32581 + Interview Questions in Mathematics Page 111 InterviewSolution

5501.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Monthly consumption: (in units) 65−85 85−105 105−125 125−145 145−165 165−185 185−205 No. of consumers: 4 5 13 20 14 8 4

Answer» The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption: (in units)	65−85	85−105	105−125	125−145	145−165	165−185	185−205
No. of consumers:	4	5	13	20	14	8	4

Discussion

5502.	(1+x+2x2)20 = a0+a1x+a2x2...................a40x40, If a0+a1+a2+a3..................a40=2a a0−a1+a2−a3......................a40=2b. Find the value of a + b ___
Answer» $(1 + x + 2 x^{2})^{20}$ = $a_{0} + a_{1} x + a_{2} x^{2}$ ................... $a_{40} x^{40}$ , If $a_{0} + a_{1} + a_{2} + a_{3} . . . . . . . . . . . . . . . . . . a_{40} = 2^{a}$ $a_{0} - a_{1} + a_{2} - a_{3} . . . . . . . . . . . . . . . . . . . . . . a_{40} = 2^{b}$ . Find the value of a + b ___

5502.

(1+x+2x2)20 = a0+a1x+a2x2...................a40x40, If a0+a1+a2+a3..................a40=2a a0−a1+a2−a3......................a40=2b. Find the value of a + b ___

Answer»

$(1 + x + 2 x^{2})^{20}$ = $a_{0} + a_{1} x + a_{2} x^{2}$ ................... $a_{40} x^{40}$ , If $a_{0} + a_{1} + a_{2} + a_{3} . . . . . . . . . . . . . . . . . . a_{40} = 2^{a}$

$a_{0} - a_{1} + a_{2} - a_{3} . . . . . . . . . . . . . . . . . . . . . . a_{40} = 2^{b}$ . Find the value of a + b

___

Discussion

5503.	Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.
Answer» Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

Discussion

5504.	If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =(a) 8(b) −8(c) 16(d) −16
Answer» If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q = (a) 8 (b) −8 (c) 16 (d) −16

Discussion

5505.	In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is choosen at random. What is the probability that the chosen lady dislikes coffee?
Answer» In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is choosen at random. What is the probability that the chosen lady dislikes coffee?

Discussion

5506.	If α and β are the zeroes of a polynomial 2x2 + 7x + 5, write the value of α + β + αβ. [CBSE 2010]
Answer» If α and β are the zeroes of a polynomial 2x² + 7x + 5, write the value of α + β + αβ. [CBSE 2010]

Discussion

5507.	Question 4Write ‘True’ or ‘False’ and justify your answer in each of the following:√(1−cos2θ)sec2θ=tanθ
Answer» Question 4 Write ‘True’ or ‘False’ and justify your answer in each of the following: $\sqrt{(1 - c o s^{2} θ) s e c^{2} θ} = t a n θ$

Discussion

5508.	Find the equation of a line which divides the line segment joining the points (1,1) and (2,3) in the ratio 2:3 perpendicularly.
Answer» Find the equation of a line which divides the line segment joining the points (1,1) and (2,3) in the ratio 2:3 perpendicularly.

Discussion

5509.

Fill in the blanks given in the contract note of sale-purchase of shares. (B - buy S - sell) No. of shares MV of shares Total value Brokerage 0.2% 9% CGST on brokerage 9% SGST on brokerage Total value of shares 100 B Rs 45 75 S Rs 200

Answer» Fill in the blanks given in the contract note of sale-purchase of shares.

(B - buy S - sell)

No. of shares	MV of shares	Total value	Brokerage 0.2%	9% CGST on brokerage	9% SGST on brokerage	Total value of shares
100 B	Rs 45
75 S	Rs 200

Discussion

5510.	In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.
Answer» In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

5510.

In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

Answer»

In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

Discussion

5511.	A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between the two vessels is filled with cork dust for heat insultation purposes. How many cubic centimeters of cork dust will be required?
Answer» A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between the two vessels is filled with cork dust for heat insultation purposes. How many cubic centimeters of cork dust will be required?

