24740 + Interview Questions in Mathematics Page 29 InterviewSolution

1401.	In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]
Answer» In Fig. AC = AE, AB = AD and $∠$ BAD = $∠$ EAC. Prove that BC = DE. [2 MARKS]

1401.

In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]

Answer»

In Fig. AC = AE, AB = AD and $∠$ BAD = $∠$ EAC. Prove that BC = DE.

[2 MARKS]

i12

1402.	In the given figure, if ABCD is a parallelogram of area 90 cm2. Then, ar(\|\|gm ABEF) = ________ ar(ΔABD) = _______ and ar(ΔBEF) = _________.
Answer» In the given figure, if ABCD is a parallelogram of area 90 cm². Then, ar(\|\|^gm ABEF) = ________ ar(ΔABD) = _______ and ar(ΔBEF) = _________.

Discussion

1403.	Question 2 (ii) Write True or False. Give reasons for your answers. (ii) A circle has only finite number of equal chords.
Answer» Question 2 (ii) Write True or False. Give reasons for your answers. (ii) A circle has only finite number of equal chords.

Discussion

1404.	Find the first three common multiples of:6 and 8
Answer» Find the first three common multiples of: 6 and 8

Discussion

1405.	ColumnAColumnB1.Areaa.67m2.Perimeterb.Rs.6/m23.Cost per m2c.100m2d.Rs.6m2e.100/m2 Which of the following options show the correct match of parameters in column A with possible values in column B?
Answer» $\begin{matrix} C o l u m n A & C o l u m n B 1. Area & a . 67 m 2. Perimeter & b . R s .6 / m^{2} 3. Cost per m^{2} & c . 100 m^{2} d . R s . 6 m^{2} e . 100 / m^{2} \end{matrix}$ Which of the following options show the correct match of parameters in column A with possible values in column B?

1405.

ColumnAColumnB1.Areaa.67m2.Perimeterb.Rs.6/m23.Cost per m2c.100m2d.Rs.6m2e.100/m2 Which of the following options show the correct match of parameters in column A with possible values in column B?

Answer»

$\begin{matrix} C o l u m n A & C o l u m n B 1. Area & a . 67 m 2. Perimeter & b . R s .6 / m^{2} 3. Cost per m^{2} & c . 100 m^{2} d . R s . 6 m^{2} e . 100 / m^{2} \end{matrix}$

Which of the following options show the correct match of parameters in column A with possible values in column B?

Discussion

1406.

Marks secured by 42 students in Economics are: Marks 15 20 22 23 27 35 18 Number of Students 8 4 7 3 8 7 5 Find average marks.

Answer» Marks secured by 42 students in Economics are:

Marks	15	20	22	23	27	35	18
Number of Students	8	4	7	3	8	7	5

Find average marks.

Discussion

1407.	Prove that:(i) xaxba2+ab+b2×xbxcb2+bc+c2×xcxac2+ca+a2=1(ii) xax-ba2-ab+b2×xbx-cb2-bc+c2×xcx-ac2-ca+a2=1(iii) xaxbc×xbxca×xcxab=1
Answer» Prove that: (i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$ (ii) ${(\frac{x^{a}}{x^{- b}})}^{a^{2} - a b + b^{2}} \times {(\frac{x^{b}}{x^{- c}})}^{b^{2} - b c + c^{2}} \times {(\frac{x^{c}}{x^{- a}})}^{c^{2} - c a + a^{2}} = 1$ (iii) ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

Discussion

1408.	The length, breadth and height of a cuboidal reservoir is 7 m,6 m and 15 m respectively. 8400 L of water is pumped out from the reservoir. Find the fall in the water level in the reservoir.
Answer» The length, breadth and height of a cuboidal reservoir is $7 m, 6 m$ and $15 m$ respectively. $8400$ L of water is pumped out from the reservoir. Find the fall in the water level in the reservoir.

