24740 + Interview Questions in Mathematics Page 130 InterviewSolution

6451.	Question 80(i)This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.Point A represents a resort that is located 5 km East and 3km North of point B. The values 5 and 3 are the coordinates of point A. The coordinates can be given as the ordered pair (5,3), where 5 is the horizontal coordinate and 3 is the vertical coordinate.(i) On a copy of the map, mark the point that is 3 km East and 5 km North of point B and label it S. Is point S in the water or on the island? Is point S in the same place as point A?
Answer» Question 80(i) This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km. Point A represents a resort that is located 5 km East and 3km North of point B. The values 5 and 3 are the coordinates of point A. The coordinates can be given as the ordered pair (5,3), where 5 is the horizontal coordinate and 3 is the vertical coordinate. (i) On a copy of the map, mark the point that is 3 km East and 5 km North of point B and label it S. Is point S in the water or on the island? Is point S in the same place as point A?

Discussion

6452.	If N=(2log980070)(5log14070)(7log270) then N is equal to
Answer» If $N = (2^{l o g_{70}^{9800}}) (5^{l o g_{70}^{140}}) (7^{l o g_{70}^{2}})$ then N is equal to

Discussion

6453.	A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.If quadrilateral ABCD is a parallelogram, what can be said about sides SP and QR?
Answer» A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively. If quadrilateral ABCD is a parallelogram, what can be said about sides SP and QR?

6453.

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.If quadrilateral ABCD is a parallelogram, what can be said about sides SP and QR?

Answer»

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.

If quadrilateral ABCD is a parallelogram, what can be said about sides SP and QR?

Discussion

6454.	In the given figure, chords AC and DE intersect at B. If ∠ ABE = 108°, m(arc AE) = 95°, find m(arc DC).
Answer» In the given figure, chords AC and DE intersect at B. If ∠ ABE = 108°, m(arc AE) = 95°, find m(arc DC).

Discussion

6455.	PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.
Answer» PQRS is a square such that PR and SQ intersect at O. State the measure of $∠ P O Q .$

Discussion

6456.	Simplify and solve the following linear equation.0.25(4f−3)=0.05(10f−9)
Answer» Simplify and solve the following linear equation. $0.25 (4 f - 3) = 0.05 (10 f - 9)$

Discussion

6457.	In the given figure, point S is equidistant from the points A and K. If ∠ACS = (3x+33)° and ∠KCS = 45°, then find the value of x.
Answer» In the given figure, point S is equidistant from the points A and K. If ∠ACS = (3x+33)° and ∠KCS = 45°, then find the value of x.

Discussion

6458.	Pedal triangle of an obtuse angled triangle lies
Answer» Pedal triangle of an obtuse angled triangle lies

Discussion

6459.	Prove that √15 is an irrational number.
Answer» Prove that √15 is an irrational number.

Discussion

6460.	If the value of (6+√5)×(6−√5)=6x−5y then the value of x= and y=.
Answer» If the value of $(6 + \sqrt{5}) \times (6 - \sqrt{5}) = 6 x - 5 y$ then the value of $x =$ and $y =$ .

Discussion

6461.	Question 5 ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
Answer» Question 5 ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

Discussion

6462.	The following quadratic equation has the equal root of opposite sign. Find the value of k in term of a and b. x2−bxax−c=k−1k+1
Answer» The following quadratic equation has the equal root of opposite sign. Find the value of k in term of a and b. $\frac{x^{2} - b x}{a x - c} = \frac{k - 1}{k + 1}$

Discussion

6463.	Which of the following represents a line parallel to x-axis?
Answer» Which of the following represents a line parallel to x-axis?

Discussion

6464.	Question 17Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Answer» Question 17 Find the $20^{t h}$ term from the last term of the A.P. 3, 8, 13, …, 253.

Discussion

6465.	Expand the following, using suitable identities: 1)(−2x+3y+2z)2 2)(−2x+5y−3z)2. [4 MARKS]
Answer» Expand the following, using suitable identities: $1) {(- 2 x + 3 y + 2 z)}^{2}$ $2) {(- 2 x + 5 y - 3 z)}^{2}$ . [4 MARKS]

Discussion

6466.	Factorise: (i) x3−2x2−x+2(ii) x3−3x2−9x−5(iii) x3+13x2+32x+20(iv) 2y3+y2−2y−1
Answer» Factorise: $(i) x^{3} - 2 x^{2} - x + 2$ $(i i) x^{3} - 3 x^{2} - 9 x - 5$ $(i i i) x^{3} + 13 x^{2} + 32 x + 20$ $(i v) 2 y^{3} + y^{2} - 2 y - 1$

Discussion

6467.	What is the value of (a + b) (a – b)?
Answer» What is the value of (a + b) (a – b)?

Discussion

6468.	A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.
Answer» A cuboid has total surface area of 372 cm² and its lateral surface area is 180 cm², find the area of its base.

