32581 + Interview Questions in Mathematics Page 240 InterviewSolution

11951.	Question 4The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Answer» Question 4 The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Discussion

11952.	The value of sin 0° is
Answer» The value of sin 0° is

Discussion

11953.	43. If the altitude of a right circular cone is cutto its base in such a way that thermed areplane parallelvolume of the cone and the frustum so foin the ratio 1: 26, then find the ratio of the heightof the cone and the frustum.
Answer» 43. If the altitude of a right circular cone is cutto its base in such a way that thermed areplane parallelvolume of the cone and the frustum so foin the ratio 1: 26, then find the ratio of the heightof the cone and the frustum.

Discussion

11954.	Insert one arithmetic mean between 3 and 13.
Answer» Insert one arithmetic mean between 3 and 13.

Discussion

11955.	A conical tomb is made up of bricks, with each brick of lateral surface area 5 square meter.The height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate no. of bricks made used to construct the tomb are___(Take π=227)
Answer» A conical tomb is made up of bricks, with each brick of lateral surface area 5 square meter.The height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate no. of bricks made used to construct the tomb are___(Take $π = \frac{22}{7}$ )

Discussion

11956.	Ramkali would need Rs.1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs.50 in the first month of this year and increased her monthly saving by 20. After a year, how much money will she save? Will she be able to fulfill her dream of sending her daughter to school?
Answer» Ramkali would need Rs.1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs.50 in the first month of this year and increased her monthly saving by 20. After a year, how much money will she save? Will she be able to fulfill her dream of sending her daughter to school?

Discussion

11957.	Find the distance between the points (3, -6), (-2, 2).
Answer» Find the distance between the points (3, -6), (-2, 2).

Discussion

11958.	A card si drawn at random from a well- shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spades or an ace (ii) a red king (iii) either a king or a queen (iv) nether a king nor a queen.
Answer» A card si drawn at random from a well- shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spades or an ace (ii) a red king (iii) either a king or a queen (iv) nether a king nor a queen.

Discussion

11959.	Find the values of k for which the given quadratic equation has real and distinct roots:(i) kx2+6x+1=0(ii) x2-kx+9=0(iii) 9x2+3kx+4=0(iv) 5x2-kx+1=0
Answer» Find the values of k for which the given quadratic equation has real and distinct roots: (i) $k x^{2} + 6 x + 1 = 0$ (ii) $x^{2} - k x + 9 = 0$ (iii) $9 x^{2} + 3 k x + 4 = 0$ (iv) $5 x^{2} - k x + 1 = 0$

Discussion

11960.	5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from the outside. If a glass is chosen at random, what is the probability that the chosen glass is good?
Answer» 5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from the outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

Discussion

11961.	a,b,c are positive integers such that a2 + 2b2 - 2bc = 100 and 2ab - c2 = 100. Then is
Answer» a,b,c are positive integers such that a² + 2b² - 2bc = 100 and 2ab - c² = 100. Then is

Discussion

11962.

D.Chadha commenced business on 1st January, 2017. His transactions for the month are given below. Journalise them. 2018 ₹ Jan. 1 Commenced business with cash 25,000 Jan. 2 Opened Bank Account with cheque from his Savings Account 2,25,000 Jan. 3 Bought goods from Ramesh & Co., Delhi, paid CGST and SGST 6% each 54,000 Jan. 3 Sold goods to Rajesh of ₹ 60,000, charged CGST and SGST 6% each Jan. 7 Bought goods ₹ 65,000 from Rahul, Chennal, paid IGST 12% Jan. 8 Paid wages in cash 8,000 Jan. 8 Sold goods to Mahesh, Kochi of ₹ 60,000; charged IGST 12% Jan. 10 Received cheque from Rajesh(Discount allowed ₹ 1,200) 66,000 Jan. 10 Paid into bank 66,000 Jan. 11 Paid to Ramesh & Co. (discount received ₹ 2,700) 51,300 Jan. 12 Paid rent ₹ 15, 000 per month for three months up to March, paid CGST and SGST 6% each Jan. 15 Paid wages in cash 8,000 Jan. 15 Paid office expenses in cash 700 Jan. 21 Sold to Mahesh, Delhi goods of ₹ 25,000, charged CGST and SGST 6% each Jan. 22 Paid office expenses in cash 500 Jan. 22 Paid Rahul by cheque (discount ₹ 3,200) 61,300 Jan. 25 Received cheque from Mahesh Kochi (discount ₹ 1,500) 65,700 Jan. 27 Mahesh, Delhi returned goods (not up to sample) 2,000 Jan. 29 Paid wages in cash 10,000 Jan. 31 Paid office expenses in cash 400 Jan. 31 Paid salaries for the month 20,000

Answer» D.Chadha commenced business on 1st January, 2017. His transactions for the month are given below. Journalise them.

