24740 + Interview Questions in Mathematics Page 24 InterviewSolution

1151.	If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is(a) a + b + c(b) (a − b) (b − c) (c − a)(c) 0(d) none of these
Answer» If 3x = a + b + c, then the value of (x − a)³ + (x −b)³ + (x − c)³ − 3(x − a) (x − b) (x −c) is (a) a + b + c (b) (a − b) (b − c) (c − a) (c) 0 (d) none of these

Discussion

1152.	How many degrees are there in an angle which equals two-third of its complement?
Answer» How many degrees are there in an angle which equals two-third of its complement?

Discussion

1153.	Which of the following is Non terminating and Non repeating decimal ?
Answer» Which of the following is Non terminating and Non repeating decimal ?

Discussion

1154.	A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Answer» A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Discussion

1155.	Question 3(vi)Factorise the expressionsy(y+z)+9(y+z)
Answer» Question 3(vi) Factorise the expressions $y (y + z) + 9 (y + z)$

Discussion

1156.	Question 54 In a year, Ravi earns Rs. 360000 and paid Rs. 24000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.
Answer» Question 54 In a year, Ravi earns Rs. 360000 and paid Rs. 24000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.

1156.

Question 54 In a year, Ravi earns Rs. 360000 and paid Rs. 24000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.

Answer»

Question 54

In a year, Ravi earns Rs. 360000 and paid Rs. 24000 as income tax.
Find the ratio of his
a) income to income tax.
b) income tax to income after paying income tax.

Discussion

1157.	In the given figure,AB \|\| DC prove that(i) ∆DMU ∼ ∆BMV(ii) DM × BV = BM ✕ DU
Answer» In the given figure, AB \|\| DC prove that (i) ∆DMU ∼ ∆BMV (ii) DM × BV = BM ✕ DU

Discussion

1158.	Question 5How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?[Assume π=227]
Answer» Question 5 How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold? $[A s s u m e π = \frac{22}{7}]$

Discussion

1159.	Question 4 (iii)Name the quadrilateral whose diagonals:(iii) Are equal.
Answer» Question 4 (iii) Name the quadrilateral whose diagonals: (iii) Are equal.

1159.

Question 4 (iii)Name the quadrilateral whose diagonals:(iii) Are equal.

Answer»

Question 4 (iii)

Name the quadrilateral whose diagonals:

(iii) Are equal.

Discussion

1160.	The sum of two numbers is 4 more than twice their difference. One of the two numbers is three more than the other number. Find the numbers.
Answer» The sum of two numbers is 4 more than twice their difference. One of the two numbers is three more than the other number. Find the numbers.

Discussion

1161.	ABDE is a trapezium with AE∥BD and ED⊥BD. Also, AC is drawn parallel to the side DE.Find the values of cot θ and cosec θ, respectively, from the figure above.
Answer» ABDE is a trapezium with $A E ∥ B D$ and $E D ⊥ B D$ . Also, AC is drawn parallel to the side DE. Find the values of $cot θ a n d cosec θ$ , respectively, from the figure above.

Discussion

1162.	47. While determining the volume of a sphere an error of 2% occured in measurement of radius. Determine the percentage error of the volume.
Answer» 47. While determining the volume of a sphere an error of 2% occured in measurement of radius. Determine the percentage error of the volume.

Discussion

1163.	If the angle between the vectors A and B is theta, the value of the product ( B cross A)dot A is equal to1)BA^2.costheta2)BA^2.sintheta3)BA^2.sintheta.costheta4)Zero
Answer» If the angle between the vectors A and B is theta, the value of the product ( B cross A)dot A is equal to 1)BA^2.costheta 2)BA^2.sintheta 3)BA^2.sintheta.costheta 4)Zero

Discussion

1164.	ABCD is a parallelogram. E is a point on BA such That BE = 2 EA and F is a point on DC such that DF = 2FC. Prove that AECF is a parallelogram whose area is one third of the area of paralllelogram ABCD.
Answer» ABCD is a parallelogram. E is a point on BA such That BE = 2 EA and F is a point on DC such that DF = 2FC. Prove that AECF is a parallelogram whose area is one third of the area of paralllelogram ABCD.

