24740 + Interview Questions in Mathematics Page 81 InterviewSolution

4001.	Question 195Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
Answer» Question 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

Discussion

4002.	The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone.(Use π = 3.14).
Answer» The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use $π = 3.14$ ).

Discussion

4003.	In the given figure, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.
Answer» In the given figure, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.

Discussion

4004.	If rxy = 0 the variable X and Y are(i) linearly related(ii) not linearly related(iii) independent
Answer» If r_xy= 0 the variable X and Y are (i) linearly related (ii) not linearly related (iii) independent

4004.

If rxy = 0 the variable X and Y are(i) linearly related(ii) not linearly related(iii) independent

Answer»

If r_xy= 0 the variable X and Y are

(i) linearly related

(ii) not linearly related

(iii) independent

Discussion

4005.	Particle executive shm along y axis has its motion described by the equation y=2+10sin5 πt amplitude of shm is
Answer» Particle executive shm along y axis has its motion described by the equation y=2+10sin5 πt amplitude of shm is

Discussion

4006.	What value of x will satisfy the given equation:x×cos(a)×cos(90∘−a)×tan(90∘−a)×sec(a)×cosec(a)×tan(a)=1
Answer» What value of $x$ will satisfy the given equation: $x \times c o s (a) \times c o s (90^{\circ} - a) \times t a n (90^{\circ} - a) \times s e c (a) \times c o s e c (a) \times t a n (a) = 1$

4006.

What value of x will satisfy the given equation:x×cos(a)×cos(90∘−a)×tan(90∘−a)×sec(a)×cosec(a)×tan(a)=1

Answer»

What value of $x$ will satisfy the given equation:

$x \times c o s (a) \times c o s (90^{\circ} - a) \times t a n (90^{\circ} - a) \times s e c (a) \times c o s e c (a) \times t a n (a) = 1$

Discussion

4007.	Find the mean of the factors of 12.
Answer» Find the mean of the factors of 12.

Discussion

4008.	A rectangular sheet of paper 40 cm×44 cm is rolled to form a hollow cylinder of height 40 cm. Find the diameter of the cylinder.
Answer» A rectangular sheet of paper $40 c m \times 44 c m$ is rolled to form a hollow cylinder of height 40 cm. Find the diameter of the cylinder.

Discussion

4009.	how to factorise x^3-6 x^2+11x-6 could u explain it in brief?
Answer» how to factorise x^3-6 x^2+11x-6 could u explain it in brief?

Discussion

4010.	Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=3x4-6x2-8x-2, gx=x-2.
Answer» Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where $p (x) = 3 x^{4} - 6 x^{2} - 8 x - 2, g (x) = x - 2$ .

Discussion

4011.	Question 8Find the values of x and y in the following rectangle.
Answer» Question 8 Find the values of x and y in the following rectangle.

Discussion

4012.	In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.[π=227]
Answer» In a hot water heating system, there is a cylindrical pipe of length $28 m$ and diameter $5 c m$ . Find the total radiating surface in the system. [ $π = \frac{22}{7}$ ]

Discussion

4013.	Read the following paragraph and answer the questions. The angle of elevation of a tower of height h from the eye of two observers A and B on the same side of the tower are α and β. respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then, The distance between the two persons is
Answer» Read the following paragraph and answer the questions. The angle of elevation of a tower of height h from the eye of two observers A and B on the same side of the tower are $α$ and $β$ . respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then, The distance between the two persons is

Discussion

4014.	Find the mode of the following data in each case: (i) 14,25,14,28,18,17,18,14,23,22,14,18 (ii)7,9,12,13,7,12,15,7,12,7,25,18,7
Answer» Find the mode of the following data in each case: (i) 14,25,14,28,18,17,18,14,23,22,14,18 (ii)7,9,12,13,7,12,15,7,12,7,25,18,7

4014.

Find the mode of the following data in each case: (i) 14,25,14,28,18,17,18,14,23,22,14,18 (ii)7,9,12,13,7,12,15,7,12,7,25,18,7

Answer»

Find the mode of the following data in each case:

(i) 14,25,14,28,18,17,18,14,23,22,14,18

(ii)7,9,12,13,7,12,15,7,12,7,25,18,7

Discussion

4015.	The area of \|\|gm ABCD is(a) AB × BM(b) BC × BN(c) DC × DL(d) AD × DL
Answer» The area of \|\|gm ABCD is (a) AB × BM (b) BC × BN (c) DC × DL (d) AD × DL

Discussion

4016.	Fill In the Blanks If each obsevation of the data is increased by 5, then their mean is _____________ by 5.
Answer» Fill In the Blanks If each obsevation of the data is increased by 5, then their mean is _____________ by 5.