Discussion

1409.	{ 3. If }\operatorname{tan}θ=y\operatorname{tan}ϕ and }\operatorname{sin}θ=x\operatorname{sin}ϕ , then the value of }}{\operatorname{cos}^2θ is }\lbrack x≠ y\rbrack
Answer» { 3. If }\operatorname{tan}θ=y\operatorname{tan}ϕ and }\operatorname{sin}θ=x\operatorname{sin}ϕ , then the value of }}{\operatorname{cos}^2θ is }\lbrack x≠ y\rbrack

Discussion

1410.	In the given figure, PQRS is a square of} side }4cm. PSR and QSR are two quadrants} of circles. Find the } area of the circle touching} a side and both the } quadrants.
Answer» In the given figure, PQRS is a square of} side }4cm. PSR and QSR are two quadrants} of circles. Find the } area of the circle touching} a side and both the } quadrants.

Discussion

1411.	Sum of (√7 − 3) and (√2 + 3)
Answer» Sum of (√7 − 3) and (√2 + 3)

Discussion

1412.	Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.
Answer» Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

1412.

Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

Answer»

Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

Discussion

1413.	In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.
Answer» In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

1413.

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

Answer»

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

Discussion

1414.	Evaluate:- (3x4)−2 × (x12)23
Answer» Evaluate:- $(3 x^{4})^{- 2} \times (x^{12})^{\frac{2}{3}}$

Discussion

1415.	Two adjacent sides of a parallelogram are 12 cm and 8 cm. If the height corresponding to the side 12 cm is 5 cm. Find the height corresponding to the other side.
Answer» Two adjacent sides of a parallelogram are 12 cm and 8 cm. If the height corresponding to the side 12 cm is 5 cm. Find the height corresponding to the other side.

Discussion

1416.	Question 1 (b) Given here are some figures: Classify each of them on the basis of the following. (b) Simple closed curve
Answer» Question 1 (b) Given here are some figures: Classify each of them on the basis of the following. (b) Simple closed curve

Discussion

1417.	Question 7 Express sin67∘+cos75∘ in terms of trigonometric ratios of angles between 0∘ and 45∘.
Answer» Question 7 Express $s i n 67^{\circ} + c o s 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$ .

Discussion

1418.	cos70∘sin20∘+cos59∘sin31∘−8sin230∘ is equal to0
Answer» $\frac{c o s 70^{\circ}}{s i n 20^{\circ}} + \frac{c o s 59^{\circ}}{s i n 31^{\circ}} - 8 s i n^{2} 30^{\circ}$ is equal to 0

Discussion

1419.	Draw a triangle and divide it into three triangles of equal area in various ways.
Answer» Draw a triangle and divide it into three triangles of equal area in various ways.

1419.

Draw a triangle and divide it into three triangles of equal area in various ways.

Answer»

Draw a triangle and divide it into three triangles of equal area in various ways.

Discussion

1420.	If X and Y are points X(2, -1) and Y(-3,-2) respectively , What are the coordinates of P such that XP=57XY ?
Answer» If X and Y are points X(2, -1) and Y(-3,-2) respectively , What are the coordinates of P such that $X P = \frac{5}{7} X Y ?$

Discussion

1421.	Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:ar(Δ APB) ✕ ar (Δ CPD) = ar (Δ APD) ✕ ar (Δ BPC)
Answer» Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that: ar(Δ APB) ✕ ar (Δ CPD) = ar (Δ APD) ✕ ar (Δ BPC)

Discussion

1422.	The ratio of the radious of the base of a cylinder to ots height is 7:6 . If the volume of th cylinderis 294 pii then its base diameter is 1)1cm2)14cm3)7cm4)12cm
Answer» The ratio of the radious of the base of a cylinder to ots height is 7:6 . If the volume of th cylinderis 294 pii then its base diameter is 1)1cm2)14cm3)7cm4)12cm

Discussion

1423.	Question 3Find five rational numbers between 35 and 45.
Answer» Question 3 Find five rational numbers between $\frac{3}{5} a n d \frac{4}{5}$ .

Discussion

1424.	While representing a whole number, the number line extends _______ .
Answer» While representing a whole number, the number line extends _______ .

Discussion

1425.	Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.
Answer» Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.

Discussion

1426.	Find the length of the diagonal of a square whose area is 128 cm2. Also, find its perimeter.
Answer» Find the length of the diagonal of a square whose area is 128 cm². Also, find its perimeter.