2018		₹
Jan. 1	Commenced business with cash	25,000
Jan. 2	Opened Bank Account with cheque from his Savings Account	2,25,000
Jan. 3	Bought goods from Ramesh & Co., Delhi, paid CGST and SGST 6% each	54,000
Jan. 3	Sold goods to Rajesh of ₹ 60,000, charged CGST and SGST 6% each
Jan. 7	Bought goods ₹ 65,000 from Rahul, Chennal, paid IGST 12%
Jan. 8	Paid wages in cash	8,000
Jan. 8	Sold goods to Mahesh, Kochi of ₹ 60,000; charged IGST 12%
Jan. 10	Received cheque from Rajesh(Discount allowed ₹ 1,200)	66,000
Jan. 10	Paid into bank	66,000
Jan. 11	Paid to Ramesh & Co. (discount received ₹ 2,700)	51,300
Jan. 12	Paid rent ₹ 15, 000 per month for three months up to March, paid CGST and SGST 6% each
Jan. 15	Paid wages in cash	8,000
Jan. 15	Paid office expenses in cash	700
Jan. 21	Sold to Mahesh, Delhi goods of ₹ 25,000, charged CGST and SGST 6% each
Jan. 22	Paid office expenses in cash	500
Jan. 22	Paid Rahul by cheque (discount ₹ 3,200)	61,300
Jan. 25	Received cheque from Mahesh Kochi (discount ₹ 1,500)	65,700
Jan. 27	Mahesh, Delhi returned goods (not up to sample)	2,000
Jan. 29	Paid wages in cash	10,000
Jan. 31	Paid office expenses in cash	400
Jan. 31	Paid salaries for the month	20,000

Discussion

11963.	64. The nos 2,3,4,4,3x-1,3x+1,7,7,8 are in ascending order if median is 5 finf x
Answer» 64. The nos 2,3,4,4,3x-1,3x+1,7,7,8 are in ascending order if median is 5 finf x

Discussion

11964.	It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Answer» It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

Discussion

11965.	WruWr the value of cos1° cos2° cos 3° ...cos 179° cos 180°
Answer» WruWr the value of cos1° cos2° cos 3° ...cos 179° cos 180°

Discussion

11966.	125.cosA-sinA+1 upon cosA-sinA=cosecA+cotA
Answer» 125.cosA-sinA+1 upon cosA-sinA=cosecA+cotA

Discussion

11967.	If 10x = 64, find the value of 10x2+1.
Answer» If 10^x= 64, find the value of $10^{(\frac{x}{2} + 1)}$ .

Discussion

11968.	Find the value fo a, if the divisiion of ax3+9x2+4x−10byx+3 leaves a remainder 5.
Answer» Find the value fo a, if the divisiion of $a x^{3} + 9 x^{2} + 4 x - 10 b y x + 3$ leaves a remainder 5.

Discussion

11969.	What sequence will form after second consecutive difference of the series 1, 2, 7, 20, 49, 110 . . . . . .
Answer» What sequence will form after second consecutive difference of the series 1, 2, 7, 20, 49, 110 . . . . . .

Discussion

11970.	Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.
Answer» Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

Discussion

11971.	Question 6ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC is 30∘, find ∠BCD . Further, if AB = BC, find ∠ECD.
Answer» Question 6 ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 70^{\circ}, ∠ B A C is 30^{\circ}$ , find $∠ B C D$ . Further, if AB = BC, find $∠ E C D$ .

Discussion

11972.	If 2:9::x:18, then find the value of x.
Answer» If $2 : 9 :: x : 18,$ then find the value of $x .$

Discussion

11973.	Construct two tangents to a circle of radius 6 cm from a point 10 cm away from its centre.
Answer» Construct two tangents to a circle of radius 6 cm from a point 10 cm away from its centre.

