32581 + Interview Questions in Mathematics Page 81 InterviewSolution

4001.	In the given figure, PR = (a) 20 cm(b) 26 cm(c) 24 cm(d) 28 cm
Answer» In the given figure, PR = (a) 20 cm (b) 26 cm (c) 24 cm (d) 28 cm

Discussion

4002.	For the curve sinx+siny=1 lying in the first quadrant, L=limx→0xαd2ydx2 where L exists and is non-zero. Then
Answer» For the curve $sin x + sin y = 1$ lying in the first quadrant, $L = lim x \to 0 x^{α} \frac{d^{2} y}{d x^{2}}$ where $L$ exists and is non-zero. Then

Discussion

4003.	The area of a square field is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?
Answer» The area of a square field is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?

Discussion

4004.	Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.
Answer» Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.

Discussion

4005.	3. 2 cards are selected randomly from 52 cards. The prob that first card is a club and second is not a queen is
Answer» 3. 2 cards are selected randomly from 52 cards. The prob that first card is a club and second is not a queen is

Discussion

4006.	Note Take π=227, unless stated otherwise.A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
Answer» Note Take $π = \frac{22}{7}$ , unless stated otherwise. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Discussion

4007.	If x=2√3+2√2, then find 1x:
Answer» If $x = 2 \sqrt{3} + 2 \sqrt{2}$ , then find $\frac{1}{x}$ :

Discussion

4008.	Question 4 (v) State whether the following are true or false. Justify your answer. (v) cot A is not defined for A=0∘.
Answer» Question 4 (v) State whether the following are true or false. Justify your answer. (v) cot A is not defined for $A = 0^{\circ}$ .

Discussion

4009.	15.Total number of vertex angle in structure of white phosphorous
Answer» 15.Total number of vertex angle in structure of white phosphorous

Discussion

4010.	For the given concentric circles with radius 5 cm and 13 cm respectively. Find the length of the chord AB.
Answer» For the given concentric circles with radius 5 cm and 13 cm respectively. Find the length of the chord AB.

Discussion

4011.	Find the L.C.M. of the following expressions by division method.x3 + 2x2 − 13x − 10 and x3 − x2 − 10x − 8
Answer» Find the L.C.M. of the following expressions by division method. x³ + 2x² − 13x − 10 and x³ − x² − 10x − 8

4011.

Find the L.C.M. of the following expressions by division method.x3 + 2x2 − 13x − 10 and x3 − x2 − 10x − 8

Answer»

Find the L.C.M. of the following expressions by division method.

x³ + 2x² − 13x − 10 and x³ − x² − 10x − 8

Discussion

4012.	The following table gives the marks scored by 100 students in an entrance examination. Marks0.1010−2020−3030−4040−5050−6060−7070−80No. of students (Frequency)4101622201882 Represent this data in the form of a histogram
Answer» The following table gives the marks scored by 100 students in an entrance examination. $\begin{matrix} M a r k s & 0.10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 N o . o f s t u d e n t s (F r e q u e n c y) & 4 & 10 & 16 & 22 & 20 & 18 & 8 & 2 \end{matrix}$ Represent this data in the form of a histogram

4012.

The following table gives the marks scored by 100 students in an entrance examination. Marks0.1010−2020−3030−4040−5050−6060−7070−80No. of students (Frequency)4101622201882 Represent this data in the form of a histogram

Answer»

The following table gives the marks scored by 100 students in an entrance examination.

$\begin{matrix} M a r k s & 0.10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 N o . o f s t u d e n t s (F r e q u e n c y) & 4 & 10 & 16 & 22 & 20 & 18 & 8 & 2 \end{matrix}$

Represent this data in the form of a histogram

Discussion

4013.	There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 11 chocolates. Who has the average number of chocolates?
Answer» There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 11 chocolates. Who has the average number of chocolates?