Discussion

1165.	Find the area fo the triangle whose sides are 18 cm, 24 cm and 30 cm Also, find the height corresponding to the smallest side.
Answer» Find the area fo the triangle whose sides are 18 cm, 24 cm and 30 cm Also, find the height corresponding to the smallest side.

Discussion

1166.	The factor of (x + y + z)3- (x3 + y3 + z) is
Answer» The factor of (x + y + z)3- (x3 + y3 + z) is

Discussion

1167.	Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.
Answer» Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

Discussion

1168.	Pair the addition and subtraction equations which belong to the same fact family.
Answer» Pair the addition and subtraction equations which belong to the same fact family.

Discussion

1169.	Question 3 (i)A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.(i) How many students can sit in the tent, if a student on an average occupies 57m2 on the ground?
Answer» Question 3 (i) A cloth having an area of $165 m^{2}$ is shaped into the form of a conical tent of radius 5 m. (i) How many students can sit in the tent, if a student on an average occupies $\frac{5}{7} m^{2}$ on the ground?

Discussion

1170.	Victor is able to get work only for two hours in a day. Rest of the day, he is looking for work. Is he unemployed? Why? What kind of jobs could persons like Victor is doing?
Answer» Victor is able to get work only for two hours in a day. Rest of the day, he is looking for work. Is he unemployed? Why? What kind of jobs could persons like Victor is doing?

Discussion

1171.	In the given figure, if AB = AD and CB = CD, then which of the following is true ?
Answer» In the given figure, if AB = AD and CB = CD, then which of the following is true ?

1171.

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

Answer»

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

Discussion

1172.	Question 9 (ii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (ii) curved surface area of the cylinder.
Answer» Question 9 (ii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (ii) curved surface area of the cylinder.

1172.

Question 9 (ii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (ii) curved surface area of the cylinder.

Answer»

Question 9 (ii)
A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(ii) curved surface area of the cylinder.

Discussion

1173.	Which of the following statements are true (T) and which are false (F):(i) Sides opposite to equal angles of a triangle may be unequal.(ii) Angles opposite to equal sides of a triangle are equal.(iii) The measure of each angle of an equilateral triangle is 60°.(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.(v) The bisectors of two equal angles of a triangle are equal.(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.
Answer» Which of the following statements are true (T) and which are false (F): (i) Sides opposite to equal angles of a triangle may be unequal. (ii) Angles opposite to equal sides of a triangle are equal. (iii) The measure of each angle of an equilateral triangle is 60°. (iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. (v) The bisectors of two equal angles of a triangle are equal. (vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. (vii) The two altitudes corresponding to two equal sides of a triangle need not be equal. (viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. (ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

1173.

Which of the following statements are true (T) and which are false (F):(i) Sides opposite to equal angles of a triangle may be unequal.(ii) Angles opposite to equal sides of a triangle are equal.(iii) The measure of each angle of an equilateral triangle is 60°.(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.(v) The bisectors of two equal angles of a triangle are equal.(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Answer»

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Discussion

1174.	The height of an equilateral triangle is 6 cm. Find its area. [Take √3 = 1.73.]
Answer» The height of an equilateral triangle is 6 cm. Find its area. [Take $\sqrt{3}$ = 1.73.]

Discussion

1175.	If →a is perpendicular to →b and →r is a non – zero vector such that p→r+(→r.→b)→a=→c, then →r is equal to
Answer» If $\to a$ is perpendicular to $\to b$ and $\to r$ is a non – zero vector such that $p \to r + (\to r . \to b) \to a = \to c$ , then $\to r$ is equal to

Discussion

1176.	The distance of a point (-5, 6) from the y- axis is
Answer» The distance of a point (-5, 6) from the y- axis is

Discussion

1177.	Question 152 What will the following machine do to a 2 cm long piece of chalk ?
Answer» Question 152 What will the following machine do to a 2 cm long piece of chalk ?

1177.

Question 152 What will the following machine do to a 2 cm long piece of chalk ?

