32581 + Interview Questions in Mathematics Page 101 InterviewSolution

5001.	Cylinder containing gas of volume 8 litre at p 20atm . from the cylinder gas will be filled in balloon of volume 4 litre at 1 atm determine number of balloon can be filled
Answer» Cylinder containing gas of volume 8 litre at p 20atm . from the cylinder gas will be filled in balloon of volume 4 litre at 1 atm determine number of balloon can be filled

Discussion

5002.	In the frequency distribution table given below, which class interval has the lowest frequency?Class IntervalFrequency25−35135−45545−55555−65465−75075−85885−952Total25
Answer» In the frequency distribution table given below, which class interval has the lowest frequency? $\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 25 - 35 & 1 35 - 45 & 5 45 - 55 & 5 55 - 65 & 4 65 - 75 & 0 75 - 85 & 8 85 - 95 & 2 T o t a l & 25 \end{matrix}$

Discussion

5003.	From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be 30∘ and 60∘. Find the height of the tower.
Answer» From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be $30^{\circ} a n d 60^{\circ}$ . Find the height of the tower.

Discussion

5004.	Question 8 The area of the square that can be inscribed in a circle of radius 8 cm is (A) 256 cm2 (B) 128 cm2 (C) 64√2 cm2 (D) 64 cm2
Answer» Question 8 The area of the square that can be inscribed in a circle of radius 8 cm is (A) $256 c m^{2}$ (B) $128 c m^{2}$ (C) $64 \sqrt{2} c m^{2}$ (D) $64 c m^{2}$

Discussion

5005.	In the given figure, line PR touches the circle at point Q. Answer the following questions with the help of the figure.(1) What is the sum of ∠ TAQ and ∠ TSQ ?(2) Find the angles which are congruent to ∠ AQP.(3) Which angles are congruent to ∠ QTS ?(4) ∠TAS = 65°, find the measure of ∠TQS and arc TS.(5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.
Answer» In the given figure, line PR touches the circle at point Q. Answer the following questions with the help of the figure. (1) What is the sum of ∠ TAQ and ∠ TSQ ? (2) Find the angles which are congruent to ∠ AQP. (3) Which angles are congruent to ∠ QTS ? (4) ∠TAS = 65°, find the measure of ∠TQS and arc TS. (5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.

Discussion

5006.	How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm × 11 cm × 12 cm?
Answer» How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm × 11 cm × 12 cm?

Discussion

5007.	Question 6 In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.
Answer» Question 6 In a right angle $∠$ ABC is which $∠ B = 90^{\circ}$ , a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

Discussion

5008.

Change the following distribution to a 'More than type' distribution. Hence, draw the more than type' ogive for this distribution. Class – interval: 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 Frequency: 10 8 12 24 6 25 15

Answer» Change the following distribution to a 'More than type' distribution. Hence, draw the more than type' ogive for this distribution.

Class – interval:	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90
Frequency:	10	8	12	24	6	25	15

Discussion

5009.	In the given figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ____________.
Answer» In the given figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ____________.

Discussion

5010.	What is Congruency Modulo?
Answer» What is Congruency Modulo?

Discussion

5011.	A line inclined at an angle of 120° with the positive x-axis and passes through the point (4,1). Find the equation of the line.
Answer» A line inclined at an angle of 120° with the positive x-axis and passes through the point (4,1). Find the equation of the line.

Discussion

5012.	A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]
Answer» A heap of wheat is in the form of a cone whose diameter is $10.5 m$ and height is $3 m$ . Find its volume. The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required. $[A s s u m e π = \frac{22}{7}]$

Discussion

5013.	Question 11The value of the expression(sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘27∘) is(A) 3(B) 2(C) 1(D) 0
Answer» Question 11 The value of the expression $(\frac{s i n^{2} 22^{\circ} + s i n^{2} 68^{\circ}}{c o s^{2} 22^{\circ} + c o s^{2} 68^{\circ}} + s i n^{2} 63^{\circ} + c o s 63^{\circ} 27^{\circ})$ is (A) 3 (B) 2 (C) 1 (D) 0

Discussion

5014.	how many significant figures are present in a pure number 410 ?
Answer» how many significant figures are present in a pure number 410 ?

