24740 + Interview Questions in Mathematics Page 131 InterviewSolution

6501.	Prove that 3+52 is an irrational number, given that 2 is an irrational number.
Answer» Prove that $(3 + 5 \sqrt{2})$ is an irrational number, given that $\sqrt{2}$ is an irrational number.

Discussion

6502.	Which one of the following is not the graphical representation of statistical data: (a) Bar graph (b) Histogram (c) Frequency polygon (d) Cumulative frequency distribution
Answer» Which one of the following is not the graphical representation of statistical data: (a) Bar graph (b) Histogram (c) Frequency polygon (d) Cumulative frequency distribution

6502.

Which one of the following is not the graphical representation of statistical data: (a) Bar graph (b) Histogram (c) Frequency polygon (d) Cumulative frequency distribution

Answer»

Which one of the following is not the graphical representation of statistical data:

(a) Bar graph

(b) Histogram

(c) Frequency polygon

(d) Cumulative frequency distribution

Discussion

6503.	In triangle ABC, right angled at B, if one angle is 45∘, find the value of sin A and cos C, without using the table.
Answer» In triangle ABC, right angled at B, if one angle is $45^{\circ}$ , find the value of sin A and cos C, without using the table.

Discussion

6504.	In Δ ABC if ∠A = ∠B, then
Answer» In Δ ABC if ∠A = ∠B, then

6504.

In Δ ABC if ∠A = ∠B, then

Answer»

In Δ ABC if ∠A = ∠B, then

Discussion

6505.	Two different families A and B are blessed with equal number of children. There are 3 tickects to be distributed among the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 112, then the number of children in each family is :
Answer» Two different families A and B are blessed with equal number of children. There are 3 tickects to be distributed among the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $\frac{1}{12}$ , then the number of children in each family is :

Discussion

6506.	If 1176=2a×3b×7c,find the values of a,b and c. Hence,compute the value of 2a×3b×7−c as a fraction.
Answer» If $1176=2a×3b×7c,find the values of a,b and c. Hence,compute the value of 2a×3b×7−c as a fraction.$

Discussion

6507.	From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.
Answer» From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

Discussion

6508.	Which of the following is the image of z- axis in the plane x+y-2z+1=0. (A) x=y=2(z-2) (B) x=y=-2(z+2) (C) x=y=1-2z (D) x=y= 1+2z
Answer» Which of the following is the image of z- axis in the plane x+y-2z+1=0. (A) x=y=2(z-2) (B) x=y=-2(z+2) (C) x=y=1-2z (D) x=y= 1+2z

Discussion

6509.	In the above figure, ∠p+∠q= .
Answer» In the above figure, $∠ p + ∠ q =$ .

Discussion

6510.	What is the linear equation obtained by adding 7 to both sides of the equation 3x - 7 = 5x + 2 and then transposing 5x to left hand side of the equation?
Answer» What is the linear equation obtained by adding 7 to both sides of the equation 3x - 7 = 5x + 2 and then transposing 5x to left hand side of the equation?

Discussion

6511.	If the given figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm. AE = 8 cm and CF = 10 cm, find AD.
Answer» If the given figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm. AE = 8 cm and CF = 10 cm, find AD.

Discussion

6512.	In figure AC=XD, C is the mid point of AB and D is the mid point of XY.Show that AB=XY
Answer» In figure AC=XD, C is the mid point of AB and D is the mid point of XY.Show that AB=XY

Discussion

6513.	What is the minimum number of measurements required to construct a unique parallelogram? ___
Answer» What is the minimum number of measurements required to construct a unique parallelogram? ___

Discussion

6514.	Expand.(1) (5x − 7) (5x − 9)(2) (2x − 3y)3(3) (a + 12)3
Answer» Expand. (1) (5x − 7) (5x − 9) (2) (2x − 3y)³ (3) (a + $\frac{1}{2}$ )³

Discussion

6515.	The factorized form of a3 + b3 + 3ab – 1 is ____________.
Answer» The factorized form of a³ + b³ + 3ab – 1 is ____________.

