24740 + Interview Questions in Mathematics Page 117 InterviewSolution

5801.	In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.
Answer» In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

Discussion

5802.	(i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5. [CBSE 2017](ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Answer» (i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5. [CBSE 2017] (ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Discussion

5803.	In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes.Given that h∝x, find the constant of proportionality.
Answer» In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes. Given that $h \propto x$ , find the constant of proportionality.

5803.

In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes.Given that h∝x, find the constant of proportionality.

Answer»

In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes.

Given that $h \propto x$ , find the constant of proportionality.

Discussion

5804.	Question 2 (ii)Find the LCM and HCF of 510, 92 and verify that LCM × HCF = product of the two numbers.
Answer» Question 2 (ii) Find the LCM and HCF of 510, 92 and verify that LCM $\times$ HCF = product of the two numbers.

Discussion

5805.	39^3+11^3-50^3 Solve by algebraic identity
Answer» 39^3+11^3-50^3 Solve by algebraic identity

5805.

39^3+11^3-50^3 Solve by algebraic identity

Answer»

39^3+11^3-50^3

Solve by algebraic identity

Discussion

5806.	Question 4(c) Insert commas suitable and write the names according to International system of numeration: 99985102
Answer» Question 4(c) Insert commas suitable and write the names according to International system of numeration: 99985102

Discussion

5807.	If the radius of a circle is tripled, by how many times does It's circumference increase? How many times does it's area increase?
Answer» If the radius of a circle is tripled, by how many times does It's circumference increase? How many times does it's area increase?

Discussion

5808.	Find the value of expression, x3−5x−2y−3z when x=−2, y=−3, and z=4.
Answer» Find the value of expression, $x^{3} - 5 x - 2 y - 3 z$ when $x = - 2$ , $y = - 3$ , and $z = 4$ .

Discussion

5809.	Mohan started a business on 1st April, 2017 with a capital of ₹ 25,000 and a loan of ₹ 12,500 borrowed from Shyam. During 2017-18 he had introduced additional capital of 12,500 and had withdrawn ₹ 7,500 for personal use. On 31st March, 2018 his assets were ₹ 75,000. Find out his capital as on 31st March, 2018 and profit made or loss incurred during the year 2017-18.
Answer» Mohan started a business on 1st April, 2017 with a capital of ₹ 25,000 and a loan of ₹ 12,500 borrowed from Shyam. During 2017-18 he had introduced additional capital of 12,500 and had withdrawn ₹ 7,500 for personal use. On 31st March, 2018 his assets were ₹ 75,000. Find out his capital as on 31st March, 2018 and profit made or loss incurred during the year 2017-18.

Discussion

5810.	40. All chords through an external point to the circle x^2+y^2=16 are drawn having length I which is a positive integer. The sum of the squares of the distances fromcentre of circle to these chords is(a) 154 (b) 124 (c) 172 (d) 128
Answer» 40. All chords through an external point to the circle x^2+y^2=16 are drawn having length I which is a positive integer. The sum of the squares of the distances fromcentre of circle to these chords is(a) 154 (b) 124 (c) 172 (d) 128

Discussion

5811.	In the given figure, straight lines AB and CD intersect at O. If ∠AOC+∠BOD=130∘ then ∠AOD=? (a)65∘ (b)115∘ (c)110∘ (d)125∘
Answer» In the given figure, straight lines AB and CD intersect at O. If $∠ A O C + ∠ B O D = 130^{\circ}$ then $∠ A O D = ?$ $(a) 65^{\circ}$ $(b) 115^{\circ}$ $(c) 110^{\circ}$ $(d) 125^{\circ}$

5811.

In the given figure, straight lines AB and CD intersect at O. If ∠AOC+∠BOD=130∘ then ∠AOD=? (a)65∘ (b)115∘ (c)110∘ (d)125∘

Answer»

In the given figure, straight lines AB and CD intersect at O. If $∠ A O C + ∠ B O D = 130^{\circ}$ then $∠ A O D = ?$

$(a) 65^{\circ}$

$(b) 115^{\circ}$

$(c) 110^{\circ}$

$(d) 125^{\circ}$

Discussion

5812.	Question 77(iii)This graph shows the percent of students who dropped out of school after completing high school. The point labelled A shown that, in 1996, about 4.7% of students dropped out.About what percent of students dropped out of high school in 2007? About what percent of students stayed in high school in 2008?
Answer» Question 77(iii) This graph shows the percent of students who dropped out of school after completing high school. The point labelled A shown that, in 1996, about 4.7% of students dropped out. About what percent of students dropped out of high school in 2007? About what percent of students stayed in high school in 2008?