Discussion

5015.	Matrix A=⎛⎜⎝600060006⎞⎟⎠ is a ___ matrix
Answer» Matrix $A = ⎛ ⎜ ⎝ \begin{matrix} 6 & 0 & 0 0 & 6 & 0 0 & 0 & 6 \end{matrix} ⎞ ⎟ ⎠$ is a ___ matrix

Discussion

5016.	Choose the correct answer of the following question:If a pole 12 m high casts a shadow 43 m long on the ground, then the sun's elevation is(a) 60° (b) 45° (c) 30° (d) 90° [CBSE 2013C]
Answer» Choose the correct answer of the following question: If a pole 12 m high casts a shadow $4 \sqrt{3}$ m long on the ground, then the sun's elevation is (a) 60° (b) 45° (c) 30° (d) 90° [CBSE 2013C]

Discussion

5017.	Given: sin (B+C)=√32 sin (A+C)=sin B and sin A=12 Find sin (A+B−C)
Answer» Given: $s i n (B + C) = \frac{\sqrt{3}}{2}$ $s i n (A + C) = s i n B$ and $s i n A = \frac{1}{2}$ Find $s i n (A + B - C)$

Discussion

5018.	Find the area of the shaded portion:
Answer» Find the area of the shaded portion:

Discussion

5019.	A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by(a) 29 cm(b) 49 cm(c) 94 cm(d) 92 cm
Answer» A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by (a) $\frac{2}{9}$ cm (b) $\frac{4}{9}$ cm (c) $\frac{9}{4}$ cm (d) $\frac{9}{2}$ cm

Discussion

5020.	12 defective pens are accidentally mixed up the 132 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from the lot. Find the probability that the pen taken out is (i) a good one, (ii) defective
Answer» 12 defective pens are accidentally mixed up the 132 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from the lot. Find the probability that the pen taken out is (i) a good one, (ii) defective

Discussion

5021.	If the value of tan α=52, then find the value of cot θ.Given : α+θ=90∘.
Answer» If the value of $t a n α = \frac{5}{2}$ , then find the value of $c o t θ$ . Given : $α + θ = 90^{\circ} .$

Discussion

5022.	A positive integer is of the form 3q + 1 ,q being a anatural number. Can you write its square in any form other than 3m + 1,3m or 3m + 2 for some integer m ? Justify your answer.
Answer» A positive integer is of the form $3 q + 1, q$ being a anatural number. Can you write its square in any form other than $3 m + 1, 3 m$ or $3 m + 2$ for some integer $m$ ? Justify your answer.

Discussion

5023.	Use graph paper for the question. The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R. Find area of figure PQR.
Answer» Use graph paper for the question. The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R. Find area of figure PQR.

5023.

Use graph paper for the question. The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R. Find area of figure PQR.

Answer»

Use graph paper for the question.

The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R.

Find area of figure PQR.

Discussion

5024.	The set of values of x for which [x2+12]+[x2+22]+[x2+32]+⋯[x2+202]=140 is/are(where [.] is greatest integer function)
Answer» The set of values of $x$ for which $[\frac{x^{2} + 1}{2}] + [\frac{x^{2} + 2}{2}] + [\frac{x^{2} + 3}{2}] + \dots [\frac{x^{2} + 20}{2}] = 140$ is/are (where $[.]$ is greatest integer function)

Discussion

5025.	Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find: [6 MARKS] i) lower quartile ii) upper quartile iii) semi-interquartile range Class intervalFrequency5−10310−15415−20620−25925−30730−351
Answer» Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find: [6 MARKS] i) lower quartile ii) upper quartile iii) semi-interquartile range $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 5 - 10 & 3 10 - 15 & 4 15 - 20 & 6 20 - 25 & 9 25 - 30 & 7 30 - 35 & 1 \end{matrix}$

Discussion

5026.	If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ? (a) 27 (b) 25 (c) 24 (d) 23
Answer» If (tan $θ$ + cot $θ$ ) = 5 then ( $t a n^{2} θ$ + $c o t^{2} θ$ ) = ? (a) 27 (b) 25 (c) 24 (d) 23

5026.

