24740 + Interview Questions in Mathematics Page 76 InterviewSolution

3751.	Question 21Which of the following is equal to x?A) x127−x57B) 12√(x4)13C) (√x3)23D) x127×x712
Answer» Question 21 Which of the following is equal to x? A) $x^{\frac{12}{7}} - x^{\frac{5}{7}}$ B) $\sqrt[12]{(x^{4})^{\frac{1}{3}}}$ C) ${(\sqrt{x^{3}})}^{\frac{2}{3}}$ D) $x^{\frac{12}{7}} \times x^{\frac{7}{12}}$

Discussion

3752.

The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student. No. of saplings (Scores) xi No. of students (frequncy) fi fi×xi 1 4 4 2 6 0 3 12 0 4 8 0 N = 0 ∑fixi= 0 Mean x = 0 N = 0 0 = 0 ∴ The average number of trees planted 0

Answer» The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student.

No. of saplings (Scores) x_i	No. of students (frequncy) f_i	f_i×x_i
1	4	4
2	6	$0$
3	12	$0$
4	8	$0$
	N = $0$	∑f_ix_i= $0$

Mean

x

=

\frac{0}{N}

=

\frac{0}{0}

=

0

∴ The average number of trees planted

0

Discussion

3753.	Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use? IF ∠B=50°, what is the measure of ∠R?
Answer» Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use? IF $∠ B = 50 °$ , what is the measure of $∠ R$ ?

Discussion

3754.	Question 5 (ii) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, Show that: ar(BDE)=12ar(BAE)
Answer» Question 5 (ii) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, Show that: $a r (B D E) = \frac{1}{2} a r (B A E)$

Discussion

3755.	All the formula of polynomials (like a - b whole squre , a+ b whole squre, a squre - b square
Answer» All the formula of polynomials (like a - b whole squre , a+ b whole squre, a squre - b square

Discussion

3756.	By rowing half the distance and walking the other half, a man can travel 24 km on a river in 5 hours with the stream, and in 7 hours against the stream. If there were no current, the journey would take (17/3) hours; find the rate of his walking and rowing and the rate of the stream.
Answer» By rowing half the distance and walking the other half, a man can travel 24 km on a river in 5 hours with the stream, and in 7 hours against the stream. If there were no current, the journey would take (17/3) hours; find the rate of his walking and rowing and the rate of the stream.

Discussion

3757.	Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two is the same throughout. Similarly, he draws one more line in the same manner. He names these line as l, m and n. Which of the following is correct?
Answer» Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two is the same throughout. Similarly, he draws one more line in the same manner. He names these line as l, m and n. Which of the following is correct?

Discussion

3758.	Find the value of cot^-1(cot 5)
Answer» Find the value of cot^-1(cot 5)

Discussion

3759.	In a carton of 120 fruits, 24 are rotten. A fruit is selected without looking. What will be the probability that selected fruit will be good?
Answer» In a carton of 120 fruits, 24 are rotten. A fruit is selected without looking. What will be the probability that selected fruit will be good?

Discussion

3760.	Study the bar graph representing the number of persons in various age groups in a town shown in Fig. 23.9. Observe the bar graph and answer the following questions:(i) What is the percentage of the youngest age-group persons over those in the oldest age group?(ii) What is the total population of the town?(iii) What is the number of persons in the age-group 60-65?(iv) How many persons are more in the age-group 10-15 than in the age group 30-35?(v) What is the age-group of exactly 1200 persons living in the town?(vi) What is the total number of persons living in the town in the age-group 50-55?(vii) What is the total number of persons living in the town in the age-groups 10-15 and 60-65?(vii) Whether the population in general increases, decreases or remains constant with the increase in the age-group.
Answer» Study the bar graph representing the number of persons in various age groups in a town shown in Fig. 23.9. Observe the bar graph and answer the following questions: (i) What is the percentage of the youngest age-group persons over those in the oldest age group? (ii) What is the total population of the town? (iii) What is the number of persons in the age-group 60-65? (iv) How many persons are more in the age-group 10-15 than in the age group 30-35? (v) What is the age-group of exactly 1200 persons living in the town? (vi) What is the total number of persons living in the town in the age-group 50-55? (vii) What is the total number of persons living in the town in the age-groups 10-15 and 60-65? (vii) Whether the population in general increases, decreases or remains constant with the increase in the age-group.