Discussion

1427.	Simplify: 164-63433+18×2435-196
Answer» Simplify: $\sqrt[4]{16} - 6 \sqrt[3]{343} + 18 \times \sqrt[5]{243} - \sqrt{196}$

Discussion

1428.	if 1 is the zero of the polynomial p(x)=ax^2-3(a-1)
Answer» if 1 is the zero of the polynomial p(x)=ax^2-3(a-1)

Discussion

1429.	The diameter of a garden roller is 1.4 m and it is 2 m long. Total area covered in 5 revolutions is
Answer» The diameter of a garden roller is 1.4 m and it is 2 m long. Total area covered in 5 revolutions is

Discussion

1430.	Write 19-1/2×(64)-1/3 as a rational number.
Answer» Write ${(\frac{1}{9})}^{- 1 / 2} \times (64)^{- 1 / 3}$ as a rational number.

Discussion

1431.	x+y=18 and x−2y=0 Find the value of x and y.
Answer» $x + y = 18 and x - 2 y = 0$ $Find the value of x and y .$

Discussion

1432.	In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Then:
Answer» In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Then:

Discussion

1433.	Diagonals of a quadrilateral ABCD bisect each other. If ∠A= 45°, then ∠B =(i) 115°(ii) 120°(iii) 125°(iv) 135°
Answer» Diagonals of a quadrilateral ABCD bisect each other. If ∠A= 45°, then ∠B = (i) 115° (ii) 120° (iii) 125° (iv) 135°

Discussion

1434.	The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.
Answer» The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

Discussion

1435.	If A = 60∘ and B = 30∘, find the value of (sinAcosB+cosAsinB)2+(cosAcosB−sinAsinB)2.
Answer» If A = $60^{\circ}$ and B = $30^{\circ}$ , find the value of $(sin A cos B + cos A sin B)^{2} + (cos A cos B - sin A sin B)^{2}$ .

Discussion

1436.	ΔABC∼ΔPQR. If ∠B of ΔABC and ∠R of ΔPQR are 60∘, then ∠ RPQ =
Answer» $Δ A B C \sim Δ P Q R$ . If $∠ B$ of $Δ A B C$ and $∠ R$ of $Δ P Q R$ are $60^{\circ}$ , then $∠$ RPQ =

Discussion

1437.	Question 19The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is (a) 124 cm2(b) 118 cm2(c) 128 cm2(d) 112 cm2
Answer» Question 19 The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is $(a) 124 c m^{2}$ $(b) 118 c m^{2}$ $(c) 128 c m^{2}$ $(d) 112 c m^{2}$

1437.

Question 19The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is (a) 124 cm2(b) 118 cm2(c) 128 cm2(d) 112 cm2

Answer»

Question 19

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

$(a) 124 c m^{2}$

$(b) 118 c m^{2}$

$(c) 128 c m^{2}$

$(d) 112 c m^{2}$

Discussion

1438.	Q-1 Find the remainder when 10^6 i s divided by 143 ?Q-2 Find the remainder When 5^100 is divided by 31 ?
Answer» Q-1 Find the remainder when 10^6 i s divided by 143 ? Q-2 Find the remainder When 5^100 is divided by 31 ?

Discussion

1439.	AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
Answer» AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that $∠ A$ > $∠ C$ and $∠ B$ > $∠ D$ .

Discussion

1440.	O is the centre of the circle. If ∠BAC= 50∘, find ∠OBC. ___
Answer» O is the centre of the circle. If $∠$ BAC= $50^{\circ}$ , find ∠OBC. ___

1440.

O is the centre of the circle. If ∠BAC= 50∘, find ∠OBC. ___

Answer»

O is the centre of the circle. If $∠$ BAC= $50^{\circ}$ , find ∠OBC.

___

Discussion

1441.	Which of the following statement is not true?
Answer» Which of the following statement is not true?

Discussion

1442.	Question 4 (ii)The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:Length (in mm)Number of leaves118−1263127−1355136−1449145−15312154−1625163−1714172−1802(ii) Is there any other suitable graphical representation for the same data?
Answer» Question 4 (ii) The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: $\begin{matrix} Length (in mm) & Number of leaves 118 - 126 & 3 127 - 135 & 5 136 - 144 & 9 145 - 153 & 12 154 - 162 & 5 163 - 171 & 4 172 - 180 & 2 \end{matrix}$ (ii) Is there any other suitable graphical representation for the same data?