If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ? (a) 27 (b) 25 (c) 24 (d) 23

Answer»

If (tan $θ$ + cot $θ$ ) = 5 then ( $t a n^{2} θ$ + $c o t^{2} θ$ ) = ?

(a) 27 (b) 25 (c) 24 (d) 23

Discussion

5027.	In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .
Answer» In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .

5027.

In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .

Answer»

In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .

Discussion

5028.	The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Answer» The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

Discussion

5029.	If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains ___________.
Answer» If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains ___________.

Discussion

5030.	If a and b are distinct integers, prove that a-b is a factor of an−bn, whenever n is a positive integer.
Answer» If a and b are distinct integers, prove that a-b is a factor of $a^{n} - b^{n}$ , whenever n is a positive integer.

Discussion

5031.	If the zeros of the polynomial f(x)=2x^3-15x^2+37x-30 are in A.P., find them.
Answer» If the zeros of the polynomial f(x)=2x^3-15x^2+37x-30 are in A.P., find them.

Discussion

5032.	From the following table, identify the variation and also find the constant of proportionality. x245510y50252012.510
Answer» From the following table, identify the variation and also find the constant of proportionality. $\begin{matrix} x & 2 & 4 & 5 & 5 & 10 y & 50 & 25 & 20 & 12.5 & 10 \end{matrix}$

5032.

From the following table, identify the variation and also find the constant of proportionality. x245510y50252012.510

Answer»

From the following table, identify the variation and also find the constant of proportionality.

$\begin{matrix} x & 2 & 4 & 5 & 5 & 10 y & 50 & 25 & 20 & 12.5 & 10 \end{matrix}$

Discussion

5033.	∫ x sec^2x †an x dx=
Answer» ∫ x sec^2x †an x dx=

Discussion

5034.	Consider the following statements and choose the correct option. 1) A tangent is a line that touches the circle at one point. 2) A tangent is a special case of the secant where the points of intersection coincide.
Answer» Consider the following statements and choose the correct option. 1) A tangent is a line that touches the circle at one point. 2) A tangent is a special case of the secant where the points of intersection coincide.

Discussion

5035.	Question 1 (v) Find the roots of the quadratic equations by using the quadratic formula in the following question. x2+2√2x−6=0
Answer» Question 1 (v) Find the roots of the quadratic equations by using the quadratic formula in the following question. $x^{2} + 2 \sqrt{2} x - 6 = 0$

5035.

Question 1 (v) Find the roots of the quadratic equations by using the quadratic formula in the following question. x2+2√2x−6=0

Answer»

Question 1 (v)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$x^{2} + 2 \sqrt{2} x - 6 = 0$

Discussion

5036.	The 16th term of the AP: 15,252,10,152,5,.... is:
Answer» The $16^{t h}$ term of the AP: $15, \frac{25}{2}, 10, \frac{15}{2}, 5, . . . .$ is:

Discussion

5037.	find the new coordinates of 2,3 if the coordinate axis becomes x+y+1 =0 and x-y+2 = 0
Answer» find the new coordinates of 2,3 if the coordinate axis becomes x+y+1 =0 and x-y+2 = 0

Discussion

5038.	Find the discriminant of the quadratic equation 3x2–5x+2=0 and find the nature of their roots.
Answer» Find the discriminant of the quadratic equation $3 x^{2} - 5 x + 2 = 0$ and find the nature of their roots.

Discussion

5039.	Question 13A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Answer» Question 13 A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Discussion

5040.	Solve for x and y: bxa−ayb+a+b=0,bx−ay+2ab=0.
Answer» Solve for x and y: $\frac{b x}{a} - \frac{a y}{b} + a + b = 0, b x - a y + 2 a b = 0.$

5040.

Solve for x and y: bxa−ayb+a+b=0,bx−ay+2ab=0.