Discussion

4017.	In Fig. 88 PR is a straight line and ∠PQS : ∠SQR = 7 : 5. The measure of ∠SQR is(a) 60°(b) 6212°(c) 6712°(d) 75°
Answer» In Fig. 88 PR is a straight line and ∠PQS : ∠SQR = 7 : 5. The measure of ∠SQR is (a) 60° (b) ${(62 \frac{1}{2})}^{°}$ (c) ${(67 \frac{1}{2})}^{°}$ (d) 75°

Discussion

4018.	In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).
Answer» In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).

Discussion

4019.	If a:b=c:d=e:f=2:1, then (a+2c+3e):(5b+10d+15f) is equal to:
Answer» If $a : b = c : d = e : f = 2 : 1$ , then $(a + 2 c + 3 e) : (5 b + 10 d + 15 f)$ is equal to:

Discussion

4020.

The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years: Year 1960-61 1970-71 1980-81 1990-91 2000-2001 Route length (in thousand km) 56 60 61 74 98 Represent the above data with the help of a bar graph.

Answer» The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:

Year	1960-61	1970-71	1980-81	1990-91	2000-2001
Route length (in thousand km)	56	60	61	74	98

Represent the above data with the help of a bar graph.

Discussion

4021.	What is the difference between basic proportionality theorem and mid point theorem?
Answer» What is the difference between basic proportionality theorem and mid point theorem?

Discussion

4022.	The bisectors of any two adjacent angles of a parallelogram intersect at
Answer» The bisectors of any two adjacent angles of a parallelogram intersect at

Discussion

4023.	Which of the following rational numbers does not lie between 711 and 1113?
Answer» Which of the following rational numbers does not lie between $\frac{7}{11}$ and $\frac{11}{13}$ ?

Discussion

4024.	The area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6) is
Answer» The area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6) is

Discussion

4025.	In the given figure,l \|\| m in and a transversal t cuts them. If ∠7=80∘, find the measure of each of the remaining marked angles.
Answer» In the given figure,l \|\| m in and a transversal t cuts them. If $∠ 7 = 80^{\circ}$ , find the measure of each of the remaining marked angles.

4025.

In the given figure,l || m in and a transversal t cuts them. If ∠7=80∘, find the measure of each of the remaining marked angles.

Answer»

In the given figure,l || m in and a transversal t cuts them. If $∠ 7 = 80^{\circ}$ , find the measure of each of the remaining marked angles.

Discussion

4026.	Simplify each of the following:(i) (x+3)3 + (x−3)3(ii) x2+y33-x2-y33(iii) x+2x3+x-2x3(iv) (2x − 5y)3 − (2x + 5y)3
Answer» Simplify each of the following: (i) (x+3)³ + (x−3)³ (ii) ${(\frac{x}{2} + \frac{y}{3})}^{3} - {(\frac{x}{2} - \frac{y}{3})}^{3}$ (iii) ${(x + \frac{2}{x})}^{3} + {(x - \frac{2}{x})}^{3}$ (iv) (2x − 5y)³ − (2x + 5y)³

Discussion

4027.	Factorization of x2−10x+25 is equal to
Answer» Factorization of $x^{2} - 10 x + 25$ is equal to

Discussion

4028.	In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?
Answer» In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?

Discussion

4029.	Which of the following is always irrational?
Answer» Which of the following is always irrational?

Discussion

4030.	The percentage error in the measurement of three radius of a sphere is 1.5% what would be the percentage error in the volume of the sphere
Answer» The percentage error in the measurement of three radius of a sphere is 1.5% what would be the percentage error in the volume of the sphere

Discussion

4031.	Represent √2.9 on a number line
Answer» Represent √2.9 on a number line

Discussion

4032.	Use a suitable identity to get each of the following products: (x2+3y4)(x2+3y4)
Answer» Use a suitable identity to get each of the following products: $(\frac{x}{2} + \frac{3 y}{4}) (\frac{x}{2} + \frac{3 y}{4})$

Discussion

4033.	If α and β are the zeros of the polynomial f(x)=x2−5x+k such that α−β=1, find the value of k.
Answer» If $α$ and $β$ are the zeros of the polynomial $f (x) = x^{2} - 5 x + k$ such that $α - β = 1$ , find the value of k.

Discussion

4034.	A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 cm3, find the total surface area of the cone. (Take π = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.
Answer» A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 ${c m}^{3}$ , find the total surface area of the cone. (Take $π$ = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.

Discussion

4035.	Show that g(x) is a factor of f(x), wheref(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Answer» Show that g(x) is a factor of f(x), where f(x) = 2x³ − 9x² + x + 12, g(x) = 3 − 2x

4035.