Discussion

11974.	From the information given below, draft receipts and Payments Account of Friends club, Delhi, for the year ended March 31, 2013: Cash on April 1, 2012 Rs 3,600, Subscriptions Rs 37,600, donations Rs 8000, Entrance Fees Rs 4,300, Rent Realized from club Hall Rs 5,250, Electric charges Rs 3,440, Taxes Rs 500, Salaries and wages Rs 21,500, Honorarium to secretary Rs 2,500, Interest Received on Investments Rs 2,950, Printing and Stationery Rs 350, Pretty cash Payments Rs 100, Insurance Premium Paid Rs 310.
Answer» From the information given below, draft receipts and Payments Account of Friends club, Delhi, for the year ended March 31, 2013: Cash on April 1, 2012 Rs 3,600, Subscriptions Rs 37,600, donations Rs 8000, Entrance Fees Rs 4,300, Rent Realized from club Hall Rs 5,250, Electric charges Rs 3,440, Taxes Rs 500, Salaries and wages Rs 21,500, Honorarium to secretary Rs 2,500, Interest Received on Investments Rs 2,950, Printing and Stationery Rs 350, Pretty cash Payments Rs 100, Insurance Premium Paid Rs 310.

Discussion

11975.	In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?
Answer» In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ Statement 1 : This is an inconsistent pair of linear equations. Statement 2 : There exists infinitely many solutions. Statement 3 : The lines representing these linese are parallel. Which of the above statements is/are true?

11975.

In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?

Answer»

In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?

Discussion

11976.	If √a + √b + √c = 0, then the value of (a + b - c) whole square = ?
Answer» If √a + √b + √c = 0, then the value of (a + b - c) whole square = ?

Discussion

11977.	If the normals to the parabola y^2 =4ax at (at_1^2,2at_1) and (at_2^2,2at_2) are mutually perpendicular ,then the †an gents to the curve at these points will always intersect on the line
Answer» If the normals to the parabola y^2 =4ax at (at_1^2,2at_1) and (at_2^2,2at_2) are mutually perpendicular ,then the †an gents to the curve at these points will always intersect on the line

Discussion

11978.	How can we know that in a particular question we have to find HCF or LCM?
Answer» How can we know that in a particular question we have to find HCF or LCM?

Discussion

11979.	Some one rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of these coins are in the ratio 3 : 4 : 5. The number of coins of each denomination respectively are:
Answer» Some one rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of these coins are in the ratio 3 : 4 : 5. The number of coins of each denomination respectively are:

Discussion

11980.	Check whether the following are quadratic equations:
Answer» Check whether the following are quadratic equations:

11980.

Check whether the following are quadratic equations:

Answer»

Check whether the following are quadratic equations:

Discussion

11981.	A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.[Use π = 3.14 and]
Answer» A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. [Use π = 3.14 and]

11981.

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.[Use π = 3.14 and]

Answer»

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.

[Use π = 3.14 and]

Discussion

11982.	Find the mode of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598 ___
Answer» Find the mode of the following data. $\begin{matrix} Class interval & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 Frequency & 7 & 11 & 15 & 9 & 8 \end{matrix}$ ___

11982.

Find the mode of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598 ___

Answer»

Find the mode of the following data.

$\begin{matrix} Class interval & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 Frequency & 7 & 11 & 15 & 9 & 8 \end{matrix}$

___

Discussion

11983.	If a,b,c,d and p are distinct real number such that (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd )p + ( b^2 + c^2 + d^2 )
Answer» If a,b,c,d and p are distinct real number such that (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd )p + ( b^2 + c^2 + d^2 ) <= 0 Then a, b, c ,d are in a . Ap b . GP c . HP

Discussion

11984.	A function f is defined by f(x)=2x−5. Write down the values of(i) f(0) (ii) f(7) (iii) f(−3)
Answer» A function $f$ is defined by $f (x) = 2 x - 5$ . Write down the values of $(i) f (0) (i i) f (7) (i i i) f (- 3)$

Discussion

11985.	13. Consider a polynomial f(x) = ax + bx + c such that f(0) = 4. When f(x) is divided by x+1, then the remainder is 4. Also, when it is divided by x+2, then the remainder is 6. Then (i) a=3,b=-7 (ii) a=b=1,c=4 (iii) a=-3, b=7 (iv) a=3, b=-7, c=2
Answer» 13. Consider a polynomial f(x) = ax + bx + c such that f(0) = 4. When f(x) is divided by x+1, then the remainder is 4. Also, when it is divided by x+2, then the remainder is 6. Then (i) a=3,b=-7 (ii) a=b=1,c=4 (iii) a=-3, b=7 (iv) a=3, b=-7, c=2

Discussion

11986.	Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
Answer» Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Discussion

11987.	If HCF (1008, 20) = HCF (20, a) = HCF(a,b) where 1008=20×q+aand 20=a×m+b.Here, q, a, m and b being positive integers satisfying Euclid’s division lemma. What could be the values of a and b?
Answer» $If HCF (1008, 20) = HCF (20, a) = HCF(a,b) where 1008 = 20 \times q + a and 20 = a \times m + b .$ Here, q, a, m and b being positive integers satisfying Euclid’s division lemma. What could be the values of a and b?