Answer»

Solve for x and y:

$\frac{b x}{a} - \frac{a y}{b} + a + b = 0, b x - a y + 2 a b = 0.$

Discussion

5041.	8. A boy standing on a horizontal plane finds a kite flyingat a distance of 150 m from him at an elevation of 60^° A girl standing on a roof of 15 m high building finds theangle of elevation of the same kite at the same timeto be 450. If the boy and the girl are on opposite sides of the kite, then the distance of the kite from the girl is \lbrack Neglects the height of boy and girl\rbrack(1) 30 m(3) 60 m(2) 30/2 m(4) (75/6 -15/2) m32СА-
Answer» 8. A boy standing on a horizontal plane finds a kite flyingat a distance of 150 m from him at an elevation of 60^° A girl standing on a roof of 15 m high building finds theangle of elevation of the same kite at the same timeto be 450. If the boy and the girl are on opposite sides of the kite, then the distance of the kite from the girl is \lbrack Neglects the height of boy and girl\rbrack(1) 30 m(3) 60 m(2) 30/2 m(4) (75/6 -15/2) m32СА-

Discussion

5042.	A bag contains cards which are numbered form 2 to 90. A card is drawn at random from the bag. Find the probability that it bears(i) a two digit number(ii) a number which is a perfect square.
Answer» A bag contains cards which are numbered form 2 to 90. A card is drawn at random from the bag. Find the probability that it bears (i) a two digit number (ii) a number which is a perfect square.

Discussion

5043.	Question 19Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90∘ at the centre.
Answer» Question 19 Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of $90^{\circ}$ at the centre.

Discussion

5044.	In a birthday celebration, Mango, Vanilla, Chocolate flavoured ice-creams were served. If you want to represent the number of people who like different flavours, the best way to represent it can be given by option___
Answer» In a birthday celebration, Mango, Vanilla, Chocolate flavoured ice-creams were served. If you want to represent the number of people who like different flavours, the best way to represent it can be given by option___

5044.

In a birthday celebration, Mango, Vanilla, Chocolate flavoured ice-creams were served. If you want to represent the number of people who like different flavours, the best way to represent it can be given by option___

Answer»

In a birthday celebration, Mango, Vanilla, Chocolate flavoured ice-creams were served. If you want to represent the number of people who like different flavours, the best way to represent it can be given by option___

Discussion

5045.	Question 1 (d)Write all the factors of the given number:27
Answer» Question 1 (d) Write all the factors of the given number: 27

5045.

Question 1 (d)Write all the factors of the given number:27

Answer»

Question 1 (d)

Write all the factors of the given number:

27

Discussion

5046.	Construct a ΔABC in which AB = 6 cm, ∠A=30∘ and ∠B=60∘. Construct another ΔAB′C′ similar to ΔABC with base AB' = 8 cm.
Answer» Construct a $Δ A B C$ in which AB = 6 cm, $∠ A = 30^{\circ} a n d ∠ B = 60^{\circ} .$ Construct another $Δ A B^{'} C^{'} similar to Δ A B C$ with base AB' = 8 cm.

Discussion

5047.	You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, − 6), B (3, − 2) and C (5, 2)
Answer» You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, − 6), B (3, − 2) and C (5, 2)

Discussion

5048.	The pair of equations y = 0 and y = –7 has _________ solution.
Answer» The pair of equations y = 0 and y = –7 has _________ solution.

Discussion

5049.	If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?
Answer» If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

Discussion

5050.	The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are(a) (−6, 5)(b) (5, 6)(c) (−5, 6)(d) (6, 5)
Answer» The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are (a) (−6, 5) (b) (5, 6) (c) (−5, 6) (d) (6, 5)

Discussion

Explore topic-wise InterviewSolutions in .

Cylinder containing gas of volume 8 litre at p 20atm . from the cylinder gas will be filled in balloon of volume 4 litre at 1 atm determine number of balloon can be filled

In the frequency distribution table given below, which class interval has the lowest frequency?Class IntervalFrequency25−35135−45545−55555−65465−75075−85885−952Total25

From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be 30∘ and 60∘. Find the height of the tower.