Discussion

6516.	The polynomial , x6 + 64y6 on factorization gives _____________.
Answer» The polynomial , x⁶ + 64y⁶ on factorization gives _____________.

Discussion

6517.	In △ABC, if (a−b)2cos2C2+(a+b)2sin2C2=mc2. The value of m is
Answer» In $△ A B C,$ if $(a - b)^{2} {cos}^{2} \frac{C}{2} + (a + b)^{2} {sin}^{2} \frac{C}{2} = m c^{2}$ . The value of m is

Discussion

6518.	In the following figure, a circle with centre O is drawn and ∠BAC = 50°. Find x.
Answer» In the following figure, a circle with centre O is drawn and ∠BAC = 50°. Find x.

Discussion

6519.	Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.
Answer» Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

Discussion

6520.	For any sets A and B, show that P(A∩B)=P(A)∩P(B).
Answer» For any sets $A$ and $B$ , show that $P (A \cap B) = P (A) \cap P (B)$ .

Discussion

6521.	In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =
Answer» In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

6521.

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

Answer»

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

Discussion

6522.	Prove that two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of other triangle.
Answer» Prove that two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of other triangle.

Discussion

6523.	the equation of a straight line equally inclined to the axis and equidistant from the points (1,-2) and (3,4) is
Answer» the equation of a straight line equally inclined to the axis and equidistant from the points (1,-2) and (3,4) is

Discussion

6524.	Question 11 (vi)In ΔABC and ΔDEF, AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that ΔABC≅ΔDEF .
Answer» Question 11 (vi) In $Δ A B C$ and $Δ D E F$ , AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that $Δ A B C ≅ Δ D E F$ .

Discussion

6525.	26. p=\sqrt{}-1 then (1-p) whole to the power 20 value
Answer» 26. p=\sqrt{}-1 then (1-p) whole to the power 20 value

Discussion

6526.	What are two types of irrational number explain in brief.
Answer» What are two types of irrational number explain in brief.

Discussion

6527.

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. Section Number of girls per thousand boys Scheduled Caste (SC) Scheduled Tribe (ST) Non SC/ST Backward districts Non-backward districts Rural Urban 940 970 920 950 920 930 910 (i) Represent the information above by a bar graph.(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Answer»

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.

Section

Number of girls per thousand boys

Scheduled Caste (SC)

Scheduled Tribe (ST)

Non SC/ST

Backward districts

Non-backward districts

Rural

Urban

940

970

920

950

920

930

910

(i) Represent the information above by a bar graph.

(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Discussion

6528.	What is the location of 1-√2 on number line?
Answer» What is the location of 1-√2 on number line?

Discussion

6529.	Draw the graph of the linear equation whose solutions are represented by the points having sum of coordinates as 10 units.
Answer» Draw the graph of the linear equation whose solutions are represented by the points having sum of coordinates as 10 units.

Discussion

6530.	AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Figure). Show that the line PQ is perpendicular bisector of AB.
Answer» AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Figure). Show that the line PQ is perpendicular bisector of AB.

Discussion

6531.	Using the given graph which of the following could be the equation of line L2.
Answer» Using the given graph which of the following could be the equation of line $L_{2}$ .

6531.

Using the given graph which of the following could be the equation of line L2.

Answer»

Using the given graph which of the following could be the equation of line $L_{2}$ .

Discussion

6532.	Line AB \|\| CD and transversal XY meets AB at M and CD at N. If ∠AMX=x and ∠CNX=2x−60, then x= .
Answer» Line AB \|\| CD and transversal XY meets AB at M and CD at N. If $∠ A M X = x and ∠ C N X = 2 x - 60$ , then $x =$ .

Discussion

6533.	Factorize:x^2+6x+9-25^2
Answer» Factorize: x^2+6x+9-25^2

Discussion

6534.	How many coins of radius 1 cm and thickness 0.28 cm should be melted to form a soild cylinder of height 7 cm and diameter 8 cm.
Answer» How many coins of radius 1 cm and thickness 0.28 cm should be melted to form a soild cylinder of height 7 cm and diameter 8 cm.

