of the tower, the angle of elevation becomes $60^{\circ}$ . Show that the height of the tower is 129.9 metres. [Take $\sqrt{3} = 1.732.$ ]

Discussion

9563.	320 apples were sold at the CP of 400 apples what is the gain %?
Answer» 320 apples were sold at the CP of 400 apples what is the gain %?

Discussion

9564.	If two zeros x3 + x2 − 5x − 5 are 5 and -5, then its third zero is(a) 1(b) −1(c) 2(d) −2
Answer» If two zeros x³ + x² − 5x − 5 are $\sqrt{5} and - \sqrt{5}$ , then its third zero is (a) 1 (b) −1 (c) 2 (d) −2

Discussion

9565.	Select the pair that has the same relationship as the original pair of words / numbers : 11 : 1210
Answer» Select the pair that has the same relationship as the original pair of words / numbers : 11 : 1210

9565.

Select the pair that has the same relationship as the original pair of words / numbers : 11 : 1210

Answer»

Select the pair that has the same relationship as the original pair of words / numbers :

11 : 1210

Discussion

9566.	Question 1 (vi)Solve the following pair of linear equations by the substitution method.3x2−5y3=−2;x3+y2=136
Answer» Question 1 (vi) Solve the following pair of linear equations by the substitution method. $\frac{3 x}{2} - \frac{5 y}{3} = - 2; \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

Discussion

9567.	In a ∆ABC, ∠A = x°, ∠B = (3x − 2)°, ∠C = y°. Also, ∠C − ∠B = 9°. Find the three angles.
Answer» In a ∆ABC, ∠A = x°, ∠B = (3x − 2)°, ∠C = y°. Also, ∠C − ∠B = 9°. Find the three angles.

Discussion

9568.	If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =(a) 8(b) −8(c) 4(d) −4
Answer» If one root of the equation 4x² − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ = (a) 8 (b) −8 (c) 4 (d) −4

Discussion

9569.	Find the value of ‘t’ for which the polynomial P(x) = x3+3x2+2x+t gives 3 as remainder when divided by( x – 1).
Answer» Find the value of ‘t’ for which the polynomial P(x) = $x^{3} + 3 x^{2} + 2 x + t$ gives 3 as remainder when divided by( x – 1).

Discussion

9570.	Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". Is not this interesting? Represent this situation algebraically and graphically.
Answer» Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". Is not this interesting? Represent this situation algebraically and graphically.

Discussion

9571.	Are single values considered including the intervals as a solution of a inequality by wavy curve method
Answer» Are single values considered including the intervals as a solution of a inequality by wavy curve method

Discussion

9572.	If,prove that
Answer» If, prove that

Discussion

9573.	Find the sums given below(i) 7 + + 14 + ………… + 84(ii) 34 + 32 + 30 + ……….. + 10(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)
Answer» Find the sums given below (i) 7 + + 14 + ………… + 84 (ii) 34 + 32 + 30 + ……….. + 10 (iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

9573.

Find the sums given below(i) 7 + + 14 + ………… + 84(ii) 34 + 32 + 30 + ……….. + 10(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

Answer»

Find the sums given below

(i) 7 + + 14 + ………… + 84

(ii) 34 + 32 + 30 + ……….. + 10

(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

Discussion

9574.	We accept paper money as a medium of exchange because
Answer» We accept paper money as a medium of exchange because

Discussion

9575.	A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at Rs. 1.25 per square metre (Take π = 3.14).
Answer» A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at Rs. 1.25 per square metre (Take π = 3.14).

Discussion

9576.	Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .
Answer» Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

Discussion

9577.	Choose the correct answer in each of the following questions:The sum of first 20 odd natural numbers is [CBSE 2012](a) 100 (b) 210 (c) 400 (d) 420
Answer» Choose the correct answer in each of the following questions: The sum of first 20 odd natural numbers is [CBSE 2012] (a) 100 (b) 210 (c) 400 (d) 420

Discussion

9578.	In Euclid Division Lemma, If a < b , what can be said about q and r ?
Answer» In Euclid Division Lemma, If a < b , what can be said about q and r ?

9578.

In Euclid Division Lemma, If a < b , what can be said about q and r ?

Answer»

In Euclid Division Lemma,

If a < b , what can be said about q and r ?

Discussion

9579.	A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.
Answer» A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

Discussion

9580.	Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its54th term?
Answer» Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its $54^{t h}$ term?

Discussion

9581.	-74,-68,-62 In this AP how many negative terms are there
Answer» -74,-68,-62 In this AP how many negative terms are there

9581.