Discussion

5813.	Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.
Answer» Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.

Discussion

5814.	Following bar chart represents the number of childern in a family What is the maximum number of children in a family ?
Answer» Following bar chart represents the number of childern in a family What is the maximum number of children in a family ?

5814.

Following bar chart represents the number of childern in a family What is the maximum number of children in a family ?

Answer»

Following bar chart represents the number of childern in a family

What is the maximum number of children in a family ?

Discussion

5815.	Which of the following is not an integer?
Answer» Which of the following is not an integer?

Discussion

5816.	If (28-x) is the mean proportional of (23-x) and (19-x) then find the vaue of x.
Answer» If (28 $- x$ ) is the mean proportional of (23 $- x$ ) and (19 $- x$ ) then find the vaue of x.

Discussion

5817.	Write the value of 2+3 2-3.
Answer» Write the value of $(2 + \sqrt{3}) (2 - \sqrt{3}) .$

Discussion

5818.	48. Evaluate -10/5+10-80-40+90.it is being given that 5=2.236 and 10=3.162
Answer» 48. Evaluate -10/5+10-80-40+90.it is being given that 5=2.236 and 10=3.162

Discussion

5819.	A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vesse, one fourth of the water flows out. Find the number of lead shots dropped in the vessel
Answer» A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vesse, one fourth of the water flows out. Find the number of lead shots dropped in the vessel

Discussion

5820.	P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them.
Answer» P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them.

Discussion

5821.	Factorize:(x+2) (x2+25) − 10x2 − 20x
Answer» Factorize: (x+2) (x²+25) − 10x² − 20x

Discussion

5822.	A person bought 312kg apples, 269kg of grapes and 158kg oranges. He wants to divide them among 4 people. Find the amount (in kg) each person will receive.
Answer» A person bought $3 \frac{1}{2}$ kg apples, $2 \frac{6}{9}$ kg of grapes and $1 \frac{5}{8}$ kg oranges. He wants to divide them among $4$ people. Find the amount (in kg) each person will receive.

Discussion

5823.	Factorise x2+√2x−24
Answer» Factorise $x^{2} + \sqrt{2} x - 24$

Discussion

5824.	In ancient India,the shapes of altars used for household rituals were (a) squares and rectangles (b) squares and circles (c) triangles and rectangles (d) trapeziums and pyramids
Answer» In ancient India,the shapes of altars used for household rituals were (a) squares and rectangles (b) squares and circles (c) triangles and rectangles (d) trapeziums and pyramids

5824.

In ancient India,the shapes of altars used for household rituals were (a) squares and rectangles (b) squares and circles (c) triangles and rectangles (d) trapeziums and pyramids

Answer»

In ancient India,the shapes of altars used for household rituals were

(a) squares and rectangles

(b) squares and circles

(c) triangles and rectangles

(d) trapeziums and pyramids

Discussion

5825.	The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .
Answer» The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .

Discussion

5826.	What fraction of the total boxes are shaded in the given figure?
Answer» What fraction of the total boxes are shaded in the given figure?

Discussion

5827.	He tends to-
Answer» He tends to-

Discussion

5828.	Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
Answer» Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.

Discussion

5829.	In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. Arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region in the figure.
Answer» In figure, ABCD is a trapezium with $A B ∥ D C$ . AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. Arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region in the figure.

Discussion

5830.	Question 95A cuboidal tin box opened at the top has dimensions 20 cm×16 cm×14 cm. What is the total area of metal sheet required to make 10 such boxes?
Answer» Question 95 A cuboidal tin box opened at the top has dimensions $20 c m \times 16 c m \times 14 c m$ . What is the total area of metal sheet required to make 10 such boxes?

5830.