Discussion

11988.	ABCD is a field in the shape of a trapezium. AB\|\|DC and ∠ABC=90∘,∠DAB=60∘. Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the i). Total area of the four Sectors. ii). Area of remaining portion given that AB=75 m and CD =50m.
Answer» ABCD is a field in the shape of a trapezium. AB\|\|DC and $∠ A B C = 90^{\circ}, ∠ D A B = 60^{\circ}$ . Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the i). Total area of the four Sectors. ii). Area of remaining portion given that AB=75 m and CD =50m.

11988.

ABCD is a field in the shape of a trapezium. AB||DC and ∠ABC=90∘,∠DAB=60∘. Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the i). Total area of the four Sectors. ii). Area of remaining portion given that AB=75 m and CD =50m.

Answer»

ABCD is a field in the shape of a trapezium. AB||DC and $∠ A B C = 90^{\circ}, ∠ D A B = 60^{\circ}$ . Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the

i). Total area of the four Sectors.

ii). Area of remaining portion given that AB=75 m and CD =50m.

Discussion

11989.	Which of the options given below is the square of the binomial 8 - 1x ?(i) 64 - 1x2 (ii) 64 +1x2 (iii) 64 - 16x + 1x2 (iv) 64 +16x + 1x2
Answer» Which of the options given below is the square of the binomial $(8 - \frac{1}{x})$ ? (i) $64 - \frac{1}{x^{2}}$ (ii) $64 + \frac{1}{x^{2}}$ (iii) $64 - \frac{16}{x} + \frac{1}{x^{2}}$ (iv) $64 + \frac{16}{x} + \frac{1}{x^{2}}$

Discussion

11990.	If the difference between the circumference and radius of a circle is 37 cm, then its area is(a) 154 cm2(b) 160 cm2(c) 200 cm2(d) 150 cm2
Answer» If the difference between the circumference and radius of a circle is 37 cm, then its area is (a) 154 cm² (b) 160 cm² (c) 200 cm² (d) 150 cm²

Discussion

11991.	Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.
Answer» Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

Discussion

11992.	The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.
Answer» The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.

Discussion

11993.	Select the option which is equivalent to the following expression: 0.00024 + 120×10−60.0000000013
Answer» Select the option which is equivalent to the following expression: $\frac{0.00024 + 120 \times 10^{- 6}}{0.0000000013}$

Discussion

11994.	Evaluate each of the followingsin 30°sin 45°+tan 45°sec 60°-sin 60°cot 45°-cos 30°sin 90°
Answer» Evaluate each of the following $\frac{\sin 30 °}{\sin 45 °} + \frac{\tan 45 °}{\sec 60 °} - \frac{\sin 60 °}{\cot 45 °} - \frac{\cos 30 °}{\sin 90 °}$

Discussion

11995.	28. Six boy and six girls are sit in a row at random . Find the the probability that boys and girls sit alternately.
Answer» 28. Six boy and six girls are sit in a row at random . Find the the probability that boys and girls sit alternately.

Discussion

11996.	If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find the quadratic polynomial whose zeros are 2αβ and 2βα.
Answer» If α and β are the zeros of the quadratic polynomial f(x) = x² − 1, find the quadratic polynomial whose zeros are $\frac{2 α}{β} and \frac{2 β}{α}$ .

Discussion

11997.	The LCM of the two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find their HCF.
Answer» The LCM of the two numbers is $9$ times their HCF. The sum of LCM and HCF is $500.$ Find their HCF.

Discussion

11998.	Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………
Answer» Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………

11998.

Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………

Answer»

Which of the following sequences form an AP?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11…….

(iii) -1, -1.25, -1.5, -1.75……

(iv) 1, -1, -3, -5…………

Discussion

11999.	If the diagonal matrix is commutative with every matrix of the same order then it is necessarily to be??
Answer» If the diagonal matrix is commutative with every matrix of the same order then it is necessarily to be??

Discussion

12000.	Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is
Answer» Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is

Discussion

Explore topic-wise InterviewSolutions in .