Discussion

5512.	Journalise the following transactions in the Journal of Navin Gupta & Sons.:-1. Out of Insurance premium paid this year, ₹ 15,000 is related to next year.2. Credit purchases from Ram & Co. for ₹ 50,000. Cash discount will be received at 5% on payment of bill within 10 days.3. Cash paid to Ram & Co. and discount availed of.4. Paid Income Tax ₹ 20,000 by cheque.5. Goods costing ₹ 2,00,000 sold for cash at a profit of 10%.6. Purchased iron safe for ₹ 2,00,000 filing cabinet for ₹ 50,000 and Computer for ₹ 1,00,000.
Answer» Journalise the following transactions in the Journal of Navin Gupta & Sons.:- 1. Out of Insurance premium paid this year, ₹ 15,000 is related to next year. 2. Credit purchases from Ram & Co. for ₹ 50,000. Cash discount will be received at 5% on payment of bill within 10 days. 3. Cash paid to Ram & Co. and discount availed of. 4. Paid Income Tax ₹ 20,000 by cheque. 5. Goods costing ₹ 2,00,000 sold for cash at a profit of 10%. 6. Purchased iron safe for ₹ 2,00,000 filing cabinet for ₹ 50,000 and Computer for ₹ 1,00,000.

Discussion

5513.	Question 4 (i)ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that(i)ΔABE≅ΔACF
Answer» Question 4 (i) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i) $Δ A B E ≅ Δ A C F$

Discussion

5514.	if A, B and C are respectively the mid points of side PQ,QR and PR of a triangle and PS is the perpendicular from P on QR , prove that A,C,B and S are concyclic
Answer» if A, B and C are respectively the mid points of side PQ,QR and PR of a triangle and PS is the perpendicular from P on QR , prove that A,C,B and S are concyclic

Discussion

5515.	Determine the ratio in which the graph of the equation 3x+y=9 divides the line segment joining the points A(2,7) and B(1,3).
Answer» Determine the ratio in which the graph of the equation $3 x + y = 9$ divides the line segment joining the points $A (2, 7)$ and $B (1, 3)$ .

Discussion

5516.	Question 2 (ii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Answer» Question 2 (ii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Discussion

5517.	Factorise the following numbers into primes.(i) 32(ii) 57(iii) 23(iv) 150(v) 216(vi) 208(vii) 765(viii) 342(ix) 377(x) 559
Answer» Factorise the following numbers into primes. (i) 32 (ii) 57 (iii) 23 (iv) 150 (v) 216 (vi) 208 (vii) 765 (viii) 342 (ix) 377 (x) 559

Discussion

5518.	The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the AP
Answer» The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the AP

Discussion

5519.	Question 16The sum of first 16 terms of the AP 10, 6, 2, … isA) -320B) 320C) -352D) -400
Answer» Question 16 The sum of first 16 terms of the AP 10, 6, 2, … is A) -320 B) 320 C) -352 D) -400

Discussion

5520.	The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
Answer» The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

Discussion

5521.	If for an A.P. Sn=n2+7n what is its third term?
Answer» If for an A.P. S_n=n²+7n what is its third term?

Discussion

5522.	The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is [CBSE 2014](a) 415(b) 215(c) 15(d) 13
Answer» The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is [CBSE 2014] (a) $\frac{4}{15}$ (b) $\frac{2}{15}$ (c) $\frac{1}{5}$ (d) $\frac{1}{3}$

Discussion

5523.	The lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm. Find (i) the radius of its base and (ii) its volume. (Take π = 3.14.)
Answer» The lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm. Find (i) the radius of its base and (ii) its volume. (Take π = 3.14.)

Discussion

5524.	The common difference of the A.P. 12b,1-6b2b,1-12b2b, ... is(a) 2b(b) −2b(c) 3(d) −3
Answer» The common difference of the A.P. $\frac{1}{2 b}, \frac{1 - 6 b}{2 b}, \frac{1 - 12 b}{2 b}, . . .$ is (a) 2b (b) −2b (c) 3 (d) −3

Discussion

5525.	Find f and g if the mean for the data is 54 Class0−2020−4040−6060−8080−100TotalFrequency5fg13950
Answer» Find f and g if the mean for the data is 54 $\begin{matrix} C l a s s & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & T o t a l F r e q u e n c y & 5 & f & g & 13 & 9 & 50 \end{matrix}$

5525.