Question 95A cuboidal tin box opened at the top has dimensions 20 cm×16 cm×14 cm. What is the total area of metal sheet required to make 10 such boxes?

Answer»

Question 95

A cuboidal tin box opened at the top has dimensions $20 c m \times 16 c m \times 14 c m$ . What is the total area of metal sheet required to make 10 such boxes?

Discussion

5831.	A diagonal of a rectangle is inclined to one side of the rectangle at 35∘. The acute angle between the diagonals is ___.
Answer» A diagonal of a rectangle is inclined to one side of the rectangle at $35^{\circ}$ . The acute angle between the diagonals is ___.

Discussion

5832.	Sarosh and his brothers inherited a square piece of land from their ancestors. However, his share of the land was only an equilateral triangular piece, with one vertex as that of the square land and side equal to half of the square. Also, one side of Sarosh'��s land coincided with one side of the square land. Sarosh wanted to fix a perimeter on his area and he had an anchor and a rope of length equal to half of that of the side of the square, to mark his territory. He fixes the anchor at one vertex, A. Sarosh was given a set of cards instructing how to mark his territory. Sarosh being inquisitive, wanted to know the reasons behind the instructions in the cards. Select the correct option for the matching of coloumn A and B from the given options NOTE: While walking, Sarosh leaves footprints so that his path can be tracked. A rope is said to be taut when it can not be stretched further, i.e it reaches its maximum length. [Column A] Instructions on card Walk along any side of the square till the rope becomes taut. Mark this point, say Q. When the rope becomes taut, with the anchor still at A, walk inside the field till you reach side AD (towards the sides AD and DC). Now put the anchor at Q and walk along side AB till the rope is taut. Now when the rope is taut, walk towards sides DC and CB (inside the field) till he meets his previous footprints (with anchor at A), at P. Join the points of intersection of his foot tracks to get the territory. [Column B] Reason Triangle is formed We need to get the length of the side of our triangle. This is similar to setting the compass length as the side of the triangle. Similar to drawing an arc, to find the point equidistant from the second vertex of the triangle. This is so that we need to find out what all points are at a distance equal to that of the side of the triangle.
Answer» Sarosh and his brothers inherited a square piece of land from their ancestors. However, his share of the land was only an equilateral triangular piece, with one vertex as that of the square land and side equal to half of the square. Also, one side of Sarosh'��s land coincided with one side of the square land. Sarosh wanted to fix a perimeter on his area and he had an anchor and a rope of length equal to half of that of the side of the square, to mark his territory. He fixes the anchor at one vertex, A. Sarosh was given a set of cards instructing how to mark his territory. Sarosh being inquisitive, wanted to know the reasons behind the instructions in the cards. Select the correct option for the matching of coloumn A and B from the given options NOTE: While walking, Sarosh leaves footprints so that his path can be tracked. A rope is said to be taut when it can not be stretched further, i.e it reaches its maximum length. [Column A] Instructions on card Walk along any side of the square till the rope becomes taut. Mark this point, say Q. When the rope becomes taut, with the anchor still at A, walk inside the field till you reach side AD (towards the sides AD and DC). Now put the anchor at Q and walk along side AB till the rope is taut. Now when the rope is taut, walk towards sides DC and CB (inside the field) till he meets his previous footprints (with anchor at A), at P. Join the points of intersection of his foot tracks to get the territory. [Column B] Reason Triangle is formed We need to get the length of the side of our triangle. This is similar to setting the compass length as the side of the triangle. Similar to drawing an arc, to find the point equidistant from the second vertex of the triangle. This is so that we need to find out what all points are at a distance equal to that of the side of the triangle.

5832.