Discussion

3761.	In the given figure, O is the centre of a circle and ∠AOC=130∘. Then ∠ABC=? (a) 50∘ (b) 65∘ (c) 115∘ (d) 130∘
Answer» In the given figure, O is the centre of a circle and $∠ A O C = 130^{\circ} . T h e n ∠ A B C = ?$ (a) $50^{\circ}$ (b) $65^{\circ}$ (c) $115^{\circ}$ (d) $130^{\circ}$

3761.

In the given figure, O is the centre of a circle and ∠AOC=130∘. Then ∠ABC=? (a) 50∘ (b) 65∘ (c) 115∘ (d) 130∘

Answer»

In the given figure, O is the centre of a circle and $∠ A O C = 130^{\circ} . T h e n ∠ A B C = ?$

(a) $50^{\circ}$

(b) $65^{\circ}$

(c) $115^{\circ}$

(d) $130^{\circ}$

Discussion

3762.	For any two vectors a→ b→ a→×b→+a→.b→ = ________________.
Answer» For any two vectors $[\vec{a} \vec{b} \vec{a} \times \vec{b}] + (\vec{a} . \vec{b})$ = ________________.

Discussion

3763.	Two circles have radii 6 cm and X cm respectively. If both the circles have the same circumference, then X=__.
Answer» Two circles have radii 6 cm and X cm respectively. If both the circles have the same circumference, then X=__.

Discussion

3764.	ABCD is a rectangle formed by the points A-1,-1, B-1, 4, C5, 4 and D5, -1. If P, Q, R and S be the mid points ofAB, BC, CD and DA respectively, show that PQRS is a rhombus.
Answer» ABCD is a rectangle formed by the points $A (- 1, - 1), B (- 1, 4), C (5, 4) and D (5, - 1)$ . If P, Q, R and S be the mid points of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

Discussion

3765.	A number of the form pq is said to be a rational number if ____________________.
Answer» A number of the form $\frac{p}{q}$ is said to be a rational number if ____________________.

Discussion

3766.	Write a linear equation in two variables to represent the statement ''Four times the cost of a table is equal to seven times the cost of a chair''. From the graph of above linear equation, find the cost of one chair if the cost of the table is ₹1050.
Answer» Write a linear equation in two variables to represent the statement ''Four times the cost of a table is equal to seven times the cost of a chair''. From the graph of above linear equation, find the cost of one chair if the cost of the table is ₹1050.

Discussion

3767.	Any pair of supplementary angles sum up to _____
Answer» Any pair of supplementary angles sum up to _____

Discussion

3768.	In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =(a) 5 cm(b) 6 cm(c) 7 cm(d) 8 cm
Answer» In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY = (a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm

Discussion

3769.	If X¯ is the mean of the ten natural numbers x1, x2, x3,..., x10, show that(x1-X¯)+(x2-X¯)+...+(x10-X¯) = 0.
Answer» If $\bar{X}$ is the mean of the ten natural numbers x₁, x₂, x₃,..., x₁₀, show that $(x_{1} - \bar{X}) + (x_{2} - \bar{X}) + . . . + (x_{10} - \bar{X}) = 0$ .

Discussion

3770.	the ratio of radii of gyration of a circular ring and circular disc of mass m and radius about an axis passing through their centre and perpendicular to their plane are
Answer» the ratio of radii of gyration of a circular ring and circular disc of mass m and radius about an axis passing through their centre and perpendicular to their plane are

Discussion

3771.	The coordinates of incentre of the triangle formed by the lines x=0; y=0 and 3x+4y=12 is
Answer» The coordinates of incentre of the triangle formed by the lines $x = 0; y = 0$ and $3 x + 4 y = 12$ is

Discussion

3772.	Examine whether you can construct Δ DEF such that EF = 7.2 cm, ∠ E = 110∘ and ∠ F = 80∘. Justify your answer:
Answer» Examine whether you can construct $Δ$ DEF such that EF = 7.2 cm, $∠$ E = $110^{\circ}$ and $∠$ F = $80^{\circ}$ . Justify your answer:

Discussion

3773.	If the radius of a wire is decreased to one-fourth of its original and its volume remains the same, then how many times will the new length becomes its original length?
Answer» If the radius of a wire is decreased to one-fourth of its original and its volume remains the same, then how many times will the new length becomes its original length?