Show that g(x) is a factor of f(x), wheref(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x

Answer»

Show that g(x) is a factor of f(x), where

f(x) = 2x³ − 9x² + x + 12, g(x) = 3 − 2x

Discussion

4036.	Variables allow us to express many common rules and relations in
Answer» Variables allow us to express many common rules and relations in

Discussion

4037.	If in a triangle ABC the altitude from the vertices A,B,C on opposite sides are in HP then sin A Sin B sin C are in
Answer» If in a triangle ABC the altitude from the vertices A,B,C on opposite sides are in HP then sin A Sin B sin C are in

Discussion

4038.	The correct factorise form of (x−y)3−8x3 is _______
Answer» The correct factorise form of $(x - y)^{3} - 8 x^{3}$ is _______

Discussion

4039.	The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is(a) 9(b) 10(c) 18(d0 20
Answer» The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is (a) 9 (b) 10 (c) 18 (d0 20

Discussion

4040.	What is the value of 2√8 + 2√18 ?
Answer» What is the value of $\sqrt[2]{8}$ + $\sqrt[2]{18}$ ?

Discussion

4041.	2y2+y-45
Answer» 2y²+y-45

Discussion

4042.	The value of (5+√7)(2+√5) is
Answer» The value of $(5 + \sqrt{7}) (2 + \sqrt{5})$ is

Discussion

4043.	In the given figure, ABCDEFG is a regular polygon. The measure of 7(∠EOD+∠FOG) is equal to
Answer» In the given figure, ABCDEFG is a regular polygon. The measure of $7 (∠ E O D + ∠ F O G)$ is equal to

Discussion

4044.	In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD ⊥ PQ and OE ⊥ RS. If ∠DOE=130∘, then ∠PDE = ___.
Answer» In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $⊥$ PQ and OE $⊥$ RS. If $∠ D O E = 130^{\circ},$ then $∠ P D E$ = ___.

4044.

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD ⊥ PQ and OE ⊥ RS. If ∠DOE=130∘, then ∠PDE = ___.

Answer»

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD $⊥$ PQ and OE $⊥$ RS. If $∠ D O E = 130^{\circ},$ then $∠ P D E$ = ___.

Discussion

4045.	8x3 + y3 + 12x2y + 6xy2
Answer» 8x³ + y³ + 12x²y + 6xy²

Discussion

4046.

Without Goods and Services Tax (GST)Record the following transactions in Double Columns Cash Book and balance the book on 31st March, 2018: 2018 ₹ March 1 Cash in Hand 12,750 Cash at Bank 72,400 March 4 Received from Asha cash ₹ 1,200 and a cheque for ₹ 3,200, allowed discount ₹ 400 March 7 Paid salary to staff by cheque 25,600 March 9 Withdrawn cash from bank for office use 21,900 March 12 Interest paid by bank for office use 1,200 March 16 Purchased furniture in cash 16,500 March 21 Paid Mohan & Co. by cheque, discount received ₹100 10,900 March 24 Proprietor withdrew from office cash for his personal use 11,600 March 29 Sold goods to Manoj for cash 14,800 March 31 Deposited office cash into bank 21,200

Answer» Without Goods and Services Tax (GST)

Record the following transactions in Double Columns Cash Book and balance the book on 31st March, 2018:

2018		₹
March 1	Cash in Hand	12,750
	Cash at Bank	72,400
March 4	Received from Asha cash ₹ 1,200 and a cheque for ₹ 3,200, allowed discount ₹ 400
March 7	Paid salary to staff by cheque	25,600
March 9	Withdrawn cash from bank for office use	21,900
March 12	Interest paid by bank for office use	1,200
March 16	Purchased furniture in cash	16,500
March 21	Paid Mohan & Co. by cheque, discount received ₹100	10,900
March 24	Proprietor withdrew from office cash for his personal use	11,600
March 29	Sold goods to Manoj for cash	14,800
March 31	Deposited office cash into bank	21,200

Discussion

4047.	By contradiction method we can also prove \surd4 is a irrational number . But as we know \surd4 is a rational number . Explain why this occur or happen .
Answer» By contradiction method we can also prove \surd4 is a irrational number . But as we know \surd4 is a rational number . Explain why this occur or happen .

Discussion

4048.	Solve the following system of linear equation by any method:A. (a-b)x + (a+b)y = a²-2ab-b² (a+b)x + (a+b)y = a²+b² (using only cross-multiplication method)B. ax - by = a²+b² x - y = 2bC. x/a + y/b = a+b x/a² + y/b² = 2D. x + y = a+b ax - by = a²-b²E. x/a + y/b = 2 ax - by = a² - b²
Answer» Solve the following system of linear equation by any method: A. (a-b)x + (a+b)y = a²-2ab-b² (a+b)x + (a+b)y = a²+b² (using only cross-multiplication method) B. ax - by = a²+b² x - y = 2b C. x/a + y/b = a+b x/a² + y/b² = 2 D. x + y = a+b ax - by = a²-b² E. x/a + y/b = 2 ax - by = a² - b²

Discussion

4049.	Which of the following figures illustrates the angle of elevation and the angle of depression from the same point?
Answer» Which of the following figures illustrates the angle of elevation and the angle of depression from the same point?