Discussion

1443.	The length L is given by
Answer» The length L is given by

1443.

The length L is given by

Answer»

The length L is given by

Discussion

1444.	Classify the following polynomials as polynomials in one-variable, two variables etc.:(i) x2 − xy + 7y2(ii) x2 − 2tx + 7t2 − x + t(iii) t3 − 3t2 + 4t − 5(iv) xy + yz + zx
Answer» Classify the following polynomials as polynomials in one-variable, two variables etc.: (i) x² − xy + 7y² (ii) x² − 2tx + 7t² − x + t (iii) t³ − 3t² + 4t − 5 (iv) xy + yz + zx

Discussion

1445.	Check whether x4+3x3+3x2+x+1 has (x + 1) as a factor.
Answer» $Check whether x^{4} + 3 x^{3} + 3 x^{2} + x + 1 has (x + 1) as a factor.$

Discussion

1446.	Question 9 Find the area of the shaded region in figure.
Answer» Question 9 Find the area of the shaded region in figure.

Discussion

1447.	Express each number as a product of its prime factors 1.1561.3825
Answer» Express each number as a product of its prime factors 1.156 1.3825

Discussion

1448.	The distance between the foci of the ellipse 3x2 + 4y2 = 48 is ___________.
Answer» The distance between the foci of the ellipse 3x² + 4y² = 48 is ___________.

Discussion

1449.	In the given question, a part of a sentence is printed in bold. Below each sentence, some phrases are given which can substitute the bold part of the sentence. Find out the phrase which can correctly substitute that part of the sentence. If the sentence is correct as it is, mark the answer as 'No correction required' or 'No Improvement'. It will be no good trying to find an excuse every time.
Answer» In the given question, a part of a sentence is printed in bold. Below each sentence, some phrases are given which can substitute the bold part of the sentence. Find out the phrase which can correctly substitute that part of the sentence. If the sentence is correct as it is, mark the answer as 'No correction required' or 'No Improvement'. It will be no good trying to find an excuse every time.

1449.

In the given question, a part of a sentence is printed in bold. Below each sentence, some phrases are given which can substitute the bold part of the sentence. Find out the phrase which can correctly substitute that part of the sentence. If the sentence is correct as it is, mark the answer as 'No correction required' or 'No Improvement'. It will be no good trying to find an excuse every time.

Answer»

In the given question, a part of a sentence is printed in bold. Below each sentence, some phrases are given which can substitute the bold part of the sentence. Find out the phrase which can correctly substitute that part of the sentence. If the sentence is correct as it is, mark the answer as 'No correction required' or 'No Improvement'.

It will be no good trying to find an excuse every time.

Discussion

1450.	Sam's cubicle is exactly in the shape of a cube of side 6 m. If it is a closed cubicle, then the total surface area of the cubicle ignoring its thickness is _______.
Answer» Sam's cubicle is exactly in the shape of a cube of side 6 m. If it is a closed cubicle, then the total surface area of the cubicle ignoring its thickness is _______.

Discussion

Explore topic-wise InterviewSolutions in .

In Fig. AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE. [2 MARKS]

In the given figure, if ABCD is a parallelogram of area 90 cm2. Then, ar(||gm ABEF) = ________ ar(ΔABD) = _______ and ar(ΔBEF) = _________.

Question 2 (ii) Write True or False. Give reasons for your answers. (ii) A circle has only finite number of equal chords.

Find the first three common multiples of:6 and 8

ColumnAColumnB1.Areaa.67m2.Perimeterb.Rs.6/m23.Cost per m2c.100m2d.Rs.6m2e.100/m2 Which of the following options show the correct match of parameters in column A with possible values in column B?

Marks secured by 42 students in Economics are: Marks 15 20 22 23 27 35 18 Number of Students 8 4 7 3 8 7 5 Find average marks.

