24740 + Interview Questions in Mathematics Page 99 InterviewSolution

4901.	Question 10Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).
Answer» Question 10 Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Discussion

4902.	The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Answer» The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per $m^{2}$ per year. A company hired one of its walls for 3 months. How much rent did it pay?

Discussion

4903.	You had a certain number of chocolates. (You don't know the number of chocolates) If you receive the same number of chocolates from your friend and another friend gives you thrice the number of chocolates you initially had, which of the following can represent the number of chocolates you have in all now ?
Answer» You had a certain number of chocolates. (You don't know the number of chocolates) If you receive the same number of chocolates from your friend and another friend gives you thrice the number of chocolates you initially had, which of the following can represent the number of chocolates you have in all now ?

Discussion

4904.	55. A rectangle with sides of lengths (2n-1) and (2m- 1) units is divided into squares of unit length. Find thenumber of rectangles which can be formed with sides of odd length.
Answer» 55. A rectangle with sides of lengths (2n-1) and (2m- 1) units is divided into squares of unit length. Find thenumber of rectangles which can be formed with sides of odd length.

Discussion

4905.	Question 14A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.
Answer» Question 14 A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.

Discussion

4906.	In a triangle ABC, AB=AC. Show that the altitude AD is median also.
Answer» In a triangle ABC, AB=AC. Show that the altitude AD is median also.

Discussion

4907.	What is the area of an equilateral triangle whose side is 8 cm?
Answer» What is the area of an equilateral triangle whose side is 8 cm?

Discussion

4908.	Find the percentage increase in the area of a triangle if it's each side is doubled. Explain in details how the answer came.
Answer» Find the percentage increase in the area of a triangle if it's each side is doubled. Explain in details how the answer came.

Discussion

4909.	In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following option is correct?
Answer» In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following option is correct?

Discussion

4910.	Why is (5ˣ + 5ˣ) an even number? Why is (7ˣ -3ˣ) divisible by 4?
Answer» Why is (5ˣ + 5ˣ) an even number? Why is (7ˣ -3ˣ) divisible by 4?

Discussion

4911.	A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m find the cost of painting it on the outside at the rate of Rs. 10 per m2
Answer» A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m find the cost of painting it on the outside at the rate of Rs. 10 per $m^{2}$

Discussion

4912.	Question 129(ii)The table shows the mass of the planets, the Sun and the Moon in our solar system.Order the planets and the Moon by mass, from least to greatest.
Answer» Question 129(ii) The table shows the mass of the planets, the Sun and the Moon in our solar system. Order the planets and the Moon by mass, from least to greatest.

4912.

Question 129(ii)The table shows the mass of the planets, the Sun and the Moon in our solar system.Order the planets and the Moon by mass, from least to greatest.

Answer»

Question 129(ii)

The table shows the mass of the planets, the Sun and the Moon in our solar system.

Order the planets and the Moon by mass, from least to greatest.

Discussion

4913.	If l, m, n are three lines such that l \|\| m and n ⊥ l. prove that n ⊥ m.
Answer» If l, m, n are three lines such that l \|\| m and n $⊥$ l. prove that n $⊥$ m.

Discussion

4914.	The side of a trianglular park are 8m,10m and 6m respectively. A small circular area of diameter 2m is to be left out and the remaining area is to be used for growing roses. How much area is used for growing roses use(π=3.14)
Answer» The side of a trianglular park are 8m,10m and 6m respectively. A small circular area of diameter 2m is to be left out and the remaining area is to be used for growing roses. How much area is used for growing roses use(π=3.14)

Discussion

4915.	In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is(a) 10(b) 12(c) 13(d) 14
Answer» In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is (a) 10 (b) 12 (c) 13 (d) 14

Discussion

4916.	Question 14After rationalizing the denominator of 73√3−2√2, we get the denominator as A) 13B) 19C) 5D) 35
Answer» Question 14 After rationalizing the denominator of $\frac{7}{3 \sqrt{3} - 2 \sqrt{2}}$ , we get the denominator as A) 13 B) 19 C) 5 D) 35

Discussion

4917.	For what condition does the pair of equations −3x + py + 10 = 0 and 4x + 4y + 17 = 0 represents a pair of intersecting lines?
Answer» For what condition does the pair of equations −3x + py + 10 = 0 and 4x + 4y + 17 = 0 represents a pair of intersecting lines?