Sarosh and his brothers inherited a square piece of land from their ancestors. However, his share of the land was only an equilateral triangular piece, with one vertex as that of the square land and side equal to half of the square. Also, one side of Sarosh'��s land coincided with one side of the square land. Sarosh wanted to fix a perimeter on his area and he had an anchor and a rope of length equal to half of that of the side of the square, to mark his territory. He fixes the anchor at one vertex, A. Sarosh was given a set of cards instructing how to mark his territory. Sarosh being inquisitive, wanted to know the reasons behind the instructions in the cards. Select the correct option for the matching of coloumn A and B from the given options NOTE: While walking, Sarosh leaves footprints so that his path can be tracked. A rope is said to be taut when it can not be stretched further, i.e it reaches its maximum length. [Column A] Instructions on card Walk along any side of the square till the rope becomes taut. Mark this point, say Q. When the rope becomes taut, with the anchor still at A, walk inside the field till you reach side AD (towards the sides AD and DC). Now put the anchor at Q and walk along side AB till the rope is taut. Now when the rope is taut, walk towards sides DC and CB (inside the field) till he meets his previous footprints (with anchor at A), at P. Join the points of intersection of his foot tracks to get the territory. [Column B] Reason Triangle is formed We need to get the length of the side of our triangle. This is similar to setting the compass length as the side of the triangle. Similar to drawing an arc, to find the point equidistant from the second vertex of the triangle. This is so that we need to find out what all points are at a distance equal to that of the side of the triangle.

Answer»

Sarosh and his brothers inherited a square piece of land from their ancestors. However, his share of the land was only an equilateral triangular piece, with one vertex as that of the square land and side equal to half of the square. Also, one side of Sarosh'��s land coincided with one side of the square land.

Sarosh wanted to fix a perimeter on his area and he had an anchor and a rope of length equal to half of that of the side of the square, to mark his territory. He fixes the anchor at one vertex, A.

Sarosh was given a set of cards instructing how to mark his territory. Sarosh being inquisitive, wanted to know

the reasons behind the instructions in the cards. Select the correct option for the matching of coloumn A and B from the given options

NOTE: While walking, Sarosh leaves footprints so that his path can be tracked.

A rope is said to be taut when it can not be stretched further, i.e it reaches its maximum length.

[Column A] Instructions on card

Walk along any side of the square till the rope becomes taut. Mark this point, say Q. When the rope becomes taut, with the anchor still at A, walk inside the field till you reach side AD (towards the sides AD and DC). Now put the anchor at Q and walk along side AB till the rope is taut. Now when the rope is taut, walk towards sides DC and CB (inside the field) till he meets his previous footprints (with anchor at A), at P. Join the points of intersection of his foot tracks to get the territory.

[Column B] Reason

Triangle is formed We need to get the length of the side of our triangle. This is similar to setting the compass length as the side of the triangle. Similar to drawing an arc, to find the point equidistant from the second vertex of the triangle. This is so that we need to find out what all points are at a distance equal to that of the side of the triangle.

Discussion

5833.	l, m and n are parallel lines intersected by a transversal p at X, Y and Z respectively. The value of ∠2 will be
Answer» l, m and n are parallel lines intersected by a transversal p at X, Y and Z respectively. The value of ∠2 will be

5833.

l, m and n are parallel lines intersected by a transversal p at X, Y and Z respectively. The value of ∠2 will be

Answer»

l, m and n are parallel lines intersected by a transversal p at X, Y and Z respectively. The value of ∠2 will be

Discussion

5834.	By grouping the terms in x3 - x2 - xy + x + y - 1, we get
Answer» By grouping the terms in x³ - x² - xy + x + y - 1, we get

Discussion

5835.	Plot the following points on the graph paper (2, 3), (-4, 2) and (3, -1) and also draw the triangle by joining the vertices.
Answer» Plot the following points on the graph paper (2, 3), (-4, 2) and (3, -1) and also draw the triangle by joining the vertices.

Discussion

5836.	The parallel sides of a trapezium are 25 cm and 11 cm. The perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.
Answer» The parallel sides of a trapezium are 25 cm and 11 cm. The perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.

Discussion

5837.	If (2x+3y)2=130 and xy=6, find the value of 4x2+9y2
Answer» If $(2 x + 3 y)^{2} = 130$ and $x y = 6,$ find the value of $4 x^{2} + 9 y^{2}$

Discussion

5838.	What is the difference between natural log and logarithm?
Answer» What is the difference between natural log and logarithm?