Question 8 The area of the square that can be inscribed in a circle of radius 8 cm is (A) 256 cm2 (B) 128 cm2 (C) 64√2 cm2 (D) 64 cm2

How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm × 11 cm × 12 cm?

Question 6 In a right angle ∠ ABC is which ∠B=90∘, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

Change the following distribution to a 'More than type' distribution. Hence, draw the more than type' ogive for this distribution. Class – interval: 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 Frequency: 10 8 12 24 6 25 15

In the given figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ____________.

What is Congruency Modulo?

A line inclined at an angle of 120° with the positive x-axis and passes through the point (4,1). Find the equation of the line.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]

Question 11The value of the expression(sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘27∘) is(A) 3(B) 2(C) 1(D) 0

how many significant figures are present in a pure number 410 ?

Matrix A=⎛⎜⎝600060006⎞⎟⎠ is a ___ matrix

Choose the correct answer of the following question:If a pole 12 m high casts a shadow 43 m long on the ground, then the sun's elevation is(a) 60° (b) 45° (c) 30° (d) 90° [CBSE 2013C]

Given: sin (B+C)=√32 sin (A+C)=sin B and sin A=12 Find sin (A+B−C)

Find the area of the shaded portion:

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by(a) 29 cm(b) 49 cm(c) 94 cm(d) 92 cm

12 defective pens are accidentally mixed up the 132 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from the lot. Find the probability that the pen taken out is (i) a good one, (ii) defective

If the value of tan α=52, then find the value of cot θ.Given : α+θ=90∘.

A positive integer is of the form 3q + 1 ,q being a anatural number. Can you write its square in any form other than 3m + 1,3m or 3m + 2 for some integer m ? Justify your answer.

Use graph paper for the question. The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R. Find area of figure PQR.

The set of values of x for which [x2+12]+[x2+22]+[x2+32]+⋯[x2+202]=140 is/are(where [.] is greatest integer function)

Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find: [6 MARKS] i) lower quartile ii) upper quartile iii) semi-interquartile range Class intervalFrequency5−10310−15415−20620−25925−30730−351

If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ? (a) 27 (b) 25 (c) 24 (d) 23

In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that .

The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains ___________.

If a and b are distinct integers, prove that a-b is a factor of an−bn, whenever n is a positive integer.

If the zeros of the polynomial f(x)=2x^3-15x^2+37x-30 are in A.P., find them.

From the following table, identify the variation and also find the constant of proportionality. x245510y50252012.510

∫ x sec^2x †an x dx=

Consider the following statements and choose the correct option. 1) A tangent is a line that touches the circle at one point. 2) A tangent is a special case of the secant where the points of intersection coincide.

Question 1 (v) Find the roots of the quadratic equations by using the quadratic formula in the following question. x2+2√2x−6=0

The 16th term of the AP: 15,252,10,152,5,.... is:

find the new coordinates of 2,3 if the coordinate axis becomes x+y+1 =0 and x-y+2 = 0

Find the discriminant of the quadratic equation 3x2–5x+2=0 and find the nature of their roots.

Question 13A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Solve for x and y: bxa−ayb+a+b=0,bx−ay+2ab=0.

A bag contains cards which are numbered form 2 to 90. A card is drawn at random from the bag. Find the probability that it bears(i) a two digit number(ii) a number which is a perfect square.

Question 19Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90∘ at the centre.

In a birthday celebration, Mango, Vanilla, Chocolate flavoured ice-creams were served. If you want to represent the number of people who like different flavours, the best way to represent it can be given by option___

Question 1 (d)Write all the factors of the given number:27

Construct a ΔABC in which AB = 6 cm, ∠A=30∘ and ∠B=60∘. Construct another ΔAB′C′ similar to ΔABC with base AB' = 8 cm.

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, − 6), B (3, − 2) and C (5, 2)

The pair of equations y = 0 and y = –7 has _________ solution.

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are(a) (−6, 5)(b) (5, 6)(c) (−5, 6)(d) (6, 5)