Discussion

4050.	Question 14Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC∼ΔPQR.
Answer» Question 14 Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that $Δ A B C \sim Δ P Q R$ .

Discussion

Explore topic-wise InterviewSolutions in .

Question 195Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone.(Use π = 3.14).

In the given figure, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.

If rxy = 0 the variable X and Y are(i) linearly related(ii) not linearly related(iii) independent

Particle executive shm along y axis has its motion described by the equation y=2+10sin5 πt amplitude of shm is

What value of x will satisfy the given equation:x×cos(a)×cos(90∘−a)×tan(90∘−a)×sec(a)×cosec(a)×tan(a)=1

Find the mean of the factors of 12.

A rectangular sheet of paper 40 cm×44 cm is rolled to form a hollow cylinder of height 40 cm. Find the diameter of the cylinder.

how to factorise x^3-6 x^2+11x-6 could u explain it in brief?

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=3x4-6x2-8x-2, gx=x-2.

Question 8Find the values of x and y in the following rectangle.

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.[π=227]

Find the mode of the following data in each case: (i) 14,25,14,28,18,17,18,14,23,22,14,18 (ii)7,9,12,13,7,12,15,7,12,7,25,18,7

The area of ||gm ABCD is(a) AB × BM(b) BC × BN(c) DC × DL(d) AD × DL

Fill In the Blanks If each obsevation of the data is increased by 5, then their mean is _____________ by 5.

In Fig. 88 PR is a straight line and ∠PQS : ∠SQR = 7 : 5. The measure of ∠SQR is(a) 60°(b) 6212°(c) 6712°(d) 75°

In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).

If a:b=c:d=e:f=2:1, then (a+2c+3e):(5b+10d+15f) is equal to:

The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years: Year 1960-61 1970-71 1980-81 1990-91 2000-2001 Route length (in thousand km) 56 60 61 74 98 Represent the above data with the help of a bar graph.

What is the difference between basic proportionality theorem and mid point theorem?

The bisectors of any two adjacent angles of a parallelogram intersect at

Which of the following rational numbers does not lie between 711 and 1113?

The area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6) is

In the given figure,l || m in and a transversal t cuts them. If ∠7=80∘, find the measure of each of the remaining marked angles.

Simplify each of the following:(i) (x+3)3 + (x−3)3(ii) x2+y33-x2-y33(iii) x+2x3+x-2x3(iv) (2x − 5y)3 − (2x + 5y)3

Factorization of x2−10x+25 is equal to

In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?

Which of the following is always irrational?

The percentage error in the measurement of three radius of a sphere is 1.5% what would be the percentage error in the volume of the sphere

Represent √2.9 on a number line

Use a suitable identity to get each of the following products: (x2+3y4)(x2+3y4)

If α and β are the zeros of the polynomial f(x)=x2−5x+k such that α−β=1, find the value of k.

Show that g(x) is a factor of f(x), wheref(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x

Variables allow us to express many common rules and relations in

If in a triangle ABC the altitude from the vertices A,B,C on opposite sides are in HP then sin A Sin B sin C are in

The correct factorise form of (x−y)3−8x3 is _______

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is(a) 9(b) 10(c) 18(d0 20

What is the value of 2√8 + 2√18 ?

2y2+y-45

The value of (5+√7)(2+√5) is

In the given figure, ABCDEFG is a regular polygon. The measure of 7(∠EOD+∠FOG) is equal to

In the adjoining figure, O is the centre of the circle and PQ, RS are its equal chords, OD ⊥ PQ and OE ⊥ RS. If ∠DOE=130∘, then ∠PDE = ___.

8x3 + y3 + 12x2y + 6xy2

By contradiction method we can also prove \surd4 is a irrational number . But as we know \surd4 is a rational number . Explain why this occur or happen .

Solve the following system of linear equation by any method:A. (a-b)x + (a+b)y = a²-2ab-b² (a+b)x + (a+b)y = a²+b² (using only cross-multiplication method)B. ax - by = a²+b² x - y = 2bC. x/a + y/b = a+b x/a² + y/b² = 2D. x + y = a+b ax - by = a²-b²E. x/a + y/b = 2 ax - by = a² - b²

Which of the following figures illustrates the angle of elevation and the angle of depression from the same point?

Question 14Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC∼ΔPQR.