Discussion

5839.	Construct a triangle with sides 5 cm,6 cm and 7 cm and then another triangle whose sides are 75 of the corresponding sides of the first triangle.
Answer» Construct a triangle with sides $5 c m, 6 c m$ and $7 c m$ and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Discussion

5840.	Question 13The positive solutions of the equation ax + by + c = 0 always lie in the:A) Ist quadrantB) IInd quadrantC) IIIrd quadrantD) IVth quadrant
Answer» Question 13 The positive solutions of the equation ax + by + c = 0 always lie in the: A) Ist quadrant B) IInd quadrant C) IIIrd quadrant D) IVth quadrant

Discussion

5841.	Evaluate : sin18∘/cos72∘___
Answer» Evaluate : $s i n 18^{\circ} / c o s 72^{\circ}$ ___

Discussion

5842.

Following is the Receipt and Payment Account of Women's Welfare Club for the year ended 31st March, 2019: RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019 Dr. Cr. Receipts ₹ Payments ₹ To Cash in Hand 22,500 Salary 1,25,000 To Cash at Bank 50,000 By Stationery 17,000 To Subscriptions 8,17,500 By Electric Charges 95,500 To Donations 30,000 By Insurance 75,000 To Government Grant 1,50,000 By Equipments 3,00,000 To Sale of Newspapers 3,000 By Petty Expenses 5,000 To Proceeds of Charity Show 1,65,000 By Expenses on Charity Show 1,29,000 To Interest on Investments 10% for full year 70,000 By Newspapers 10,000 To Sundries Income 4,000 By Lectures Fee 1,65,000 By Honorarium to secretary 1,20,000 By Cash in Hand 20,500 By Cash at Bank 2,50,000 13,12,000 13,12,000 Additional Information: Particulars 1st April, 2018 (₹) 31st March, 2019 (₹) Outstanding Salaries 12,000 18,000 Insurance Prepaid 7,000 3,000 Subscription Outstanding 37,500 25,000 Subscription received in advance 17,500 10,000 Electricity Charges outstanding ... 12,500 Stock of Stationery 22,500 7,000 Equipments 2,56,000 5,02,000 Building 12,00,000 11,40,000 Prepare Income and Expenditure Account for the year ended 31st March, 2019,and Balance Sheet as on that date.

Answer» Following is the Receipt and Payment Account of Women's Welfare Club for the year ended 31st March, 2019:

RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019
Dr.				Cr.
Receipts	₹	Payments	₹
To Cash in Hand	22,500	Salary	1,25,000
To Cash at Bank	50,000	By Stationery	17,000
To Subscriptions	8,17,500	By Electric Charges	95,500
To Donations	30,000	By Insurance	75,000
To Government Grant	1,50,000	By Equipments	3,00,000
To Sale of Newspapers	3,000	By Petty Expenses	5,000
To Proceeds of Charity Show	1,65,000	By Expenses on Charity Show	1,29,000
To Interest on Investments 10% for full year	70,000	By Newspapers	10,000
To Sundries Income	4,000	By Lectures Fee	1,65,000
		By Honorarium to secretary	1,20,000
		By Cash in Hand	20,500
		By Cash at Bank	2,50,000

	13,12,000		13,12,000

Additional Information:

Particulars	1st April, 2018 (₹)	31st March, 2019 (₹)

Outstanding Salaries	12,000	18,000
Insurance Prepaid	7,000	3,000
Subscription Outstanding	37,500	25,000
Subscription received in advance	17,500	10,000
Electricity Charges outstanding	...	12,500
Stock of Stationery	22,500	7,000
Equipments	2,56,000	5,02,000
Building	12,00,000	11,40,000

Prepare Income and Expenditure Account for the year ended 31st March, 2019,and Balance Sheet as on that date.

Discussion

5843.	Find the area of the shaded region in Fig, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Answer» Find the area of the shaded region in Fig, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Discussion

5844.	Quadrilateral in which only one pair of opposite sides is parallel is known as__
Answer» Quadrilateral in which only one pair of opposite sides is parallel is known as__

Discussion

5845.	If (a, 4) lies on the graph of 3x + y = 10, then the value of a is
Answer» If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

Discussion

5846.	Divide f(x) by g(x) and find the quotient.f(x)=x3−125, g(x)=x2+5x+25
Answer» Divide $f (x)$ by $g (x)$ and find the quotient. $f (x) = x^{3} - 125, g (x) = x^{2} + 5 x + 25$

Discussion

5847.	In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
Answer» In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.