Discussion

4918.	Find the area of a rhombus, one of whose sides is 25 cm & one of whose diagonals is 48 cm.
Answer» Find the area of a rhombus, one of whose sides is 25 cm & one of whose diagonals is 48 cm.

Discussion

4919.	Find the value of k if x – 3 is the factor of P(x) = x2–2x−k.
Answer» Find the value of k if x – 3 is the factor of P(x) = $x^{2} - 2 x - k$ .

Discussion

4920.	35. P is an interior point of triangle ABC. AP,BP,CP when produced meet the sides at D,E,F respectively.If BD=2DC and AE=3EC then (1) AP:PD = (2) BP:PE = (3) CP:PF =
Answer» 35. P is an interior point of triangle ABC. AP,BP,CP when produced meet the sides at D,E,F respectively.If BD=2DC and AE=3EC then (1) AP:PD = (2) BP:PE = (3) CP:PF =

Discussion

4921.	Given a △ABF in which BE=EF, BD=DE and BC=CD. Area of △ABF=64 sq. units. Find the area of △ABC
Answer» Given a $△ A B F$ in which $B E = E F, B D = D E$ and $B C = C D$ . Area of $△ A B F = 64$ sq. units. Find the area of $△ A B C$

4921.

Given a △ABF in which BE=EF, BD=DE and BC=CD. Area of △ABF=64 sq. units. Find the area of △ABC

Answer»

Given a $△ A B F$ in which $B E = E F, B D = D E$ and $B C = C D$ . Area of $△ A B F = 64$ sq. units.

Find the area of $△ A B C$

Discussion

4922.	Find the LCM and HCF of 336, 54 and verify that LCM × HCF = product of the two numbers.
Answer» Find the LCM and HCF of 336, 54 and verify that LCM $\times$ HCF = product of the two numbers.

Discussion

4923.	Out of the following fractions, Find the smallest and the greatest fractions. 12,63,45,32,34
Answer» Out of the following fractions, Find the smallest and the greatest fractions. $\frac{1}{2}, \frac{6}{3}, \frac{4}{5}, \frac{3}{2}, \frac{3}{4}$

Discussion

4924.	Question 1 (iii)Evaluate :cos48∘−sin42∘
Answer» Question 1 (iii) Evaluate : $c o s 48^{\circ} - s i n 42^{\circ}$

Discussion

4925.	The radius of a sphere of volume 113.04 cm3 is
Answer» The radius of a sphere of volume 113.04 cm³is

Discussion

4926.	Find the area of the shaded region from the figure given below:
Answer» Find the area of the shaded region from the figure given below:

4926.

Find the area of the shaded region from the figure given below:

Answer»

Find the area of the shaded region from the figure given below:

Discussion

4927.	If p cotθ = √q2−p2, then the value of sinθ is ___. (θ being an acute angle).
Answer» If $p c o t θ$ = $\sqrt{q^{2} - p^{2}}$ , then the value of $s i n θ$ is ___. ( $θ$ being an acute angle).

Discussion

4928.	Question 5E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
Answer» Question 5 E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Discussion

4929.	Question 6 (iii)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(iii) DA \|\| CB or ABCD is a parallelogram.
Answer» Question 6 (iii) In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (iii) DA \|\| CB or ABCD is a parallelogram.

Discussion

4930.	Two equal chords, AB and CD are at a distance of 10 cm from each other. Find the distance of chord AB from the centre.
Answer» Two equal chords, $A B$ and $C D$ are at a distance of 10 cm from each other. Find the distance of chord $A B$ from the centre.