Discussion

3774.	Question 5Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.
Answer» Question 5 Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions $20 m \times 16 m$ . Find the area of the field in which the cow can graze.

Discussion

3775.	Question 134Of the four quadrilaterals - square, rectangle, rhombus and trapezium - one is somewhat different from the others because of its design. Find it and give justification.
Answer» Question 134 Of the four quadrilaterals - square, rectangle, rhombus and trapezium - one is somewhat different from the others because of its design. Find it and give justification.

Discussion

3776.	Question 6Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar(APB)×ar(CPD)=ar(APD)×ar(BPC)
Answer» Question 6 Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that $a r (A P B) \times a r (C P D) = a r (A P D) \times a r (B P C)$

Discussion

3777.	In ΔABC given below, AB = 10 cm, AC = 8 cm, and ∠A=45∘. Find the area of ΔABC.
Answer» In $Δ A B C$ given below, AB = 10 cm, AC = 8 cm, and $∠ A = 45^{\circ}$ . Find the area of $Δ A B C$ .

3777.

In ΔABC given below, AB = 10 cm, AC = 8 cm, and ∠A=45∘. Find the area of ΔABC.

Answer»

In $Δ A B C$ given below, AB = 10 cm, AC = 8 cm, and $∠ A = 45^{\circ}$ . Find the area of $Δ A B C$ .

Discussion

3778.	A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Answer» A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Discussion

3779.	If the original size of an image is 540×680, which of the following image sizes cannot be achieved, to ensure that there is no deformation in the picture?
Answer» If the original size of an image is $540 \times 680$ , which of the following image sizes cannot be achieved, to ensure that there is no deformation in the picture?

Discussion

3780.	In the given figure, AM ⊥ BC and AN is the bisector of ∠A. What is the value of ∠MAN?
Answer» In the given figure, AM $⊥$ BC and AN is the bisector of $∠$ A. What is the value of $∠$ MAN?

3780.

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. What is the value of ∠MAN?

Answer»

In the given figure, AM $⊥$ BC and AN is the bisector of $∠$ A. What is the value of $∠$ MAN?

Discussion

3781.	Find four rational numbers between 23 and 53.
Answer» Find four rational numbers between $\frac{2}{3}$ and $\frac{5}{3}$ .

Discussion

3782.	Construct ∆PQR such that, m∠P = 80°, m∠Q = 70°, l(QR) = 5.7 cm.
Answer» Construct ∆PQR such that, m $∠$ P = 80^°, m $∠$ Q = 70^°, l(QR) = 5.7 cm.

Discussion

3783.	The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2=xyz.
Answer» The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that $V^{2} = x y z .$

Discussion

3784.	Which of the following instruments is not necessary for the method of Triangle Construction 2?
Answer» Which of the following instruments is not necessary for the method of Triangle Construction 2?

Discussion

3785.	Is a possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
Answer» Is a possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?

Discussion

3786.	If p=3−2√2, then p2+1p2= ______.
Answer» If $p = 3 - 2 \sqrt{2}$ , then $p^{2} + \frac{1}{p^{2}} =$ ______.

Discussion

3787.	In the given figure, PT=QRandPT\|\|QR and the three sides PQ=RS=TS. If ∠QPT=108°, then ∠QRS is equal to
Answer» In the given figure, $P T = Q R a n d P T \| \| Q R$ and the three sides $P Q = R S = T S$ . If $∠ Q P T = 108 °$ , then $∠ Q R S$ is equal to

Discussion

3788.	Question 9ABCD is a trapezium in which ABIIDC and P, Q are points on AD and BC respectively, such that PQIIDC, if PD = 18 cm, BQ = 35cm and QC = 15cm, find AD.
Answer» Question 9 ABCD is a trapezium in which ABIIDC and P, Q are points on AD and BC respectively, such that PQIIDC, if PD = 18 cm, BQ = 35cm and QC = 15cm, find AD.