Discussion

6469.	If x2+1x2=23, find the value of x3+1x3 if x is a positive integer.
Answer» If $x^{2} + \frac{1}{x^{2}} = 23$ , find the value of $x^{3} + \frac{1}{x^{3}}$ if $x$ is a positive integer.

Discussion

6470.	what does non integer rational number mean? is it fractions ?
Answer» what does non integer rational number mean? is it fractions ?

Discussion

6471.	Express the number 0.3178(bar on 178) in the form of rational number p/q
Answer» Express the number 0.3178(bar on 178) in the form of rational number p/q

Discussion

6472.	The perpendicular distance of the point P(3, 3,4) from the x-axis is(a) 32(b) 5(c) 3(d) 4
Answer» The perpendicular distance of the point P(3, 3,4) from the x-axis is (a) $3 \sqrt{2}$ (b) 5 (c) 3 (d) 4

Discussion

6473.	Can you find if the points of intersection of all the perpendicular bisectors for an obtuse triangle PQR with measurements as follows: PQ = 5 units, QR = 8 units, and PR = 9 units lies outside or inside the triangle?
Answer» Can you find if the points of intersection of all the perpendicular bisectors for an obtuse triangle PQR with measurements as follows: PQ = 5 units, QR = 8 units, and PR = 9 units lies outside or inside the triangle?

Discussion

6474.	What do you understand by the word statistics in (i) singular form, (ii) plural forms
Answer» What do you understand by the word statistics in (i) singular form, (ii) plural forms

Discussion

6475.	Which of the following is not a natural number?
Answer» Which of the following is not a natural number?

Discussion

6476.	The value of machinery is Rs.10000. The value is depreciating by 15% every year. What will be the value of the machinery after 2 years?
Answer» The value of machinery is Rs.10000. The value is depreciating by 15% every year. What will be the value of the machinery after 2 years?

Discussion

6477.	Factorize:2. a(a+b)3 − 3a2b (a + b)
Answer» Factorize: 2. a(a+b)³ − 3a²b (a + b)

Discussion

6478.	What is the value of y in 3x - 4y = 10 when x = 2?
Answer» What is the value of y in 3x - 4y = 10 when x = 2?

Discussion

6479.	In the given figure area of parallelogram ABCD is 160 cm2, then the area of Δ DAC is
Answer» In the given figure area of parallelogram ABCD is $160 c m^{2}$ , then the area of $Δ D A C$ is

6479.

In the given figure area of parallelogram ABCD is 160 cm2, then the area of Δ DAC is

Answer»

In the given figure area of parallelogram ABCD is $160 c m^{2}$ , then the area of $Δ D A C$ is

Discussion

6480.	If 3a - 7b = 26 and ab = 5, then the value of 9a2 + 49b2.
Answer» If 3a - 7b = 26 and ab = 5, then the value of 9a² + 49b².

Discussion

6481.	Question 3 (ii)Form the pair of linear equations for the following problems and find their solution by substitution method:The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Answer» Question 3 (ii) Form the pair of linear equations for the following problems and find their solution by substitution method: The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Discussion

6482.	Find the side of a cube (in cm) whose surface area is 1176 cm2. ___
Answer» Find the side of a cube (in cm) whose surface area is 1176 $c m^{2}$ . ___

6482.

Find the side of a cube (in cm) whose surface area is 1176 cm2. ___

Answer»

Find the side of a cube (in cm) whose surface area is 1176 $c m^{2}$ .

___

Discussion

6483.	If the value of K, of 1 M HCN is 105 then its degreeof dissociation in 0.1 M HCI will be (a
Answer» If the value of K, of 1 M HCN is 105 then its degreeof dissociation in 0.1 M HCI will be (a<< < 1 ) (1) 10-5 (2)10-4 (3)10-3 (4) 10-

Discussion

6484.	The numbers 52,53, 54, 54, (2x+1), 55, 55, 56,57 are arranged in ascending order and their median is 55. Find the mode of the given data.
Answer» The numbers 52,53, 54, 54, (2x+1), 55, 55, 56,57 are arranged in ascending order and their median is 55. Find the mode of the given data.

Discussion

6485.	Read the bar graph given in Fig. 23.20 and answer the following questions:(i) What information is given by the bar graph?(ii) What was the expenditure on health and family planning in the year 1982-83?(iii) In which year is the increase in expenditure maximum over the expenditure in previous year? What is the maximum increase?
Answer» Read the bar graph given in Fig. 23.20 and answer the following questions: (i) What information is given by the bar graph? (ii) What was the expenditure on health and family planning in the year 1982-83? (iii) In which year is the increase in expenditure maximum over the expenditure in previous year? What is the maximum increase?