Find f and g if the mean for the data is 54 Class0−2020−4040−6060−8080−100TotalFrequency5fg13950

Answer»

Find f and g if the mean for the data is 54

$\begin{matrix} C l a s s & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & T o t a l F r e q u e n c y & 5 & f & g & 13 & 9 & 50 \end{matrix}$

Discussion

5526.	An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 of iron has 8 gram mass approximately.(Use : π = 355/115)
Answer» An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm³ of iron has 8 gram mass approximately. (Use : π = 355/115)

Discussion

5527.	In the given figure, ΔOAB∼ΔOCD. If AB = 8 cm, BO = 6.4 cm, OC = 3.5 cm and CD = 5 cm, find (i) OA (ii) DO.
Answer» In the given figure, $Δ O A B \sim Δ O C D$ . If AB = 8 cm, BO = 6.4 cm, OC = 3.5 cm and CD = 5 cm, find (i) OA (ii) DO.

5527.

In the given figure, ΔOAB∼ΔOCD. If AB = 8 cm, BO = 6.4 cm, OC = 3.5 cm and CD = 5 cm, find (i) OA (ii) DO.

Answer»

In the given figure, $Δ O A B \sim Δ O C D$ . If AB = 8 cm, BO = 6.4 cm, OC = 3.5 cm and CD = 5 cm, find (i) OA (ii) DO.

Discussion

5528.	The area of the bounded by the ellipse x225+y216=1 is ______________________.
Answer» The area of the bounded by the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1 is______________________.$

Discussion

5529.	Given the figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.
Answer» Given the figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.

Discussion

5530.	In what ratio does the point 2411, y divide the line segment joining the points P(2, –2) and Q(3, 7)? Also, find the value of y. [CBSE 2017]
Answer» In what ratio does the point $(\frac{24}{11}, y)$ divide the line segment joining the points P(2, –2) and Q(3, 7)? Also, find the value of y. [CBSE 2017]

Discussion

5531.	A shopkeeper purchased an item of Rs 100 at 8% VAT and sells it at Rs 120 to the customer and customer also pays 8% VAT to the shopkeeper. How much amount did the shopkeeper deposit to the Government as VAT ?
Answer» A shopkeeper purchased an item of Rs 100 at 8% VAT and sells it at Rs 120 to the customer and customer also pays 8% VAT to the shopkeeper. How much amount did the shopkeeper deposit to the Government as VAT ?

Discussion

5532.	35.How to factorise a polynomial?
Answer» 35.How to factorise a polynomial?

Discussion

5533.	Two ships A and B, lies 33 m apart on the sea surface. There is submarine 'C' on the sea bed. The angle of depression of C from A is 60o and the distance AC is 40 m. Calculate the distance BC.
Answer» Two ships A and B, lies 33 m apart on the sea surface. There is submarine 'C' on the sea bed. The angle of depression of C from A is 60^o and the distance AC is 40 m. Calculate the distance BC.

5533.

Two ships A and B, lies 33 m apart on the sea surface. There is submarine 'C' on the sea bed. The angle of depression of C from A is 60o and the distance AC is 40 m. Calculate the distance BC.

Answer»

Two ships A and B, lies 33 m apart on the sea surface. There is submarine 'C' on the sea bed. The angle of depression of C from A is 60^o and the distance AC is 40 m. Calculate the distance BC.

Discussion

5534.	A sphere and a cube are of the same height. The ratio of their volumes is(a) 3 : 4(b) 21 : 11(c) 4 : 3(d) 11 : 21
Answer» A sphere and a cube are of the same height. The ratio of their volumes is (a) 3 : 4 (b) 21 : 11 (c) 4 : 3 (d) 11 : 21

Discussion

5535.	In figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is(a) 7.5(b) 15(c) 10(d) 9
Answer» In figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is (a) 7.5 (b) 15 (c) 10 (d) 9

Discussion

5536.	Find the values of a and b for which the following system of linear equations has an infinite number of solutions:2x+3y=72ax+a+by=28 [CBSE 2001]
Answer» Find the values of a and b for which the following system of linear equations has an infinite number of solutions: $2 x + 3 y = 7 2 a x + (a + b) y = 28$ [CBSE 2001]

Discussion

5537.	Question 4Find the mode of 14,25, 14, 28, 18,17, 18,14, 23, 22,14,18.
Answer» Question 4 Find the mode of 14,25, 14, 28, 18,17, 18,14, 23, 22,14,18.