Discussion

4014.	A natural number, when increased by 12, equals 160 times its reciprocal find the number.
Answer» A natural number, when increased by 12, equals 160 times its reciprocal find the number.

Discussion

4015.	A thief , after committing a theft , runs at a speed of 50 m/min . After 2 mins , a policeman runs to catch him. He goes 60m in the first min and increases his speed by 5 m/min every succeeding minute. After how many minutes,the policeman will catch the thief?
Answer» A thief , after committing a theft , runs at a speed of 50 m/min . After 2 mins , a policeman runs to catch him. He goes 60m in the first min and increases his speed by 5 m/min every succeeding minute. After how many minutes,the policeman will catch the thief?

Discussion

4016.	A hemispherical tank, full of water, is emptied by a pipe at the rate of 257 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m? [CBSE 2012]
Answer» A hemispherical tank, full of water, is emptied by a pipe at the rate of $\frac{25}{7}$ litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m? [CBSE 2012]

Discussion

4017.	A right triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Answer» A right triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Discussion

4018.	A rectangle of length “a” and breadth “b” is rotated by 360∘ about its length. The volume of the resulting cylinder is _____.
Answer» A rectangle of length “ $a$ ” and breadth “ $b$ ” is rotated by $360^{\circ}$ about its length. The volume of the resulting cylinder is _____.

Discussion

4019.	A diagonal matrix will always be
Answer» A diagonal matrix will always be

Discussion

4020.	The difference between the circumference and radius of a circle is 37 cm. The area of the circle is______
Answer» The difference between the circumference and radius of a circle is 37 cm. The area of the circle is______

Discussion

4021.	Find n if the given value of x is the nth term of the given A.P.(i) 25, 50, 75, 100, ...; x = 1000(ii) −1, −3, −5, −7, ...; x = −151(iii) 512, 11, 1612, 22,...; x = 550(iv) 1,2111,3111,4111,..., x = 17111
Answer» Find n if the given value of x is the nth term of the given A.P. (i) 25, 50, 75, 100, ...; x = 1000 (ii) −1, −3, −5, −7, ...; x = −151 (iii) $5 \frac{1}{2}, 11, 16 \frac{1}{2}, 22, . . .; x = 550$ (iv) $1, \frac{21}{11}, \frac{31}{11}, \frac{41}{11}, . . ., x = \frac{171}{11}$

Discussion

4022.	In a musical chair game, person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half minute after starting?
Answer» In a musical chair game, person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half minute after starting?

Discussion

4023.	Find the function corresponding to the graph given below, 1≤x≤3 ( The function which closely describes the graph )
Answer» Find the function corresponding to the graph given below, $1 \leq x \leq 3$ ( The function which closely describes the graph )

4023.

Find the function corresponding to the graph given below, 1≤x≤3 ( The function which closely describes the graph )

Answer»

Find the function corresponding to the graph given below, $1 \leq x \leq 3$ ( The function which closely describes the graph )

Discussion

4024.	Ram borrowed an amount of Rs. 15000 from a bank to buy a car at 10% simple interest. If he paid Rs. 9000 as interest while clearing the loan, determine the period of the loan.
Answer» Ram borrowed an amount of Rs. 15000 from a bank to buy a car at 10% simple interest. If he paid Rs. 9000 as interest while clearing the loan, determine the period of the loan.

Discussion

4025.	What is the value of (sin 18°)/(cos 72°)?
Answer» What is the value of (sin 18°)/(cos 72°)?

Discussion

4026.	A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100cm2.[Use π=3.14]
Answer» A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per $100 c m^{2} . [U s e π = 3.14]$

Discussion

4027.	In class 10 A , there are 24 boys and 25 girls. In class 10B , there are 20 boys and 20 girls. One student is selected from each class for an activity. What is the probability of both of them being girls ?
Answer» In class 10 A , there are 24 boys and 25 girls. In class 10B , there are 20 boys and 20 girls. One student is selected from each class for an activity. What is the probability of both of them being girls ?