Discussion

5848.	Find the solution(s) of the pair of equations ax−by=0 and ab2x+a2by=a2+b2 is:
Answer» Find the solution(s) of the pair of equations $\frac{a}{x} - \frac{b}{y} = 0 and \frac{a b^{2}}{x} + \frac{a^{2} b}{y} = a^{2} + b^{2} is:$

Discussion

5849.

An irrational number is plotted (c) on the number line as shown in the figure. Then, find the value of C.

Answer»

An irrational number is plotted (c) on the number line as shown in the figure. Then, find the value of C.

Discussion

5850.	Which of the following is irrational?
Answer» Which of the following is irrational?

Discussion

Explore topic-wise InterviewSolutions in .

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

(i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5. [CBSE 2017](ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes.Given that h∝x, find the constant of proportionality.

Question 2 (ii)Find the LCM and HCF of 510, 92 and verify that LCM × HCF = product of the two numbers.

39^3+11^3-50^3 Solve by algebraic identity

Question 4(c) Insert commas suitable and write the names according to International system of numeration: 99985102

If the radius of a circle is tripled, by how many times does It's circumference increase? How many times does it's area increase?

Find the value of expression, x3−5x−2y−3z when x=−2, y=−3, and z=4.

40. All chords through an external point to the circle x^2+y^2=16 are drawn having length I which is a positive integer. The sum of the squares of the distances fromcentre of circle to these chords is(a) 154 (b) 124 (c) 172 (d) 128

In the given figure, straight lines AB and CD intersect at O. If ∠AOC+∠BOD=130∘ then ∠AOD=? (a)65∘ (b)115∘ (c)110∘ (d)125∘

Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.

Following bar chart represents the number of childern in a family What is the maximum number of children in a family ?

Which of the following is not an integer?

If (28-x) is the mean proportional of (23-x) and (19-x) then find the vaue of x.

Write the value of 2+3 2-3.

48. Evaluate -10/5+10-80-40+90.it is being given that 5=2.236 and 10=3.162

P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them.

Factorize:(x+2) (x2+25) − 10x2 − 20x

A person bought 312kg apples, 269kg of grapes and 158kg oranges. He wants to divide them among 4 people. Find the amount (in kg) each person will receive.

Factorise x2+√2x−24

In ancient India,the shapes of altars used for household rituals were (a) squares and rectangles (b) squares and circles (c) triangles and rectangles (d) trapeziums and pyramids

The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .

What fraction of the total boxes are shaded in the given figure?

He tends to-

Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.

In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. Arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region in the figure.

Question 95A cuboidal tin box opened at the top has dimensions 20 cm×16 cm×14 cm. What is the total area of metal sheet required to make 10 such boxes?

A diagonal of a rectangle is inclined to one side of the rectangle at 35∘. The acute angle between the diagonals is ___.

l, m and n are parallel lines intersected by a transversal p at X, Y and Z respectively. The value of ∠2 will be

By grouping the terms in x3 - x2 - xy + x + y - 1, we get

Plot the following points on the graph paper (2, 3), (-4, 2) and (3, -1) and also draw the triangle by joining the vertices.

The parallel sides of a trapezium are 25 cm and 11 cm. The perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.

If (2x+3y)2=130 and xy=6, find the value of 4x2+9y2

What is the difference between natural log and logarithm?

Construct a triangle with sides 5 cm,6 cm and 7 cm and then another triangle whose sides are 75 of the corresponding sides of the first triangle.

Question 13The positive solutions of the equation ax + by + c = 0 always lie in the:A) Ist quadrantB) IInd quadrantC) IIIrd quadrantD) IVth quadrant

Evaluate : sin18∘/cos72∘___

Find the area of the shaded region in Fig, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Quadrilateral in which only one pair of opposite sides is parallel is known as__

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

Divide f(x) by g(x) and find the quotient.f(x)=x3−125, g(x)=x2+5x+25

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.

Find the solution(s) of the pair of equations ax−by=0 and ab2x+a2by=a2+b2 is:

An irrational number is plotted (c) on the number line as shown in the figure. Then, find the value of C.

Which of the following is irrational?