Discussion

3789.	Can we draw a quadrilateral ABCD with following AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?
Answer» Can we draw a quadrilateral ABCD with following AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?

Discussion

3790.	How to determine between tetrahedral and square planar? As for both, the coordination number is 4.
Answer» How to determine between tetrahedral and square planar? As for both, the coordination number is 4.

Discussion

3791.	Let f & g be function defined by f(A) = cosA & g(A) = tanA . suppose x & y satisfy 2f(x) - g(y) = 1 , then the value if 2f(y) - g(x) is
Answer» Let f & g be function defined by f(A) = cosA & g(A) = tanA . suppose x & y satisfy 2f(x) - g(y) = 1 , then the value if 2f(y) - g(x) is

Discussion

3792.	The decimal representation of an irrational number is (a) always terminating (b) either terminating or repeating (c) either terminating or nonrepeating (d) neither terminating nor repeating
Answer» The decimal representation of an irrational number is (a) always terminating (b) either terminating or repeating (c) either terminating or nonrepeating (d) neither terminating nor repeating

3792.

The decimal representation of an irrational number is (a) always terminating (b) either terminating or repeating (c) either terminating or nonrepeating (d) neither terminating nor repeating

Answer»

The decimal representation of an irrational number is

(a) always terminating

(b) either terminating or repeating

(c) either terminating or nonrepeating

(d) neither terminating nor repeating

Discussion

3793.	let p(-2,0) , q(0,0) , r(3,3\sqrt3) find the bisector of angle PQR
Answer» let p(-2,0) , q(0,0) , r(3,3\sqrt3) find the bisector of angle PQR

Discussion

3794.	Which of the following are inversely proportional?
Answer» Which of the following are inversely proportional?

Discussion

3795.	Evaluate : 43/2×125−2/3
Answer» Evaluate : $4^{3 / 2} \times 125^{- 2 / 3}$

Discussion

3796.	Find the coordinates of the point whose abscissa is 5 and which lies on the x-axis. [2 MARKS]
Answer» Find the coordinates of the point whose abscissa is 5 and which lies on the x-axis. [2 MARKS]

Discussion

3797.	Factorize (3x−2y)3+(2y−4z)3+(4z−3x)3
Answer» Factorize $(3 x - 2 y)^{3} + (2 y - 4 z)^{3} + (4 z - 3 x)^{3}$

Discussion

3798.	Out of 40 students Participating in a debate 15 are girls. The Probability that the winner is a boy is
Answer» Out of 40 students Participating in a debate 15 are girls. The Probability that the winner is a boy is

Discussion

3799.	Factorise:9a2 + 6a + 1 – 36b2
Answer» Factorise: 9a² + 6a + 1 – 36b²

Discussion

3800.

A random survey of the number of children of various age groups playing in park was found as follows: Age (in years) Number of children 1 − 2 2 − 3 3 − 5 5 − 7 7 − 10 10 − 15 15 − 17 5 3 6 12 9 10 4 Draw a histogram to represent the data above.

Answer»

A random survey of the number of children of various age groups playing in park was found as follows:

Age (in years)

Number of children

1 − 2

2 − 3

3 − 5

5 − 7

7 − 10

10 − 15

15 − 17

5

3

6

12

9

10

4

Draw a histogram to represent the data above.

Discussion

Explore topic-wise InterviewSolutions in .

Question 21Which of the following is equal to x?A) x127−x57B) 12√(x4)13C) (√x3)23D) x127×x712

Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use? IF ∠B=50°, what is the measure of ∠R?

Question 5 (ii) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, Show that: ar(BDE)=12ar(BAE)

All the formula of polynomials (like a - b whole squre , a+ b whole squre, a squre - b square

By rowing half the distance and walking the other half, a man can travel 24 km on a river in 5 hours with the stream, and in 7 hours against the stream. If there were no current, the journey would take (17/3) hours; find the rate of his walking and rowing and the rate of the stream.

Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two is the same throughout. Similarly, he draws one more line in the same manner. He names these line as l, m and n. Which of the following is correct?