Discussion

4931.	In Δ ABC, AC = 15 cm and DE∥ BC. If ABAD=3, find EC.
Answer» In $Δ$ ABC, AC = 15 cm and DE $∥$ BC. If $\frac{A B}{A D} = 3$ , find EC.

Discussion

4932.	Question 21 Fill in the blanks to make each statement true: Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................
Answer» Question 21 Fill in the blanks to make each statement true: Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................

4932.

Question 21 Fill in the blanks to make each statement true: Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................

Answer»

Question 21

Fill in the blanks to make each statement true:

Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................

Discussion

4933.	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

4934.	Draw an equilateral triangle with side 6.5 cm.
Answer» Draw an equilateral triangle with side 6.5 cm.

Discussion

4935.	Ordinate of all points on the y-axis is(a) 0(b) 1(c) 2(d) any number
Answer» Ordinate of all points on the y-axis is (a) 0 (b) 1 (c) 2 (d) any number

Discussion

4936.	Question 12Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.
Answer» Question 12 Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.

Discussion

4937.	The productof (x+7y)(7x-y) is
Answer» The productof (x+7y)(7x-y) is

Discussion

4938.	Pythagoras was a student of(i) Euclid(ii) Thales(iii) Archimedes(iv) Bhaskara
Answer» Pythagoras was a student of (i) Euclid (ii) Thales (iii) Archimedes (iv) Bhaskara

Discussion

4939.	Say True of False: (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.
Answer» Say True of False: (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.

4939.

Say True of False: (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.

Answer»

Say True
of False:

(a) Each
angle of a rectangle is a right angle.

(b) The
opposite sides of a rectangle are equal in length.

(c) The
diagonals of a square are perpendicular to one another.

(d) All
the sides of a rhombus are of equal length.

(e) All
the sides of a parallelogram are of equal length.

(f) The
opposite sides of a trapezium are parallel.

Discussion

4940.	The bisectors of two adjacent sides of a parallelogram ABCD meet at a point P inside the parallelogram. The angle made by these bisectors at point P is ____________.
Answer» The bisectors of two adjacent sides of a parallelogram ABCD meet at a point P inside the parallelogram. The angle made by these bisectors at point P is ____________.

Discussion

4941.

Given Below is the Receipts and Payments Account of a Mayur Club for the year ended 31st March , 2018: RECEIPTS AND PAYMENTS ACCOUNT Dr. Cr. Receipts Amount (₹) Payments Amount (₹) To Balance b/d By Salaries 60,000 To Subscriptions: By Expenses 7,500 2016-17 4,000 By Drama Expenses 45,000 2017-18 2,05,000 By Newspapers 15,000 2018-19 6,000 2,15,000 By Municipal Taxes 4,000 To Donations 54,000 By Charity 35,000 To Proceeds of Drama Tickets 95,000 By Investments 2,00,000 To Sale of Waste Paper 4,500 By Electricity Charges 14,500 By Balance c/d 90,000 4,71,000 4,71,000 Prepare club's Income and Expenditure Account for the year ended 31st March , 2018 and Balance Sheet as at that date after taking the following information into account:(i) There are 500 members, each paying an annual subscription of ₹ 500, ₹ 5,000 are still in arrears for the year ended 31st March, 2017.(ii) Municipal Taxes amounted to ₹ 4,000 per year is paid up to 30th June and ₹5,000 are outstanding of salaries.(iii) Building stands in the books at ₹ 5,00,000.(iv) 6% interest has accrued on investments for five months.