Prove that:(i) xaxba2+ab+b2×xbxcb2+bc+c2×xcxac2+ca+a2=1(ii) xax-ba2-ab+b2×xbx-cb2-bc+c2×xcx-ac2-ca+a2=1(iii) xaxbc×xbxca×xcxab=1

The length, breadth and height of a cuboidal reservoir is 7 m,6 m and 15 m respectively. 8400 L of water is pumped out from the reservoir. Find the fall in the water level in the reservoir.

{ 3. If }\operatorname{tan}θ=y\operatorname{tan}ϕ and }\operatorname{sin}θ=x\operatorname{sin}ϕ , then the value of }}{\operatorname{cos}^2θ is }\lbrack x≠ y\rbrack

In the given figure, PQRS is a square of} side }4cm. PSR and QSR are two quadrants} of circles. Find the } area of the circle touching} a side and both the } quadrants.

Sum of (√7 − 3) and (√2 + 3)

Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

Evaluate:- (3x4)−2 × (x12)23

Two adjacent sides of a parallelogram are 12 cm and 8 cm. If the height corresponding to the side 12 cm is 5 cm. Find the height corresponding to the other side.

Question 1 (b) Given here are some figures: Classify each of them on the basis of the following. (b) Simple closed curve

Question 7 Express sin67∘+cos75∘ in terms of trigonometric ratios of angles between 0∘ and 45∘.

cos70∘sin20∘+cos59∘sin31∘−8sin230∘ is equal to0

Draw a triangle and divide it into three triangles of equal area in various ways.

If X and Y are points X(2, -1) and Y(-3,-2) respectively , What are the coordinates of P such that XP=57XY ?

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:ar(Δ APB) ✕ ar (Δ CPD) = ar (Δ APD) ✕ ar (Δ BPC)

The ratio of the radious of the base of a cylinder to ots height is 7:6 . If the volume of th cylinderis 294 pii then its base diameter is 1)1cm2)14cm3)7cm4)12cm

Question 3Find five rational numbers between 35 and 45.

While representing a whole number, the number line extends _______ .

Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.

Find the length of the diagonal of a square whose area is 128 cm2. Also, find its perimeter.

Simplify: 164-63433+18×2435-196

if 1 is the zero of the polynomial p(x)=ax^2-3(a-1)

The diameter of a garden roller is 1.4 m and it is 2 m long. Total area covered in 5 revolutions is

Write 19-1/2×(64)-1/3 as a rational number.

x+y=18 and x−2y=0 Find the value of x and y.

In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Then:

Diagonals of a quadrilateral ABCD bisect each other. If ∠A= 45°, then ∠B =(i) 115°(ii) 120°(iii) 125°(iv) 135°

The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

If A = 60∘ and B = 30∘, find the value of (sinAcosB+cosAsinB)2+(cosAcosB−sinAsinB)2.

ΔABC∼ΔPQR. If ∠B of ΔABC and ∠R of ΔPQR are 60∘, then ∠ RPQ =

Question 19The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is (a) 124 cm2(b) 118 cm2(c) 128 cm2(d) 112 cm2

Q-1 Find the remainder when 10^6 i s divided by 143 ?Q-2 Find the remainder When 5^100 is divided by 31 ?

AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.

O is the centre of the circle. If ∠BAC= 50∘, find ∠OBC. ___

Which of the following statement is not true?

The length L is given by

Classify the following polynomials as polynomials in one-variable, two variables etc.:(i) x2 − xy + 7y2(ii) x2 − 2tx + 7t2 − x + t(iii) t3 − 3t2 + 4t − 5(iv) xy + yz + zx

Check whether x4+3x3+3x2+x+1 has (x + 1) as a factor.

Question 9 Find the area of the shaded region in figure.

Express each number as a product of its prime factors 1.1561.3825

The distance between the foci of the ellipse 3x2 + 4y2 = 48 is ___________.

Sam's cubicle is exactly in the shape of a cube of side 6 m. If it is a closed cubicle, then the total surface area of the cubicle ignoring its thickness is _______.

In the given figure, if ABCD is a parallelogram of area 90 cm2. Then, ar(||gm ABEF) = ____ ar(ΔABD) = _ and ar(ΔBEF) = _______.