-74,-68,-62 In this AP how many negative terms are there

Answer»

-74,-68,-62

In this AP how many negative terms are there

Discussion

9582.	A and B are partners sharing profits in the ratio of 3 : 2. Their books show goodwill at ₹ 2,000. C is admitted as partner for 1/4th share of profits and brings in ₹ 10,000 as his capital but is not able to bring in cash for his share of goodwill ₹ 3,000. Draft Journal entries.
Answer» A and B are partners sharing profits in the ratio of 3 : 2. Their books show goodwill at ₹ 2,000. C is admitted as partner for 1/4th share of profits and brings in ₹ 10,000 as his capital but is not able to bring in cash for his share of goodwill ₹ 3,000. Draft Journal entries.

Discussion

9583.	If ∫α0dx1−cosαcosx=Asinα+B (α≠0) the values of A and B are
Answer» If $\int_{0}^{α} \frac{d x}{1 - cos α cos x} = \frac{A}{sin α} + B (α \neq 0)$ the values of A and B are

Discussion

9584.	Solve each of the following quadratic equations: (i) xx−1+x−1x=414,x≠0,1 (ii) x−12x−1+2x−1x−1=2,x≠12,1
Answer» Solve each of the following quadratic equations: (i) $\frac{x}{x - 1} + \frac{x - 1}{x} = 4 \frac{1}{4}, x \neq 0, 1$ (ii) $\frac{x - 1}{2 x - 1} + \frac{2 x - 1}{x - 1} = 2, x \neq \frac{1}{2}, 1$

Discussion

9585.	Solve each of the following quadratic equations:x-4x-5+x-6x-7=313, x≠5, 7 [CBSE 2014]
Answer» Solve each of the following quadratic equations: $\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = 3 \frac{1}{3}, x \neq 5, 7$ [CBSE 2014]

Discussion

9586.	The zero of the polynomial p(x) =5x - 10 is ________ ___
Answer» The zero of the polynomial p(x) =5x - 10 is ________ ___

Discussion

9587.	Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.
Answer» Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Discussion

9588.	A : For an isolated system △ G=-T△ S_{total} R : For an isolated system q = 0 .
Answer» A : For an isolated system △ G=-T△ S_{total} R : For an isolated system q = 0 .

Discussion

9589.	A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
Answer» A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Discussion

9590.	A line which intersects a circle at 2 distinct points is called
Answer» A line which intersects a circle at 2 distinct points is called

Discussion

9591.	Question 12The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110∘ , find ∠ CBA.
Answer» Question 12 The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $∠ P C A = 110^{\circ}$ , find $∠$ CBA.

Discussion

9592.	Use Euclid's division algorithm to find the HCF of 135 and 225
Answer» Use Euclid's division algorithm to find the HCF of 135 and 225

Discussion

9593.	The ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height h is __________.
Answer» The ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height h is __________.

Discussion

9594.	Find the distance between the origin and P (3,√5,2).
Answer» Find the distance between the origin and P $(3, \sqrt{5}, 2)$ .

Discussion

9595.	If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___
Answer» If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___

9595.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___

Answer»

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___

Discussion

9596.	When you flip a coin, then the probability of getting a head is .
Answer» When you flip a coin, then the probability of getting a head is .

Discussion

9597.	Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….
Answer» Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….

Discussion

9598.	Find the value of k for which the quadratic equation x2–4x+k=0 has real and equal roots.
Answer» Find the value of k for which the quadratic equation $x^{2} - 4 x + k = 0$ has real and equal roots.

Discussion

9599.	If f(x) = x3 + x2 − ax + b is divisible by x2 − x write the value of a and b.
Answer» If f(x) = x³ + x² − ax + b is divisible by x² − x write the value of a and b.

Discussion

9600.

Prepare the Transfer Vouchers from the books of Mangla Agencies, Faridabad, Haryana from the Source Vouchers: 2018 ₹ Jan.7 Purchased goods from M/s. Eufora New Delhi vide Bill No. 912, paid IGST 12% 4,700 Jan. 11 Sold goods to M/s. Yardley, Faridabad, Haryana vide Bill No. 31596, charged CGST and SGST 6% each 5,000 Jan. 31 Depreciation charged on building 10% on ₹ 2,00,000 20,000

Answer» Prepare the Transfer Vouchers from the books of Mangla Agencies, Faridabad, Haryana from the Source Vouchers:

2018		₹
Jan.7	Purchased goods from M/s. Eufora New Delhi vide Bill No. 912, paid IGST 12%	4,700
Jan. 11	Sold goods to M/s. Yardley, Faridabad, Haryana vide Bill No. 31596, charged CGST and SGST 6% each	5,000
Jan. 31	Depreciation charged on building 10% on ₹ 2,00,000	20,000

Discussion

Explore topic-wise InterviewSolutions in .