Answer»

Question 152

What will the following machine do to a 2 cm long piece of chalk ?

Discussion

1178.	Two solids of right cylindrical shape are 49 cm and 35 cm high and their base diameters are 16 cm, 14 cm respectively. Both are melted and moulded into a single cylinder, 56 cm high. Find its base diameter.
Answer» Two solids of right cylindrical shape are 49 cm and 35 cm high and their base diameters are 16 cm, 14 cm respectively. Both are melted and moulded into a single cylinder, 56 cm high. Find its base diameter.

Discussion

1179.	ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?
Answer» ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?

Discussion

1180.	If the medians of Δ ABC intersect at H, then ar(Δ ABF):ar(GHFC) is equal to
Answer» If the medians of $Δ A B C$ intersect at H, then ar $(Δ A B F) : a r (G H F C)$ is equal to

Discussion

1181.	The number of arcs that have to be drawn on ray BA so as to divide BC in the ratio of 2:3.5
Answer» The number of arcs that have to be drawn on ray BA so as to divide BC in the ratio of 2:3. 5

Discussion

1182.	If x=3-8, then x-1x2= ___________.
Answer» If $x = 3 - \sqrt{8}, then {(x - \frac{1}{x})}^{2} =___________.$

Discussion

1183.	Factorise each of the following: 64 a3 – 27 b3– 144 a2b + 108a b2
Answer» Factorise each of the following: 64 $a^{3}$ – 27 $b^{3}$ – 144 $a^{2}$ b + 108a $b^{2}$

Discussion

1184.	Question 2In the given figure, lines XY and MN intersect at O. If ∠POY=90∘ and a:b = 2:3, find c.
Answer» Question 2 In the given figure, lines XY and MN intersect at O. If $∠ P O Y = 90^{\circ}$ and a:b = 2:3, find c.

Discussion

1185.	An open cuboidal box has dimensions 25 cm×10 cm×25 cm. Find the cost of painting the box from outside if the painting cost is ₹ 2/cm2.
Answer» An open cuboidal box has dimensions $25 c m \times 10 c m \times 25 c m$ . Find the cost of painting the box from outside if the painting cost is ₹ $2 / c m^{2}$ .

Discussion

1186.	In the given figure, measures of some angles are given. Using the measures find the values of x, y, z.
Answer» In the given figure, measures of some angles are given. Using the measures find the values of x, y, z.

Discussion

1187.	The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.
Answer» The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

1187.

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

Answer»

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

Discussion

1188.	A triangular park ABC has sides 120 m, 80 m and 50 m. A gardener, Dhania has to put a fence all around it and also plant grass inside. The area required and the cost of fencing it with barbed wire at the rate of Rs. 20 per metre leaving a space 3 m wide for a gate on one side will be
Answer» A triangular park ABC has sides 120 m, 80 m and 50 m. A gardener, Dhania has to put a fence all around it and also plant grass inside. The area required and the cost of fencing it with barbed wire at the rate of Rs. 20 per metre leaving a space 3 m wide for a gate on one side will be

Discussion

1189.	Question 4Write True or False and justify your answer :ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then, ar (Δ BDE) = ar (Δ ABC).
Answer» Question 4 Write True or False and justify your answer : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then, ar ( $Δ$ BDE) = ar ( $Δ$ ABC).

Discussion

1190.	Check if x=4 and y=1 is a solution of 2x−3y=5?
Answer» Check if $x = 4$ and $y = 1$ is a solution of $2 x - 3 y = 5$ ?

Discussion

1191.	How to represent 3√3 on the number line? Also, write the steps.
Answer» How to represent 3√3 on the number line? Also, write the steps.