Discussion

5538.	A 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs 40 per m2.
Answer» A 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs 40 per m².

Discussion

5539.	Question 6A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
Answer» Question 6 A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Discussion

5540.	Solve for x, 1÷(x-1)(x-2)+1÷(x-2)(x-3)+1÷(x-3)(x-4)=1÷6
Answer» Solve for x, 1÷(x-1)(x-2)+1÷(x-2)(x-3)+1÷(x-3)(x-4)=1÷6

Discussion

5541.	If for x,y∈R, x>0, y=log10x+log10x1/3+log10x1/9+…upto ∞ terms and 2+4+6+…+2y3+6+9+…+3y=4log10x, then the ordered pair (x,y) is equal to:
Answer» If for $x, y \in R, x > 0, y = {log}_{10} x + {log}_{10} x^{1 / 3} + {log}_{10} x^{1 / 9} + \dots upto \infty$ terms and $\frac{2 + 4 + 6 + \dots + 2 y}{3 + 6 + 9 + \dots + 3 y} = \frac{4}{{log}_{10} x}$ , then the ordered pair $(x, y)$ is equal to:

Discussion

5542.	What will be the defrenciation of A cost with respect to t
Answer» What will be the defrenciation of A cost with respect to t

Discussion

5543.	In the given figure, O is the centre of the circle. Tap on the angle whose value will be 2x∘.
Answer» In the given figure, O is the centre of the circle. Tap on the angle whose value will be $2 x^{\circ} .$

Discussion

5544.	If x2+ 4xm + 3 = 0, represent a quadratic equation then what is the minimum andmaximum value of m?
Answer» If x2 + 4xm + 3 = 0, represent a quadratic equation then what is the minimum and maximum value of m?

Discussion

5545.	Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speeds of the cars.
Answer» Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speeds of the cars.

Discussion

5546.	The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm, its volume is
Answer» The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm, its volume is

Discussion

5547.	How much is the length and width of each classroom?Scale : 1 cm = 5 m
Answer» How much is the length and width of each classroom? Scale : 1 cm = 5 m

Discussion

5548.	The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If third vertex is (72,y), find y.
Answer» The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If third vertex is $(\frac{7}{2}, y)$ , find y.

Discussion

5549.	In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find the value of tan P - cot R.
Answer» In $△$ PQR, PQ = 12 cm and PR = 13 cm. $∠ Q = 90^{\circ}$ . Find the value of tan P - cot R.

Discussion

5550.	There are 25 tickets numbered as 1, 2, 3, 4,..., 25 respectively. One ticket is drawn at random. What is the probability that the number on the ticket is a multiple of 3 or 5? (a) 25 (b) 1125 (c) 1225 (d) 1325
Answer» There are 25 tickets numbered as 1, 2, 3, 4,..., 25 respectively. One ticket is drawn at random. What is the probability that the number on the ticket is a multiple of 3 or 5? (a) $\frac{2}{5}$ (b) $\frac{11}{25}$ (c) $\frac{12}{25}$ (d) $\frac{13}{25}$

Discussion

Explore topic-wise InterviewSolutions in .

(1+x+2x2)20 = a0+a1x+a2x2...................a40x40, If a0+a1+a2+a3..................a40=2a a0−a1+a2−a3......................a40=2b. Find the value of a + b ___

Two concentric circles of radii a and b (a &gt; b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =(a) 8(b) −8(c) 16(d) −16

In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is choosen at random. What is the probability that the chosen lady dislikes coffee?

If α and β are the zeroes of a polynomial 2x2 + 7x + 5, write the value of α + β + αβ. [CBSE 2010]

Question 4Write ‘True’ or ‘False’ and justify your answer in each of the following:​​​​​​​√(1−cos2θ)sec2θ=tanθ

Find the equation of a line which divides the line segment joining the points (1,1) and (2,3) in the ratio 2:3 perpendicularly.

Fill in the blanks given in the contract note of sale-purchase of shares. (B - buy S - sell) No. of shares MV of shares Total value Brokerage 0.2% 9% CGST on brokerage 9% SGST on brokerage Total value of shares 100 B Rs 45 75 S Rs 200

In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between the two vessels is filled with cork dust for heat insultation purposes. How many cubic centimeters of cork dust will be required?