Discussion

6535.	Find median of following data: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Answer» Find median of following data: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Discussion

6536.	If a line angles α, β, γ with positive directions of the coordinate axes, then the value of sin2 α + sin2 β + sin2 γ is __________.
Answer» If a line angles α, β, γ with positive directions of the coordinate axes, then the value of sin²α + sin²β + sin² γ is __________.

Discussion

6537.	Decrease 225 by 5 : 3
Answer» Decrease 225 by 5 : 3

Discussion

6538.	Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.
Answer» Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

Discussion

6539.	Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.
Answer» Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Discussion

6540.	A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
Answer» A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm², find the total expenses required for polishing and painting the surface of the bookshelf.

6540.

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.

Answer»

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm², find the total expenses required for polishing and painting the surface of the bookshelf.

Discussion

6541.

From the following information, prepare Cash Flow Statement: Particulars (₹) Opening Cash and Bank Balances 1,50,000 Closing Cash and Bank Balances 1,70,000 Decrease in Stock 80,000 Increase in Bills Payable 1,20,000 Sale of Fixed Assets 3,00,000 Repayment of Long-term Loan 5,00,000 Net Profit for the Year 20,000

Answer»

From the following information, prepare Cash Flow Statement:

Particulars	(₹)
Opening Cash and Bank Balances	1,50,000
Closing Cash and Bank Balances	1,70,000
Decrease in Stock	80,000
Increase in Bills Payable	1,20,000
Sale of Fixed Assets	3,00,000
Repayment of Long-term Loan	5,00,000
Net Profit for the Year	20,000

Discussion

6542.	Construct each of the following angles, using ruler and compasses:(i) 75∘ (ii) 37.5∘ (iii) 135∘ (iv) 22.5∘
Answer» $Construct each of the following angles, using ruler and compasses: (i) 75^{\circ} (i i) {37.5}^{\circ} (i i i) 135^{\circ} (i v) {22.5}^{\circ}$

Discussion

6543.	If l, l, l are direction cosines of a line, then l = ___________________.
Answer» If l, l, l are direction cosines of a line, then l = ___________________.

Discussion

6544.	Identify a cylinder from the below given three-dimensional shapes.
Answer» Identify a cylinder from the below given three-dimensional shapes.

Discussion

6545.	Find the principal, if the C.I. compounded, annually at the rate of 10% p.a. for 3 years is Rs 331.
Answer» Find the principal, if the C.I. compounded, annually at the rate of 10% p.a. for 3 years is Rs 331.

Discussion

6546.	Question 10In the figure, ABCD and AEFD are two parallelograms. Prove that ar(ΔPEA)=ar(ΔQFD).
Answer» Question 10 In the figure, ABCD and AEFD are two parallelograms. Prove that $a r (Δ P E A) = a r (Δ Q F D)$ .

Discussion

6547.	Which 2 nos. are needed to represent \sqrt{17} on the number line?
Answer» Which 2 nos. are needed to represent \sqrt{17} on the number line?

Discussion

6548.	A man invests ₹ 46,875 at 4 % per annum compound interest for 3 years. Calculate : (i) the interest for the 1st year (ii) the amount standing to his credit at the end of 2nd year:
Answer» A man invests ₹ 46,875 at 4 % per annum compound interest for 3 years. Calculate : (i) the interest for the 1st year (ii) the amount standing to his credit at the end of 2nd year:

6548.

A man invests ₹ 46,875 at 4 % per annum compound interest for 3 years. Calculate : (i) the interest for the 1st year (ii) the amount standing to his credit at the end of 2nd year:

Answer»

A man invests ₹ 46,875 at 4 % per annum compound interest for 3 years. Calculate :

(i) the interest for the 1st year

(ii) the amount standing to his credit at the end of 2nd year:

Discussion

6549.	What's the remainder when5^2009+13^2009 is dividedby18?
Answer» What's the remainder when5^2009+13^2009 is dividedby18?

Discussion

6550.	Sodium metal crystallises in a body centred cubic lattice with unit cell edge of 4.29 A∘. The radius of sodium atom in A∘ is approximately
Answer» Sodium metal crystallises in a body centred cubic lattice with unit cell edge of 4.29 $A^{\circ}$ . The radius of sodium atom in $A^{\circ}$ is approximately

Discussion

Explore topic-wise InterviewSolutions in .

Prove that 3+52 is an irrational number, given that 2 is an irrational number.

Which one of the following is not the graphical representation of statistical data: (a) Bar graph (b) Histogram (c) Frequency polygon (d) Cumulative frequency distribution

In triangle ABC, right angled at B, if one angle is 45∘, find the value of sin A and cos C, without using the table.

In Δ ABC if ∠A = ∠B, then

If 1176=2a×3b×7c,find the values of a,b and c. Hence,compute the value of 2a×3b×7−c as a fraction.

From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

Which of the following is the image of z- axis in the plane x+y-2z+1=0. (A) x=y=2(z-2) (B) x=y=-2(z+2) (C) x=y=1-2z (D) x=y= 1+2z

In the above figure, ∠p+∠q= .

What is the linear equation obtained by adding 7 to both sides of the equation 3x - 7 = 5x + 2 and then transposing 5x to left hand side of the equation?

If the given figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm. AE = 8 cm and CF = 10 cm, find AD.

In figure AC=XD, C is the mid point of AB and D is the mid point of XY.Show that AB=XY

What is the minimum number of measurements required to construct a unique parallelogram? ___

Expand.(1) (5x − 7) (5x − 9)(2) (2x − 3y)3(3) (a + 12)3

The factorized form of a3 + b3 + 3ab – 1 is ____________.

The polynomial , x6 + 64y6 on factorization gives _____________.

In △ABC, if (a−b)2cos2C2+(a+b)2sin2C2=mc2. The value of m is

In the following figure, a circle with centre O is drawn and ∠BAC = 50°. Find x.

Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

For any sets A and B, show that P(A∩B)=P(A)∩P(B).

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

Prove that two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of other triangle.

the equation of a straight line equally inclined to the axis and equidistant from the points (1,-2) and (3,4) is

Question 11 (vi)In ΔABC and ΔDEF, AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that ΔABC≅ΔDEF .

26. p=\sqrt{}-1 then (1-p) whole to the power 20 value

What are two types of irrational number explain in brief.

What is the location of 1-√2 on number line?

Draw the graph of the linear equation whose solutions are represented by the points having sum of coordinates as 10 units.

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Figure). Show that the line PQ is perpendicular bisector of AB.

Using the given graph which of the following could be the equation of line L2.

Line AB || CD and transversal XY meets AB at M and CD at N. If ∠AMX=x and ∠CNX=2x−60, then x= .

Factorize:x^2+6x+9-25^2

How many coins of radius 1 cm and thickness 0.28 cm should be melted to form a soild cylinder of height 7 cm and diameter 8 cm.

Find median of following data: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54

If a line angles α, β, γ with positive directions of the coordinate axes, then the value of sin2 α + sin2 β + sin2 γ is __________.

Decrease 225 by 5 : 3

Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Construct each of the following angles, using ruler and compasses:(i) 75∘ (ii) 37.5∘ (iii) 135∘ (iv) 22.5∘

If l, l, l are direction cosines of a line, then l = ___________________.

Identify a cylinder from the below given three-dimensional shapes.

Find the principal, if the C.I. compounded, annually at the rate of 10% p.a. for 3 years is Rs 331.

Question 10In the figure, ABCD and AEFD are two parallelograms. Prove that ar(ΔPEA)=ar(ΔQFD).

Which 2 nos. are needed to represent \sqrt{17} on the number line?

A man invests ₹ 46,875 at 4 % per annum compound interest for 3 years. Calculate : (i) the interest for the 1st year (ii) the amount standing to his credit at the end of 2nd year:

What's the remainder when5^2009+13^2009 is dividedby18?

Sodium metal crystallises in a body centred cubic lattice with unit cell edge of 4.29 A∘. The radius of sodium atom in A∘ is approximately