Discussion

1192.	Parth went to Coorg on a holiday. He wanted to make a tent using a canvas cloth and a few bamboo sticks as support. Initially, he made a sketch of the tent as shown in the figure. He wanted to make the tent as an exact replica of the sketch. So, he placed the bamboo stick DE parallel to the ground BC and AG perpendicular to the ground. Let’s analyse his sketch.In his sketch, Area of ΔADEArea of ΔABC=[1 mark]
Answer» Parth went to Coorg on a holiday. He wanted to make a tent using a canvas cloth and a few bamboo sticks as support. Initially, he made a sketch of the tent as shown in the figure. He wanted to make the tent as an exact replica of the sketch. So, he placed the bamboo stick DE parallel to the ground BC and AG perpendicular to the ground. Let’s analyse his sketch. In his sketch, $\frac{A r e a o f Δ A D E}{A r e a o f Δ A B C} =$ [1 mark]

Discussion

1193.	Find the mean salary of 60 workers of a factory from the following table:Salary in Rs.Number of workers3000164000125000106000870006800049000310,0001
Answer» Find the mean salary of $60$ workers of a factory from the following table: $\begin{matrix} Salary in Rs. & Number of workers 3000 & 16 4000 & 12 5000 & 10 6000 & 8 7000 & 6 8000 & 4 9000 & 3 10, 000 & 1 \end{matrix}$

1193.

Find the mean salary of 60 workers of a factory from the following table:Salary in Rs.Number of workers3000164000125000106000870006800049000310,0001

Answer»

Find the mean salary of $60$ workers of a factory from the following table:

$\begin{matrix} Salary in Rs. & Number of workers 3000 & 16 4000 & 12 5000 & 10 6000 & 8 7000 & 6 8000 & 4 9000 & 3 10, 000 & 1 \end{matrix}$

Discussion

1194.	Draw a line segment AB of length 8 cm and name its midpoint as M. Find the point which is 5 cm away from point B and equidistant from A and B. Name this point to be P. Then the length of PM is
Answer» Draw a line segment AB of length 8 cm and name its midpoint as M. Find the point which is 5 cm away from point B and equidistant from A and B. Name this point to be P. Then the length of PM is

Discussion

1195.	Interval of x in which f(x) is increasing is given by
Answer» Interval of $x$ in which $f (x)$ is increasing is given by

Discussion

1196.	In the given figure, prove that(i) CD + DA + AB > BC(ii) CD + DA + AB + BC > 2AC.
Answer» In the given figure, prove that (i) CD + DA + AB > BC (ii) CD + DA + AB + BC > 2AC.

Discussion

1197.	In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.
Answer» In the given figure, lengths of the chords $A B$ and $C D$ are $12 c m$ and $18 c m$ respectively and distance between them is $15 c m$ . Find the radius of the circle.

1197.

In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.

Answer»

In the given figure, lengths of the chords $A B$ and $C D$ are $12 c m$ and $18 c m$ respectively and distance between them is $15 c m$ . Find the radius of the circle.

Discussion

1198.	A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of Rs. 15 per litre and the cost of the metal sheet used, if it costs Rs. 5 per 100 cm2. (Take π= 3·14)
Answer» A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of Rs. 15 per litre and the cost of the metal sheet used, if it costs Rs. 5 per 100 $c m^{2}$ . (Take $π$ = 3·14)

Discussion

1199.	The sum of the angles in the four segments exterior to a cyclic quadrilateral is
Answer» The sum of the angles in the four segments exterior to a cyclic quadrilateral is

Discussion

1200.	Find the area of the equilateral triangle given below: Given: AD=10 cm.
Answer» Find the area of the equilateral triangle given below: Given: AD=10 cm.

1200.

Find the area of the equilateral triangle given below: Given: AD=10 cm.

Answer»

Find the area of the equilateral triangle given below:

Given: AD=10 cm.

Discussion

Explore topic-wise InterviewSolutions in .

If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is(a) a + b + c(b) (a − b) (b − c) (c − a)(c) 0(d) none of these

How many degrees are there in an angle which equals two-third of its complement?

Which of the following is Non terminating and Non repeating decimal ?

A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Question 3(vi)Factorise the expressionsy(y+z)+9(y+z)

Question 54 In a year, Ravi earns Rs. 360000 and paid Rs. 24000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.

In the given figure,AB || DC prove that(i) ∆DMU ∼ ∆BMV(ii) DM × BV = BM ✕ DU

Question 5How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?[Assume π=227]

Question 4 (iii)Name the quadrilateral whose diagonals:(iii) Are equal.

The sum of two numbers is 4 more than twice their difference. One of the two numbers is three more than the other number. Find the numbers.

ABDE is a trapezium​​​​​​ with AE∥BD and ED⊥BD. Also, AC is drawn parallel to the side DE.Find the values of cot θ and cosec θ, respectively, from the figure above.

47. While determining the volume of a sphere an error of 2% occured in measurement of radius. Determine the percentage error of the volume.

If the angle between the vectors A and B is theta, the value of the product ( B cross A)dot A is equal to1)BA^2.costheta2)BA^2.sintheta3)BA^2.sintheta.costheta4)Zero

ABCD is a parallelogram. E is a point on BA such That BE = 2 EA and F is a point on DC such that DF = 2FC. Prove that AECF is a parallelogram whose area is one third of the area of paralllelogram ABCD.

Find the area fo the triangle whose sides are 18 cm, 24 cm and 30 cm Also, find the height corresponding to the smallest side.

The factor of (x + y + z)3- (x3 + y3 + z) is

Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

Pair the addition and subtraction equations which belong to the same fact family.

Question 3 (i)A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.(i) How many students can sit in the tent, if a student on an average occupies 57m2 on the ground?

Victor is able to get work only for two hours in a day. Rest of the day, he is looking for work. Is he unemployed? Why? What kind of jobs could persons like Victor is doing?

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

Question 9 (ii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (ii) curved surface area of the cylinder.

The height of an equilateral triangle is 6 cm. Find its area. [Take √3 = 1.73.]

If →a is perpendicular to →b and →r is a non – zero vector such that p→r+(→r.→b)→a=→c, then →r is equal to

The distance of a point (-5, 6) from the y- axis is

Question 152 What will the following machine do to a 2 cm long piece of chalk ?

Two solids of right cylindrical shape are 49 cm and 35 cm high and their base diameters are 16 cm, 14 cm respectively. Both are melted and moulded into a single cylinder, 56 cm high. Find its base diameter.

ABC is a triangle in which E is mid-point of median AD. Which of the following is not true?

If the medians of Δ ABC intersect at H, then ar(Δ ABF):ar(GHFC) is equal to

The number of arcs that have to be drawn on ray BA so as to divide BC in the ratio of 2:3.5

If x=3-8, then x-1x2= ___________.

Factorise each of the following: 64 a3 – 27 b3– 144 a2b + 108a b2

Question 2In the given figure, lines XY and MN intersect at O. If ∠POY=90∘ and a:b = 2:3, find c.

An open cuboidal box has dimensions 25 cm×10 cm×25 cm. Find the cost of painting the box from outside if the painting cost is ₹ 2/cm2.

In the given figure, measures of some angles are given. Using the measures find the values of x, y, z.

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

A triangular park ABC has sides 120 m, 80 m and 50 m. A gardener, Dhania has to put a fence all around it and also plant grass inside. The area required and the cost of fencing it with barbed wire at the rate of Rs. 20 per metre leaving a space 3 m wide for a gate on one side will be

Question 4Write True or False and justify your answer :ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then, ar (Δ BDE) = ar (Δ ABC).

Check if x=4 and y=1 is a solution of 2x−3y=5?

How to represent 3√3 on the number line? Also, write the steps.

Find the mean salary of 60 workers of a factory from the following table:Salary in Rs.Number of workers3000164000125000106000870006800049000310,0001

Draw a line segment AB of length 8 cm and name its midpoint as M. Find the point which is 5 cm away from point B and equidistant from A and B. Name this point to be P. Then the length of PM is

Interval of x in which f(x) is increasing is given by

In the given figure, prove that(i) CD + DA + AB > BC(ii) CD + DA + AB + BC > 2AC.

In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.

The sum of the angles in the four segments exterior to a cyclic quadrilateral is

Find the area of the equilateral triangle given below: Given: AD=10 cm.

ABDE is a trapezium with AE∥BD and ED⊥BD. Also, AC is drawn parallel to the side DE.Find the values of cot θ and cosec θ, respectively, from the figure above.