Answer» Given Below is the Receipts and Payments Account of a Mayur Club for the year ended 31st March , 2018:

RECEIPTS AND PAYMENTS ACCOUNT
Dr.				Cr.
Receipts		Amount (₹)	Payments	Amount (₹)
To Balance b/d			By Salaries	60,000
To Subscriptions:			By Expenses	7,500
2016-17	4,000		By Drama Expenses	45,000
2017-18	2,05,000		By Newspapers	15,000
2018-19	6,000	2,15,000	By Municipal Taxes	4,000
To Donations		54,000	By Charity	35,000
To Proceeds of Drama Tickets		95,000	By Investments	2,00,000
To Sale of Waste Paper		4,500	By Electricity Charges	14,500
			By Balance c/d	90,000

		4,71,000		4,71,000

Prepare club's Income and Expenditure Account for the year ended 31st March , 2018 and Balance Sheet as at that date after taking the following information into account:

(i) There are 500 members, each paying an annual subscription of ₹ 500, ₹ 5,000 are still in arrears for the year ended 31st March, 2017.

(ii) Municipal Taxes amounted to ₹ 4,000 per year is paid up to 30th June and ₹5,000 are outstanding of salaries.

(iii) Building stands in the books at ₹ 5,00,000.

(iv) 6% interest has accrued on investments for five months.

Discussion

4942.	A random survey of the number of children of various age groups playing in park was found as follows: Age (in years)Number of children1−252−333−565−7127−10910−151015−174 Draw a histogram to represent the data above. [4 MARKS]
Answer» A random survey of the number of children of various age groups playing in park was found as follows: $\begin{matrix} A g e (i n y e a r s) & N u m b e r o f c h i l d r e n 1 - 2 & 5 2 - 3 & 3 3 - 5 & 6 5 - 7 & 12 7 - 10 & 9 10 - 15 & 10 15 - 17 & 4 \end{matrix}$ Draw a histogram to represent the data above. [4 MARKS]

Discussion

4943.	A number ′x′was found to be represented in the simplest pq form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.
Answer» A number $^{'} x^{'}$ was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

Discussion

4944.	A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Answer» A suitcase with measures 80 cm $\times$ 48 cm $\times$ 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?

Discussion

4945.	4yz(z2+6z−16)÷2y(z+8) gives
Answer» $4 y z (z^{2} + 6 z - 16) \div 2 y (z + 8)$ gives

Discussion

4946.	L and M are the midpoints of sides AB and DC respectively of parallelogram ABCD prove that segments DL and BM trisect diagonal AC.
Answer» L and M are the midpoints of sides AB and DC respectively of parallelogram ABCD prove that segments DL and BM trisect diagonal AC.

Discussion

4947.	To prove that the sum of angles of hexagon is 720 degree
Answer» To prove that the sum of angles of hexagon is 720 degree

Discussion

4948.	What is the area of an equilateral triangle whose side is 8 cm?
Answer» What is the area of an equilateral triangle whose side is $8 cm$ ?

Discussion

4949.	Given 3 points with position vectors ¯p1,¯p2 and ¯p3 which form the vertices of a triangle with side lengths a=\|¯p2−¯p1\|,b=\|¯p3−¯p2\|,c=\|¯p1−¯p3\|. Then the in-centre is given by
Answer» Given 3 points with position vectors $_{1},_{2} a n d_{3}$ which form the vertices of a triangle with side lengths $a = \|_{2} -_{1} \|, b = \|_{3} -_{2} \|, c = \|_{1} -_{3} \|$ . Then the in-centre is given by

Discussion

4950.

Question 5 (i) It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel of 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find (i) Inner curved surface area of the vessel. [Assume π=227]

Answer»

Question 5 (i)
It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel of 10 m deep. If the cost of painting is at the rate of $R s 20 p e r m^{2}$ , find

(i) Inner curved surface area of the vessel.

$[A s s u m e π = \frac{22}{7}]$

Discussion

Explore topic-wise InterviewSolutions in .

Question 10Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

55. A rectangle with sides of lengths (2n-1) and (2m- 1) units is divided into squares of unit length. Find thenumber of rectangles which can be formed with sides of odd length.

Question 14A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.

In a triangle ABC, AB=AC. Show that the altitude AD is median also.

What is the area of an equilateral triangle whose side is 8 cm?