Find the value of cot^-1(cot 5)

In a carton of 120 fruits, 24 are rotten. A fruit is selected without looking. What will be the probability that selected fruit will be good?

In the given figure, O is the centre of a circle and ∠AOC=130∘. Then ∠ABC=? (a) 50∘ (b) 65∘ (c) 115∘ (d) 130∘

For any two vectors a→ b→ a→×b→+a→.b→ = ________________.

Two circles have radii 6 cm and X cm respectively. If both the circles have the same circumference, then X=__.

ABCD is a rectangle formed by the points A-1,-1, B-1, 4, C5, 4 and D5, -1. If P, Q, R and S be the mid points ofAB, BC, CD and DA respectively, show that PQRS is a rhombus.

A number of the form pq is said to be a rational number if ____________________.

Write a linear equation in two variables to represent the statement ''Four times the cost of a table is equal to seven times the cost of a chair''. From the graph of above linear equation, find the cost of one chair if the cost of the table is ₹1050.

Any pair of supplementary angles sum up to _____

In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =(a) 5 cm(b) 6 cm(c) 7 cm(d) 8 cm

If X¯ is the mean of the ten natural numbers x1, x2, x3,..., x10, show that(x1-X¯)+(x2-X¯)+...+(x10-X¯) = 0.

the ratio of radii of gyration of a circular ring and circular disc of mass m and radius about an axis passing through their centre and perpendicular to their plane are

The coordinates of incentre of the triangle formed by the lines x=0; y=0 and 3x+4y=12 is

Examine whether you can construct Δ DEF such that EF = 7.2 cm, ∠ E = 110∘ and ∠ F = 80∘. Justify your answer:

If the radius of a wire is decreased to one-fourth of its original and its volume remains the same, then how many times will the new length becomes its original length?

Question 5Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.

Question 134Of the four quadrilaterals - square, rectangle, rhombus and trapezium - one is somewhat different from the others because of its design. Find it and give justification.

Question 6Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar(APB)×ar(CPD)=ar(APD)×ar(BPC)

In ΔABC given below, AB = 10 cm, AC = 8 cm, and ∠A=45∘. Find the area of ΔABC.

A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

If the original size of an image is 540×680, which of the following image sizes cannot be achieved, to ensure that there is no deformation in the picture?

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. What is the value of ∠MAN?

Find four rational numbers between 23 and 53.

Construct ∆PQR such that, m∠P = 80°, m∠Q = 70°, l(QR) = 5.7 cm.

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2=xyz.

Which of the following instruments is not necessary for the method of Triangle Construction 2?

Is a possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?

If p=3−2√2, then p2+1p2= ______.

In the given figure, PT=QRandPT||QR and the three sides PQ=RS=TS. If ∠QPT=108°, then ∠QRS is equal to

Question 9ABCD is a trapezium in which ABIIDC and P, Q are points on AD and BC respectively, such that PQIIDC, if PD = 18 cm, BQ = 35cm and QC = 15cm, find AD.

Can we draw a quadrilateral ABCD with following AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?

How to determine between tetrahedral and square planar? As for both, the coordination number is 4.

Let f & g be function defined by f(A) = cosA & g(A) = tanA . suppose x & y satisfy 2f(x) - g(y) = 1 , then the value if 2f(y) - g(x) is

The decimal representation of an irrational number is (a) always terminating (b) either terminating or repeating (c) either terminating or nonrepeating (d) neither terminating nor repeating

let p(-2,0) , q(0,0) , r(3,3\sqrt3) find the bisector of angle PQR

Which of the following are inversely proportional?

Evaluate : 43/2×125−2/3

Find the coordinates of the point whose abscissa is 5 and which lies on the x-axis. [2 MARKS]

Factorize (3x−2y)3+(2y−4z)3+(4z−3x)3

Out of 40 students Participating in a debate 15 are girls. The Probability that the winner is a boy is

Factorise:9a2 + 6a + 1 – 36b2

A random survey of the number of children of various age groups playing in park was found as follows: Age (in years) Number of children 1 − 2 2 − 3 3 − 5 5 − 7 7 − 10 10 − 15 15 − 17 5 3 6 12 9 10 4 Draw a histogram to represent the data above.