Discussion

4028.	x+3/8=1
Answer» x+3/8=1

Discussion

4029.	38. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number
Answer» 38. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number

Discussion

4030.

The marks obtained by 110 students in an examination are given below: Marks: 30 – 35 35 – 40 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 Frequency: 14 16 28 23 18 8 3 Find the mean marks of the students.

Answer» The marks obtained by 110 students in an examination are given below:

Marks:	30 – 35	35 – 40	40 – 45	45 – 50	50 – 55	55 – 60	60 – 65
Frequency:	14	16	28	23	18	8	3

Find the mean marks of the students.

Discussion

4031.	At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age. Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
Answer» At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age. Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Discussion

4032.	if l= m sec theta + n tan theta and k= n sec theta + m tan theta
Answer» if l= m sec theta + n tan theta and k= n sec theta + m tan theta

Discussion

4033.	In the given figure, if PR is tangent to the circle at P and Q is the centre of the circle, then ∠POQ = (a) 110°(b) 100°(c) 120°(d) 90°
Answer» In the given figure, if PR is tangent to the circle at P and Q is the centre of the circle, then ∠POQ = (a) 110° (b) 100° (c) 120° (d) 90°

Discussion

4034.	Show that:sin42∘sec48∘+cos42∘ cosec48∘=2
Answer» Show that: $sin 42^{\circ} sec 48^{\circ} + cos 42^{\circ} c o s e c 48^{\circ} = 2$

4034.

Show that:sin42∘sec48∘+cos42∘ cosec48∘=2

Answer»

Show that:

$sin 42^{\circ} sec 48^{\circ} + cos 42^{\circ} c o s e c 48^{\circ} = 2$

Discussion

4035.	If x = √a tan α and y = √a sec α. Find the value of y2 – x2 __
Answer» If x = $\sqrt{a} t a n α$ and y = $\sqrt{a} s e c α$ . Find the value of $y^{2}$ – $x^{2}$ __

4035.

If x = √a tan α and y = √a sec α. Find the value of y2 – x2 __

Answer»

If x = $\sqrt{a} t a n α$ and y = $\sqrt{a} s e c α$ . Find the value of $y^{2}$ – $x^{2}$

__

Discussion

4036.	let f: R-R, f(x)= x^3 + x -1 find the solution of f(x)= f^-1 (x)
Answer» let f: R-R, f(x)= x^3 + x -1 find the solution of f(x)= f^-1 (x)

Discussion

4037.	Which of the following fractions is greater than 811?
Answer» Which of the following fractions is greater than $\frac{8}{11}$ ?

Discussion

4038.	2.¯¯¯¯¯¯35 is (a) an integer (b) a rational number (c) an irrational number (d) none of these
Answer» $2. ¯ ¯¯¯¯ ¯ 35$ is (a) an integer (b) a rational number (c) an irrational number (d) none of these

4038.

2.¯¯¯¯¯¯35 is (a) an integer (b) a rational number (c) an irrational number (d) none of these

Answer»

$2. ¯ ¯¯¯¯ ¯ 35$ is

(a) an integer (b) a rational number

(c) an irrational number (d) none of these

Discussion

4039.	How many circles can be drawn passing through three collinear points?
Answer» How many circles can be drawn passing through three collinear points?

Discussion

4040.