Find the percentage increase in the area of a triangle if it's each side is doubled. Explain in details how the answer came.

In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following option is correct?

Why is (5ˣ + 5ˣ) an even number? Why is (7ˣ -3ˣ) divisible by 4?

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m find the cost of painting it on the outside at the rate of Rs. 10 per m2

Question 129(ii)The table shows the mass of the planets, the Sun and the Moon in our solar system.Order the planets and the Moon by mass, from least to greatest.

If l, m, n are three lines such that l || m and n ⊥ l. prove that n ⊥ m.

The side of a trianglular park are 8m,10m and 6m respectively. A small circular area of diameter 2m is to be left out and the remaining area is to be used for growing roses. How much area is used for growing roses use(π=3.14)

In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is(a) 10(b) 12(c) 13(d) 14

Question 14After rationalizing the denominator of 73√3−2√2, we get the denominator as A) 13B) 19C) 5D) 35

For what condition does the pair of equations −3x + py + 10 = 0 and 4x + 4y + 17 = 0 represents a pair of intersecting lines?

Find the area of a rhombus, one of whose sides is 25 cm &amp; one of whose diagonals is 48 cm.

Find the value of k if x – 3 is the factor of P(x) = x2–2x−k.

35. P is an interior point of triangle ABC. AP,BP,CP when produced meet the sides at D,E,F respectively.If BD=2DC and AE=3EC then (1) AP:PD = (2) BP:PE = (3) CP:PF =

Given a △ABF in which BE=EF, BD=DE and BC=CD. Area of △ABF=64 sq. units. Find the area of △ABC

Find the LCM and HCF of 336, 54 and verify that LCM × HCF = product of the two numbers.

Out of the following fractions, Find the smallest and the greatest fractions. 12,63,45,32,34

Question 1 (iii)Evaluate :cos48∘−sin42∘

The radius of a sphere of volume 113.04 cm3 is

Find the area of the shaded region from the figure given below:

If p cotθ = √q2−p2, then the value of sinθ is ___. (θ being an acute angle).

Question 5E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Question 6 (iii)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(iii) DA || CB or ABCD is a parallelogram.

Two equal chords, AB and CD are at a distance of 10 cm from each other. Find the distance of chord AB from the centre.

In Δ ABC, AC = 15 cm and DE∥ BC. If ABAD=3, find EC.

Question 21 Fill in the blanks to make each statement true: Three consecutive numbers whose sum is 12 are ......................, ......................., and ........................

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

Draw an equilateral triangle with side 6.5 cm.

Ordinate of all points on the y-axis is(a) 0(b) 1(c) 2(d) any number

Question 12Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.

The productof (x+7y)(7x-y) is

Pythagoras was a student of(i) Euclid(ii) Thales(iii) Archimedes(iv) Bhaskara

The bisectors of two adjacent sides of a parallelogram ABCD meet at a point P inside the parallelogram. The angle made by these bisectors at point P is ____________.

A random survey of the number of children of various age groups playing in park was found as follows: Age (in years)Number of children1−252−333−565−7127−10910−151015−174 Draw a histogram to represent the data above. [4 MARKS]

A number ′x′was found to be represented in the simplest pq form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?

4yz(z2+6z−16)÷2y(z+8) gives

L and M are the midpoints of sides AB and DC respectively of parallelogram ABCD prove that segments DL and BM trisect diagonal AC.

To prove that the sum of angles of hexagon is 720 degree

What is the area of an equilateral triangle whose side is 8 cm?

Given 3 points with position vectors ¯p1,¯p2 and ¯p3 which form the vertices of a triangle with side lengths a=|¯p2−¯p1|,b=|¯p3−¯p2|,c=|¯p1−¯p3|. Then the in-centre is given by

Question 5 (i) It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel of 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find (i) Inner curved surface area of the vessel. [Assume π=227]

Find the area of a rhombus, one of whose sides is 25 cm & one of whose diagonals is 48 cm.