Question 32 How many terms of the AP –15, –13, –11,. … are needed to make the sum –55?

If one root of the equation 2x2+ax+6=0 is 3, then the value of a is ___________.

There is a natural number x. What is the next natural number from x?

Mark the correct alternative in the following question:Two-third of a number is greater than one-third of the number by 5. The number is(a) 10 (b) 5 (c) 15 (d) 12

Solve each of the following systems of equations graphically: 2x−5y+4=0,2x+y−8=0.

A vector A points towards north and vector B points upwards then A×B point toward

(sin2 A cos2 B−cos2 A sin2 B)=

From a set of 18 cards, numbered 1, 2, 3, .....,17, 18 one card is drawn. What is the probability that the number on the card is multiple of 3 or 7?

List price of a pair of shoes is Rs. 540. If Amit paid Rs. 45 as sales tax for it, find the rate of sales tax.

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠PAO = 30∘ then ∠CPB + ∠ACP is equal to(a) 60∘(b) 90∘(c) 120∘(d) 150∘

Find the roots by method of completing the square :3x2−7x−20=0

The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30∘. On advancing 150 m towards the foot of the tower, the angle of elevation becomes 60∘. Show that the height of the tower is 129.9 metres. [Take √3=1.732.]

320 apples were sold at the CP of 400 apples what is the gain %?

If two zeros x3 + x2 − 5x − 5 are 5 and -5, then its third zero is(a) 1(b) −1(c) 2(d) −2

Select the pair that has the same relationship as the original pair of words / numbers : 11 : 1210

Question 1 (vi)Solve the following pair of linear equations by the substitution method.3x2−5y3=−2;x3+y2=136

In a ∆ABC, ∠A = x°, ∠B = (3x − 2)°, ∠C = y°. Also, ∠C − ∠B = 9°. Find the three angles.

If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =(a) 8(b) −8(c) 4(d) −4

Find the value of ‘t’ for which the polynomial P(x) = x3+3x2+2x+t gives 3 as remainder when divided by( x – 1).

Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". Is not this interesting? Represent this situation algebraically and graphically.

Are single values considered including the intervals as a solution of a inequality by wavy curve method

If,prove that

Find the sums given below(i) 7 + + 14 + ………… + 84(ii) 34 + 32 + 30 + ……….. + 10(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

We accept paper money as a medium of exchange because

A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at Rs. 1.25 per square metre (Take π = 3.14).

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

Choose the correct answer in each of the following questions:The sum of first 20 odd natural numbers is [CBSE 2012](a) 100 (b) 210 (c) 400 (d) 420

In Euclid Division Lemma, If a &lt; b , what can be said about q and r ?

A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its54th term?

-74,-68,-62 In this AP how many negative terms are there

A and B are partners sharing profits in the ratio of 3 : 2. Their books show goodwill at ₹ 2,000. C is admitted as partner for 1/4th share of profits and brings in ₹ 10,000 as his capital but is not able to bring in cash for his share of goodwill ₹ 3,000. Draft Journal entries.

If ∫α0dx1−cosαcosx=Asinα+B (α≠0) the values of A and B are

Solve each of the following quadratic equations: (i) xx−1+x−1x=414,x≠0,1 (ii) x−12x−1+2x−1x−1=2,x≠12,1

Solve each of the following quadratic equations:x-4x-5+x-6x-7=313, x≠5, 7 [CBSE 2014]

The zero of the polynomial p(x) =5x - 10 is ________ ___

Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

A : For an isolated system △ G=-T△ S_{total} R : For an isolated system q = 0 .

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A line which intersects a circle at 2 distinct points is called

Question 12The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110∘ , find ∠ CBA.

Use Euclid's division algorithm to find the HCF of 135 and 225

The ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height h is __________.

Find the distance between the origin and P (3,√5,2).

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'C' is ___

When you flip a coin, then the probability of getting a head is .

Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….

Find the value of k for which the quadratic equation x2–4x+k=0 has real and equal roots.

If f(x) = x3 + x2 − ax + b is divisible by x2 − x write the value of a and b.

In Euclid Division Lemma, If a < b , what can be said about q and r ?

The zero of the polynomial p(x) =5x - 10 is ______ _