Following balances were extracted from the books of Vijay Kumar on 31st March, 2018: Particulars ₹ Particulars ₹ Capital 2,45,000 Loan 78,800 Drawings 20,000 Sales 6,53,600 General Expenses 47,400 Purchases 4,70,000 Building 1,10,000 Motor Car 20,000 Machinery 93,400 Provision for Doubtful Debts 9,000 Stock on 1st April, 2017 1,62,000 Commission (Cr.) 13,200 Insurance 13,150 Car Expenses 18,000 Wages 72,000 Bills Payable 38,500 Debtors 62,800 Cash 800 Creditors 25,000 Bank Overdraft 33,000 Bad Debts 5,500 Charity 1,050 Prepare Trading and Profit and Loss Account for the year ended 31st March, 2018 and Balance Sheet as at that date after giving effect to the following adjustments:(a) Stock as on 31st March, 2018 was valued at ₹ 2,30,000.(b) Write off further ₹ 1,800 as Bad Debts and maintain the Provision for Doubtful Debts at 5%.(c) Depreciate Machinery at 10%.(d) Provide ₹ 7,000 as outstanding interest on loan.

Answer» Following balances were extracted from the books of Vijay Kumar on 31st March, 2018:

Particulars	₹	Particulars	₹
Capital	2,45,000	Loan	78,800
Drawings	20,000	Sales	6,53,600
General Expenses	47,400	Purchases	4,70,000
Building	1,10,000	Motor Car	20,000
Machinery	93,400	Provision for Doubtful Debts	9,000
Stock on 1st April, 2017	1,62,000	Commission (Cr.)	13,200
Insurance	13,150	Car Expenses	18,000
Wages	72,000	Bills Payable	38,500
Debtors	62,800	Cash	800
Creditors	25,000	Bank Overdraft	33,000
Bad Debts	5,500	Charity	1,050

Prepare Trading and Profit and Loss Account for the year ended 31st March, 2018 and Balance Sheet as at that date after giving effect to the following adjustments:

(a) Stock as on 31st March, 2018 was valued at ₹ 2,30,000.

(b) Write off further ₹ 1,800 as Bad Debts and maintain the Provision for Doubtful Debts at 5%.

(c) Depreciate Machinery at 10%.

(d) Provide ₹ 7,000 as outstanding interest on loan.

Discussion

4041.	If one zero of the polynomial 5z2+13z - p is reciprocal of the other, then find p.
Answer» If one zero of the polynomial 5z²+13z - p is reciprocal of the other, then find p.

Discussion

4042.	How to know the splitting numbers in splitting the middle term method ?? ( especially big no's )
Answer» How to know the splitting numbers in splitting the middle term method ?? ( especially big no's )

Discussion

4043.	If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then
Answer» If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

Discussion

4044.	An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms. [CBSE 2015]
Answer» An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms. [CBSE 2015]

Discussion

4045.	The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC. If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.
Answer» The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC. If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.

4045.

The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC. If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.

Answer»

The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.

If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.

Discussion

4046.	The sum of the first n terms of an AP is (3n2 + 6n). Find the nth term and the 15th term of this AP. [CBSE 2014]
Answer» The sum of the first n terms of an AP is (3n²+ 6n). Find the nth term and the 15th term of this AP. [CBSE 2014]

Discussion

4047.	If the line makes angle π6 and π3 with positive direction of x and y axes respectively, then it makes with z-axis is
Answer» If the line makes angle $\frac{π}{6}$ and $\frac{π}{3}$ with positive direction of x and y axes respectively, then it makes with z-axis is

Discussion

4048.	34.The complex numbers z1 ,z2,z3 are the vertices of a triangle .Then what us the complex number z which make triangle into parallelogarm?
Answer» 34.The complex numbers z1 ,z2,z3 are the vertices of a triangle .Then what us the complex number z which make triangle into parallelogarm?

Discussion

4049.	If z = xy In(xy), then
Answer» If z = xy In(xy), then

Discussion

4050.	What number should be added to 9x2 + 18 x to make it a perfect square?
Answer» What number should be added to ${9 x}^{2}$ + 18 $x$ to make it a perfect square?

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, PR = (a) 20 cm(b) 26 cm(c) 24 cm(d) 28 cm

For the curve sinx+siny=1 lying in the first quadrant, L=limx→0xαd2ydx2 where L exists and is non-zero. Then

The area of a square field is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?

Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.

3. 2 cards are selected randomly from 52 cards. The prob that first card is a club and second is not a queen is

Note Take π=227, unless stated otherwise.A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

If x=2√3+2√2, then find 1x:

Question 4 (v) State whether the following are true or false. Justify your answer. (v) cot A is not defined for A=0∘.

15.Total number of vertex angle in structure of white phosphorous

For the given concentric circles with radius 5 cm and 13 cm respectively. Find the length of the chord AB.

Find the L.C.M. of the following expressions by division method.x3 + 2x2 − 13x − 10 and x3 − x2 − 10x − 8

The following table gives the marks scored by 100 students in an entrance examination. Marks0.1010−2020−3030−4040−5050−6060−7070−80No. of students (Frequency)4101622201882 Represent this data in the form of a histogram

There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 11 chocolates. Who has the average number of chocolates?

A natural number, when increased by 12, equals 160 times its reciprocal find the number.

A thief , after committing a theft , runs at a speed of 50 m/min . After 2 mins , a policeman runs to catch him. He goes 60m in the first min and increases his speed by 5 m/min every succeeding minute. After how many minutes,the policeman will catch the thief?

A hemispherical tank, full of water, is emptied by a pipe at the rate of 257 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m? [CBSE 2012]

A right triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

A rectangle of length “a” and breadth “b” is rotated by 360∘ about its length. The volume of the resulting cylinder is _____.

A diagonal matrix will always be

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is______

Find n if the given value of x is the nth term of the given A.P.(i) 25, 50, 75, 100, ...; x = 1000(ii) −1, −3, −5, −7, ...; x = −151(iii) 512, 11, 1612, 22,...; x = 550(iv) 1,2111,3111,4111,..., x = 17111

In a musical chair game, person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half minute after starting?

Find the function corresponding to the graph given below, 1≤x≤3 ( The function which closely describes the graph )

Ram borrowed an amount of Rs. 15000 from a bank to buy a car at 10% simple interest. If he paid Rs. 9000 as interest while clearing the loan, determine the period of the loan.

What is the value of (sin 18°)/(cos 72°)?

In class 10 A , there are 24 boys and 25 girls. In class 10B , there are 20 boys and 20 girls. One student is selected from each class for an activity. What is the probability of both of them being girls ?

x+3/8=1

38. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number

The marks obtained by 110 students in an examination are given below: Marks: 30 – 35 35 – 40 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 Frequency: 14 16 28 23 18 8 3 Find the mean marks of the students.

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age. Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

if l= m sec theta + n tan theta and k= n sec theta + m tan theta

In the given figure, if PR is tangent to the circle at P and Q is the centre of the circle, then ∠POQ = (a) 110°(b) 100°(c) 120°(d) 90°

Show that:sin42∘sec48∘+cos42∘ cosec48∘=2

If x = √a tan α and y = √a sec α. Find the value of y2 – x2 __

let f: R-R, f(x)= x^3 + x -1 find the solution of f(x)= f^-1 (x)

Which of the following fractions is greater than 811?

2.¯¯¯¯¯¯35 is (a) an integer (b) a rational number (c) an irrational number (d) none of these

How many circles can be drawn passing through three collinear points?

If one zero of the polynomial 5z2+13z - p is reciprocal of the other, then find p.

How to know the splitting numbers in splitting the middle term method ?? ( especially big no's )

If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms. [CBSE 2015]

The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC. If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.

The sum of the first n terms of an AP is (3n2 + 6n). Find the nth term and the 15th term of this AP. [CBSE 2014]

If the line makes angle π6 and π3 with positive direction of x and y axes respectively, then it makes with z-axis is

34.The complex numbers z1 ,z2,z3 are the vertices of a triangle .Then what us the complex number z which make triangle into parallelogarm?

If z = xy In(xy), then

What number should be added to 9x2 + 18 x to make it a perfect square?