Question 4 (i)ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that(i)ΔABE≅ΔACF

if A, B and C are respectively the mid points of side PQ,QR and PR of a triangle and PS is the perpendicular from P on QR , prove that A,C,B and S are concyclic

Determine the ratio in which the graph of the equation 3x+y=9 divides the line segment joining the points A(2,7) and B(1,3).

Question 2 (ii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Factorise the following numbers into primes.(i) 32(ii) 57(iii) 23(iv) 150(v) 216(vi) 208(vii) 765(viii) 342(ix) 377(x) 559

The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the AP ​​​

Question 16The sum of first 16 terms of the AP 10, 6, 2, … isA) -320B) 320C) -352D) -400​​​​​​​

The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

If for an A.P. Sn=n2+7n what is its third term?

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is [CBSE 2014](a) 415(b) 215(c) 15(d) 13

The lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm. Find (i) the radius of its base and (ii) its volume. (Take π = 3.14.)

The common difference of the A.P. 12b,1-6b2b,1-12b2b, ... is(a) 2b(b) −2b(c) 3(d) −3

Find f and g if the mean for the data is 54 Class0−2020−4040−6060−8080−100TotalFrequency5fg13950

An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 of iron has 8 gram mass approximately.(Use : π = 355/115)

In the given figure, ΔOAB∼ΔOCD. If AB = 8 cm, BO = 6.4 cm, OC = 3.5 cm and CD = 5 cm, find (i) OA (ii) DO.

​The area of the bounded by the ellipse x225+y216=1 is ______________________.

Given the figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.

In what ratio does the point 2411, y divide the line segment joining the points P(2, –2) and Q(3, 7)? Also, find the value of y. [CBSE 2017]

A shopkeeper purchased an item of Rs 100 at 8% VAT and sells it at Rs 120 to the customer and customer also pays 8% VAT to the shopkeeper. How much amount did the shopkeeper deposit to the Government as VAT ?

35.How to factorise a polynomial?

Two ships A and B, lies 33 m apart on the sea surface. There is submarine 'C' on the sea bed. The angle of depression of C from A is 60o and the distance AC is 40 m. Calculate the distance BC.

A sphere and a cube are of the same height. The ratio of their volumes is(a) 3 : 4(b) 21 : 11(c) 4 : 3(d) 11 : 21

In figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is(a) 7.5(b) 15(c) 10(d) 9

Find the values of a and b for which the following system of linear equations has an infinite number of solutions:2x+3y=72ax+a+by=28 [CBSE 2001]

Question 4Find the mode of 14,25, 14, 28, 18,17, 18,14, 23, 22,14,18.

A 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs 40 per m2.

Question 6A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Solve for x, 1÷(x-1)(x-2)+1÷(x-2)(x-3)+1÷(x-3)(x-4)=1÷6

If for x,y∈R, x&gt;0, y=log10x+log10x1/3+log10x1/9+…upto ∞ terms and 2+4+6+…+2y3+6+9+…+3y=4log10x, then the ordered pair (x,y) is equal to:

What will be the defrenciation of A cost with respect to t

In the given figure, O is the centre of the circle. Tap on the angle whose value will be 2x∘.

If x2+ 4xm + 3 = 0, represent a quadratic equation then what is the minimum andmaximum value of m?

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speeds of the cars.

The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm, its volume is

How much is the length and width of each classroom?Scale : 1 cm = 5 m

The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If third vertex is (72,y), find y.

In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find the value of tan P - cot R.

There are 25 tickets numbered as 1, 2, 3, 4,..., 25 respectively. One ticket is drawn at random. What is the probability that the number on the ticket is a multiple of 3 or 5? (a) 25 (b) 1125 (c) 1225 (d) 1325

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

Question 4Write ‘True’ or ‘False’ and justify your answer in each of the following:√(1−cos2θ)sec2θ=tanθ

The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the AP

Question 16The sum of first 16 terms of the AP 10, 6, 2, … isA) -320B) 320C) -352D) -400

The area of the bounded by the ellipse x225+y216=1 is ______________________.

If for x,y∈R, x>0, y=log10x+log10x1/3+log10x1/9+…upto ∞ terms and 2+4+6+…+2y3+6+9+…+3y=4log10x, then the ordered pair (x,y) is equal to: