32581 + Interview Questions in Mathematics Page 145 InterviewSolution

7201.	The perimeter of a rectangle is 20cm and the difference between its length and breadth is 4cm.Find the length and breadth of the rectangle.
Answer» The perimeter of a rectangle is 20cm and the difference between its length and breadth is 4cm. Find the length and breadth of the rectangle.

Discussion

7202.	The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β. Prove that the height of the cloud is h(tanβ+tanα)(tanβ−tanα) metres [4 MARKS]
Answer» The angle of elevation of a cloud from a point h metres above a lake is $α$ and the angle of depression of its reflection in the lake is $β$ . Prove that the height of the cloud is $\frac{h (t a n β + t a n α)}{(t a n β - t a n α)} m e t r e s$ [4 MARKS]

Discussion

7203.	The decimal expansion of 141120 will terminate after how many places?
Answer» The decimal expansion of $\frac{141}{120}$ will terminate after how many places?

Discussion

7204.	The sequence of squares of odd natural numbers is ___
Answer» The sequence of squares of odd natural numbers is ___

Discussion

7205.	Find the value of a and b so that the polynomial x^3-4x^2+ax+b is exactly divisible by x-2 as well as x+1?
Answer» Find the value of a and b so that the polynomial x^3-4x^2+ax+b is exactly divisible by x-2 as well as x+1?

Discussion

7206.	Sum of the probabilities of all the outcomes in an experiment is ___.
Answer» Sum of the probabilities of all the outcomes in an experiment is ___.

Discussion

7207.	Subtract (ap+bq-cr) from (a+b+c)(p+q+r) .
Answer» Subtract (ap+bq-cr) from (a+b+c)(p+q+r) .

Discussion

7208.	Let three points P(3,2,−1),Q(1,3,4) and R(2,1,−2) and the distance of point P from the plane OQR is d. Then 3d+3=(Where O is the origin)
Answer» Let three points $P (3, 2, - 1), Q (1, 3, 4)$ and $R (2, 1, - 2)$ and the distance of point $P$ from the plane $O Q R$ is $d .$ Then $3 d + 3 =$ $($ Where $O$ is the origin $)$

Discussion

7209.	In the given figure, AB is the diameter of the circle. Find the value of ∠ ACD
Answer» In the given figure, AB is the diameter of the circle. Find the value of $∠$ ACD

7209.

In the given figure, AB is the diameter of the circle. Find the value of ∠ ACD

Answer»

In the given figure, AB is the diameter of the circle. Find the value of $∠$ ACD

Discussion

7210.	Question 1 (i)In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine:(i) sin A, cos A
Answer» Question 1 (i) In $Δ$ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine: (i) sin A, cos A

Discussion

7211.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then find the common difference of the AP.
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then find the common difference of the AP.

Discussion

7212.	Find the slopes m1 and m2 of the straight lines y=3x−2 and x+3y+5=0Calculate m1⋅m2What do you perceive?
Answer» Find the slopes $m_{1}$ and $m_{2}$ of the straight lines $y = 3 x - 2$ and $x + 3 y + 5 = 0$ Calculate $m_{1} \cdot m_{2}$ What do you perceive?

Discussion

7213.	Question 3A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. Age (in years)Number of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100
Answer» Question 3 A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. $\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

7213.

Question 3A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. Age (in years)Number of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100

Answer»

Question 3

A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

Discussion

7214.	A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm, respectively. Find the cost of metal sheet used to make the container, if it costs ₹10 per 100 cm2. [CBSE 2013]
Answer» A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm, respectively. Find the cost of metal sheet used to make the container, if it costs ₹10 per 100 cm². [CBSE 2013]

Discussion

7215.	In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at(1) 8.(2) an odd number.(3) a number greater than 2.(4) a number less than 9
Answer» In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at (1) 8. (2) an odd number. (3) a number greater than 2. (4) a number less than 9

Discussion

7216.	is the cubic polynomial whose zeroes are 2, - 3 and 4.
Answer» is the cubic polynomial whose zeroes are 2, - 3 and 4.

Discussion

7217.	In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, then x =(a) 10 (b) 9 (c) 8 (d) 7 [CBSE 2014]
Answer» In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, then x = (a) 10 (b) 9 (c) 8 (d) 7 [CBSE 2014]

Discussion

7218.	What is the value of cot θ in the given right triangle?
Answer» What is the value of cot $θ$ in the given right triangle?

7218.

What is the value of cot θ in the given right triangle?

Answer»

What is the value of cot $θ$ in the given right triangle?

Discussion

7219.	There are 7 girls in a class room. Ashwini is one of them. In how many ways a committee of 5 be formed so as to exclude Ashwini?
Answer» There are 7 girls in a class room. Ashwini is one of them. In how many ways a committee of 5 be formed so as to exclude Ashwini?

Discussion

7220.	If p, q are prime positive integers, prove that p+q is an irrational number.
Answer» If p, q are prime positive integers, prove that $\sqrt{p} + \sqrt{q}$ is an irrational number.

Discussion

7221.	In figure, AC = 13 cm, BC = 12 cm, then sec θ equals :
Answer» In figure, AC = 13 cm, BC = 12 cm, then sec θ equals :

7221.

In figure, AC = 13 cm, BC = 12 cm, then sec θ equals :

Answer»

In figure, AC = 13 cm, BC = 12 cm, then sec θ equals :

Discussion

7222.	6. prove that: 1+sin2A/cos2A=cosA+sinA/cosA-sinA
Answer» 6. prove that: 1+sin2A/cos2A=cosA+sinA/cosA-sinA

Discussion

7223.	Question 4 (ii) Find the value(s) of p for the following pair of equations – x + py = 1 and px – y = 1, if the pair of equations has no solution.
Answer» Question 4 (ii) Find the value(s) of p for the following pair of equations – x + py = 1 and px – y = 1, if the pair of equations has no solution.

Discussion

7224.	In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,· then find the perimeter of the top of the table. [CBSE 2012]
Answer» In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,· then find the perimeter of the top of the table. [CBSE 2012]

Discussion

7225.	In the adjoining figure AD bisects ∠A. Arrange AB, BD, and DC in the descending order of their heights.
Answer» In the adjoining figure AD bisects ∠A. Arrange AB, BD, and DC in the descending order of their heights.

Discussion

7226.

The marks scored by 60 students in a mathematics test are given below. Marks (X) 10 20 30 40 50 60 No. of students (f) 8 12 20 10 7 3 Find the Variance and Standard Deviation of the marks.

Answer»

The marks scored by 60 students in a mathematics test are given below.

Marks (X)	10	20	30	40	50	60
No. of students (f)	8	12	20	10	7	3

Find the Variance and Standard Deviation of the marks.

Discussion

7227.	Tap on the cake which has been divided into equal parts.
Answer» Tap on the cake which has been divided into equal parts.

Discussion

7228.	Question 1 (i) Sides of a triangle are given below. Determine whether it forms a right triangle? In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm
Answer» Question 1 (i) Sides of a triangle are given below. Determine whether it forms a right triangle? In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm

Discussion

7229.	A factory manufactures 120,000 pencils daily The pencils are cylindrical in shape each of length 25cm and circumference of base is 1.5cm. Determine the cost of colouring the curved surfaces of the pencils manufatured in one day at Rs.0.05 per dm2.
Answer» A factory manufactures 120,000 pencils daily The pencils are cylindrical in shape each of length 25cm and circumference of base is 1.5cm. Determine the cost of colouring the curved surfaces of the pencils manufatured in one day at Rs.0.05 per $d m^{2}$ .

Discussion

7230.	9. obtain all zeroes of x*3-7x+6 if one of its zeroes is 1.
Answer» 9. obtain all zeroes of x*3-7x+6 if one of its zeroes is 1.

Discussion

7231.

Ram, Mohan, Sohan and Hari were partners in a firm sharing profits in the ratio of 4 : 3 : 2 : 1. On 1st April, 2016, their Balance Sheet was as follows: BALANCE SHEET OF RAM, MOHAN, SOHAN AND HARI as on 1st April, 2016 Liabilities ₹ Assets ₹ Capital A/cs: Fixed Assets 9,00,000 Ram 4,00,000 Current Assets 5,20,000 Mohan 4,50,000 Sohan 2,50,000 Hari 2,00,000 13,00,000 Workmen Compensation Reserve 1,20,000 14,20,000 14,20,000 From the above date, the partners decided to share the future profits in the ratio of 1 : 2 : 3 : 4. For this purpose the goodwill of the firm was valued at ₹ 1,80,000. The partners also agreed for the following:(a) The Claim for workmen compensation has been estimated at ₹ 1,50,000.(b) Adjust the capitals of the partners according to the new profit-sharing ratio by opening Partners' Current Accounts.Prepare Revaluation Account, Partners' Capital Accounts and the Balance Sheet of the reconstituted firm.

Answer» Ram, Mohan, Sohan and Hari were partners in a firm sharing profits in the ratio of 4 : 3 : 2 : 1. On 1st April, 2016, their Balance Sheet was as follows:

BALANCE SHEET OF RAM, MOHAN, SOHAN AND HARI as on 1st April, 2016
Liabilities		₹	Assets	₹
Capital A/cs:			Fixed Assets	9,00,000
Ram	4,00,000		Current Assets	5,20,000
Mohan	4,50,000
Sohan	2,50,000
Hari	2,00,000	13,00,000
Workmen Compensation Reserve		1,20,000



		14,20,000		14,20,000

From the above date, the partners decided to share the future profits in the ratio of 1 : 2 : 3 : 4. For this purpose the goodwill of the firm was valued at ₹ 1,80,000. The partners also agreed for the following:(a) The Claim for workmen compensation has been estimated at ₹ 1,50,000.

(b) Adjust the capitals of the partners according to the new profit-sharing ratio by opening Partners' Current Accounts.

Prepare Revaluation Account, Partners' Capital Accounts and the Balance Sheet of the reconstituted firm.

Discussion

7232.	Question 9 (iii)Solve the following pair of equations4x+6y=15, 6x−8y=14
Answer» Question 9 (iii) Solve the following pair of equations $4 x + \frac{6}{y} = 15, 6 x - \frac{8}{y} = 14$

Discussion

7233.	ABCD and AECF are two parallelograms and side EF is parallel to AD. Suppose AF and DE meets X and BF,CE meet at Y, then prove that XY is parallel to AB.
Answer» ABCD and AECF are two parallelograms and side EF is parallel to AD. Suppose AF and DE meets X and BF,CE meet at Y, then prove that XY is parallel to AB.

Discussion

7234.	The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age .Age below (in years) : 30 40 50 60 70 80 Number of persons: 100 220 350 750 950 1000
Answer» The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age . Age below (in years) : 30 40 50 60 70 80 Number of persons: 100 220 350 750 950 1000

Discussion

7235.	If A and B are square matrices of order n, such that \|A\|=2 and \|B\|=1, then the value of \|2A\|\|3B\| is
Answer» If $A$ and $B$ are square matrices of order $n,$ such that $\| A \| = 2$ and $\| B \| = 1,$ then the value of $\| 2 A \| \| 3 B \|$ is

Discussion

7236.	Let A and B are square matrices of order 2, such that \|A\|=6 and \|B\|=5. If the value of \|3A\|\|4B\|=α, then the value of α144 is
Answer» Let $A$ and $B$ are square matrices of order $2,$ such that $\| A \| = 6$ and $\| B \| = 5.$ If the value of $\| 3 A \| \| 4 B \| = α,$ then the value of $\frac{α}{144}$ is

Discussion

7237.	The coordinates of the point whose ordinate is –4 and which lies on y-axis, are ___________.
Answer» The coordinates of the point whose ordinate is –4 and which lies on y-axis, are ___________.

Discussion

7238.	A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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» A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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

7239.	In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.
Answer» In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

Discussion

7240.	A , B are any non empty sets and n(A) = n(B) can A ,B are equal sets ?Justify?
Answer» A , B are any non empty sets and n(A) = n(B) can A ,B are equal sets ?Justify?

Discussion

7241.	From the given histogram find the cumulative frequency for the class interval 40-50 ?
Answer» From the given histogram find the cumulative frequency for the class interval 40-50 ?

7241.

From the given histogram find the cumulative frequency for the class interval 40-50 ?

Answer»

From the given histogram find the cumulative frequency for the class interval 40-50 ?

Discussion

7242.	7.P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.
Answer» 7.P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.

Discussion

7243.	The relation R = {(x, x13):x is a natural number less than 1000}. Find range such that all the elements of the range are integers.
Answer» The relation R = {(x, $x^{\frac{1}{3}}$ ):x is a natural number less than 1000}. Find range such that all the elements of the range are integers.

Discussion

7244.	Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Answer» Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

7244.

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

Answer»

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

Discussion

7245.	Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The difference between the sum of 5 consecutive odd numbers and 4 consecutive even numbers is
Answer» Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The difference between the sum of 5 consecutive odd numbers and 4 consecutive even numbers is

Discussion

7246.	Simplify and solve the following linear equation.3(t−3)=5(2t+1)
Answer» Simplify and solve the following linear equation. $3 (t - 3) = 5 (2 t + 1)$

Discussion

7247.	If one root of the equation x2+px+12=0~is~4,while the equation x2+px+q=0 has equal roots, the value of q is
Answer» If one root of the equation $x^{2} + p x + 12 = 0$ ~is~4,while the equation $x^{2} + p x + q = 0$ has equal roots, the value of q is

7247.

If one root of the equation x2+px+12=0~is~4,while the equation x2+px+q=0 has equal roots, the value of q is

Answer»

If one root of the equation $x^{2} + p x + 12 = 0$ ~is~4,while the equation

$x^{2} + p x + q = 0$ has equal roots, the value of q is

Discussion

7248.	AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed.Prove that Area (∆ADE) : Area (∆ABC) = 3 : 4.
Answer» AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (∆ADE) : Area (∆ABC) = 3 : 4.

Discussion

7249.	21x + 47y = 11047x + 21y = 162
Answer» 21x + 47y = 110 47x + 21y = 162

Discussion

7250.	Find two irrational numbers between 2 and 3,
Answer» Find two irrational numbers between $2$ and $3$ ,

Discussion

Explore topic-wise InterviewSolutions in .

The perimeter of a rectangle is 20cm and the difference between its length and breadth is 4cm.Find the length and breadth of the rectangle.

The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β. Prove that the height of the cloud is h(tanβ+tanα)(tanβ−tanα) metres [4 MARKS]

The decimal expansion of 141120 will terminate after how many places?

The sequence of squares of odd natural numbers is ___

Find the value of a and b so that the polynomial x^3-4x^2+ax+b is exactly divisible by x-2 as well as x+1?

Sum of the probabilities of all the outcomes in an experiment is ___.

Subtract (ap+bq-cr) from (a+b+c)(p+q+r) .

Let three points P(3,2,−1),Q(1,3,4) and R(2,1,−2) and the distance of point P from the plane OQR is d. Then 3d+3=(Where O is the origin)

In the given figure, AB is the diameter of the circle. Find the value of ∠ ACD

Question 1 (i)In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine:(i) sin A, cos A

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then find the common difference of the AP.

Find the slopes m1 and m2 of the straight lines y=3x−2 and x+3y+5=0Calculate m1⋅m2What do you perceive?

A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm, respectively. Find the cost of metal sheet used to make the container, if it costs ₹10 per 100 cm2. [CBSE 2013]

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at(1) 8.(2) an odd number.(3) a number greater than 2.(4) a number less than 9

is the cubic polynomial whose zeroes are 2, - 3 and 4.

In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, then x =(a) 10 (b) 9 (c) 8 (d) 7 [CBSE 2014]

What is the value of cot θ in the given right triangle?

There are 7 girls in a class room. Ashwini is one of them. In how many ways a committee of 5 be formed so as to exclude Ashwini?

If p, q are prime positive integers, prove that p+q is an irrational number.

In figure, AC = 13 cm, BC = 12 cm, then sec θ equals :

6. prove that: 1+sin2A/cos2A=cosA+sinA/cosA-sinA

Question 4 (ii) Find the value(s) of p for the following pair of equations – x + py = 1 and px – y = 1, if the pair of equations has no solution.

In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,· then find the perimeter of the top of the table. [CBSE 2012]

In the adjoining figure AD bisects ∠A. Arrange AB, BD, and DC in the descending order of their heights.

The marks scored by 60 students in a mathematics test are given below. Marks (X) 10 20 30 40 50 60 No. of students (f) 8 12 20 10 7 3 Find the Variance and Standard Deviation of the marks.

Tap on the cake which has been divided into equal parts.

Question 1 (i) Sides of a triangle are given below. Determine whether it forms a right triangle? In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm

A factory manufactures 120,000 pencils daily The pencils are cylindrical in shape each of length 25cm and circumference of base is 1.5cm. Determine the cost of colouring the curved surfaces of the pencils manufatured in one day at Rs.0.05 per dm2.

9. obtain all zeroes of x*3-7x+6 if one of its zeroes is 1.

Question 9 (iii)Solve the following pair of equations4x+6y=15, 6x−8y=14

ABCD and AECF are two parallelograms and side EF is parallel to AD. Suppose AF and DE meets X and BF,CE meet at Y, then prove that XY is parallel to AB.

The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age .Age below (in years) : 30 40 50 60 70 80 Number of persons: 100 220 350 750 950 1000

If A and B are square matrices of order n, such that |A|=2 and |B|=1, then the value of |2A||3B| is

Let A and B are square matrices of order 2, such that |A|=6 and |B|=5. If the value of |3A||4B|=α, then the value of α144 is

The coordinates of the point whose ordinate is –4 and which lies on y-axis, are ___________.

A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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.

In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

A , B are any non empty sets and n(A) = n(B) can A ,B are equal sets ?Justify?

From the given histogram find the cumulative frequency for the class interval 40-50 ?

7.P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.

The relation R = {(x, x13):x is a natural number less than 1000}. Find range such that all the elements of the range are integers.

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

Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The difference between the sum of 5 consecutive odd numbers and 4 consecutive even numbers is

Simplify and solve the following linear equation.3(t−3)=5(2t+1)

If one root of the equation x2+px+12=0~is~4,while the equation x2+px+q=0 has equal roots, the value of q is

AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed.Prove that Area (∆ADE) : Area (∆ABC) = 3 : 4.

21x + 47y = 11047x + 21y = 162

Find two irrational numbers between 2 and 3,