Question 4The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

The value of sin 0° is

43. If the altitude of a right circular cone is cutto its base in such a way that thermed areplane parallelvolume of the cone and the frustum so foin the ratio 1: 26, then find the ratio of the heightof the cone and the frustum.

Insert one arithmetic mean between 3 and 13.

A conical tomb is made up of bricks, with each brick of lateral surface area 5 square meter.The height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate no. of bricks made used to construct the tomb are___(Take π=227)

Find the distance between the points (3, -6), (-2, 2).

A card si drawn at random from a well- shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spades or an ace (ii) a red king (iii) either a king or a queen (iv) nether a king nor a queen.

Find the values of k for which the given quadratic equation has real and distinct roots:(i) kx2+6x+1=0(ii) x2-kx+9=0(iii) 9x2+3kx+4=0(iv) 5x2-kx+1=0

5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from the outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

a,b,c are positive integers such that a2 + 2b2 - 2bc = 100 and 2ab - c2 = 100. Then is

64. The nos 2,3,4,4,3x-1,3x+1,7,7,8 are in ascending order if median is 5 finf x

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

WruWr the value of cos1° cos2° cos 3° ...cos 179° cos 180°

125.cosA-sinA+1 upon cosA-sinA=cosecA+cotA

If 10x = 64, find the value of 10x2+1.

Find the value fo a, if the divisiion of ax3+9x2+4x−10byx+3 leaves a remainder 5.

What sequence will form after second consecutive difference of the series 1, 2, 7, 20, 49, 110 . . . . . .

Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

Question 6ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC is 30∘, find ∠BCD . Further, if AB = BC, find ∠ECD.

If 2:9::x:18, then find the value of x.

Construct two tangents to a circle of radius 6 cm from a point 10 cm away from its centre.

In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,a1a2=b1b2≠c1c2Statement 1 : This is an inconsistent pair of linear equations.Statement 2 : There exists infinitely many solutions.Statement 3 : The lines representing these linese are parallel.Which of the above statements is/are true?

If √a + √b + √c = 0, then the value of (a + b - c) whole square = ?

If the normals to the parabola y^2 =4ax at (at_1^2,2at_1) and (at_2^2,2at_2) are mutually perpendicular ,then the †an gents to the curve at these points will always intersect on the line

How can we know that in a particular question we have to find HCF or LCM?

Some one rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of these coins are in the ratio 3 : 4 : 5. The number of coins of each denomination respectively are:

Check whether the following are quadratic equations:

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.[Use π = 3.14 and]

Find the mode of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598 ___

If a,b,c,d and p are distinct real number such that (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd )p + ( b^2 + c^2 + d^2 )

A function f is defined by f(x)=2x−5. Write down the values of(i) f(0) (ii) f(7) (iii) f(−3)

13. Consider a polynomial f(x) = ax + bx + c such that f(0) = 4. When f(x) is divided by x+1, then the remainder is 4. Also, when it is divided by x+2, then the remainder is 6. Then (i) a=3,b=-7 (ii) a=b=1,c=4 (iii) a=-3, b=7 (iv) a=3, b=-7, c=2

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

If HCF (1008, 20) = HCF (20, a) = HCF(a,b) where 1008=20×q+aand 20=a×m+b.Here, q, a, m and b being positive integers satisfying Euclid’s division lemma. What could be the values of a and b?

ABCD is a field in the shape of a trapezium. AB||DC and ∠ABC=90∘,∠DAB=60∘. Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the i). Total area of the four Sectors. ii). Area of remaining portion given that AB=75 m and CD =50m.

Which of the options given below is the square of the binomial 8 - 1x ?(i) 64 - 1x2 (ii) 64 +1x2 (iii) 64 - 16x + 1x2 (iv) 64 +16x + 1x2

If the difference between the circumference and radius of a circle is 37 cm, then its area is(a) 154 cm2(b) 160 cm2(c) 200 cm2(d) 150 cm2

Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.

Select the option which is equivalent to the following expression: 0.00024 + 120×10−60.0000000013

Evaluate each of the followingsin 30°sin 45°+tan 45°sec 60°-sin 60°cot 45°-cos 30°sin 90°

28. Six boy and six girls are sit in a row at random . Find the the probability that boys and girls sit alternately.

If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find the quadratic polynomial whose zeros are 2αβ and 2βα.

The LCM of the two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find their HCF.

Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………

If the diagonal matrix is commutative with every matrix of the same order then it is necessarily to be??

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is