Discussion

6486.	The equations of the lines passing through the point (1, 0) and at a distance 32 from the origin are(a) 3x±y–3=0(b) 3x±y+3=0(c) x±3y–3=0(d) none of these
Answer» The equations of the lines passing through the point (1, 0) and at a distance $\frac{\sqrt{3}}{2}$ from the origin are (a) $\sqrt{3} x \pm y - \sqrt{3} = 0$ (b) $\sqrt{3} x \pm y + \sqrt{3} = 0$ (c) $x \pm \sqrt{3} y - \sqrt{3} = 0$ (d) none of these

Discussion

6487.	In the figure BD = DC and ∠DBC=25∘. What is the value of ∠BAC?
Answer» In the figure BD = DC and $∠ D B C = 25^{\circ}$ . What is the value of $∠ B A C$ ?

Discussion

6488.	Write the class size and class limits in each of the following:(i) 104, 114, 124, 134, 144, 154 and 164(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5
Answer» Write the class size and class limits in each of the following: (i) 104, 114, 124, 134, 144, 154 and 164 (ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102 (iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

6488.

Write the class size and class limits in each of the following:(i) 104, 114, 124, 134, 144, 154 and 164(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

Answer»

Write the class size and class limits in each of the following:

(i) 104, 114, 124, 134, 144, 154 and 164

(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102

(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

Discussion

6489.	A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?
Answer» A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?

Discussion

6490.	The value of (12)×(12)+(12)(12)+(12)×(34) is ___.
Answer» The value of $\frac{(\frac{1}{2}) \times (\frac{1}{2}) + (\frac{1}{2})}{(\frac{1}{2}) + (\frac{1}{2}) \times (\frac{3}{4})}$ is ___.

Discussion

6491.	Find the value of x in the given figure.
Answer» Find the value of x in the given figure.

6491.

Find the value of x in the given figure.

Answer»

Find the value of x in the given figure.

Discussion

6492.	Which of these points does not lie on the graph of y = -x + 3?
Answer» Which of these points does not lie on the graph of y = -x + 3?

Discussion

6493.	Given below is the concentration of SO2 in air (in ppm = parts per million) in 30 localities:SO2 concentration (in ppm)Number of localities0.00−0.0440.04−0.0890.08−0.1290.12−0.1620.16−0.2040.20−0.242Find the mean of SO2 concentration using assumed - mean method.0.099
Answer» Given below is the concentration of SO₂ in air (in ppm = parts per million) in 30 localities: $\begin{matrix} S O_{2} concentration (in ppm) & Number of localities 0.00 - 0.04 & 4 0.04 - 0.08 & 9 0.08 - 0.12 & 9 0.12 - 0.16 & 2 0.16 - 0.20 & 4 0.20 - 0.24 & 2 \end{matrix}$ Find the mean of $S O_{2}$ concentration using assumed - mean method. 0.099

Discussion

6494.	What is Pythagoras theorm?
Answer» What is Pythagoras theorm?

Discussion

6495.	(b) Find the area bounded by the curves }4y=\vert x^2-4\vert and }y+\vert x\vert=7
Answer» (b) Find the area bounded by the curves }4y=\vert x^2-4\vert and }y+\vert x\vert=7

Discussion

6496.	The value of 50 and 40 (lower and upper limit resp][d theta/theta-theta not where theta not=30 C (a constant )is
Answer» The value of 50 and 40 (lower and upper limit resp] [d theta/theta-theta not where theta not=30 C (a constant )is

Discussion

6497.	If two circles are internally touching at point P. a line intersect those two circles at points A,B,C,D respectively.then prove that angleAPD=angleCPD.
Answer» If two circles are internally touching at point P. a line intersect those two circles at points A,B,C,D respectively.then prove that angleAPD=angleCPD.

Discussion

6498.	In the given figure, if D and E are the mid points of sides AB and AC, respectively, and DE is produced to F such that E is the mid point of FD, which of the following options is correct?
Answer» In the given figure, if D and E are the mid points of sides AB and AC, respectively, and DE is produced to F such that E is the mid point of FD, which of the following options is correct?

Discussion

6499.	Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and obtain the range of monthly household expenditure on food.
Answer» Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and obtain the range of monthly household expenditure on food.

Discussion

6500.	Which of the following points lies on the line 3x + 2y = 6?
Answer» Which of the following points lies on the line 3x + 2y = 6?

Discussion

Explore topic-wise InterviewSolutions in .

If N=(2log980070)(5log14070)(7log270) then N is equal to

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.If quadrilateral ABCD is a parallelogram, what can be said about sides SP and QR?

In the given figure, chords AC and DE intersect at B. If ∠ ABE = 108°, m(arc AE) = 95°, find m(arc DC).

PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.

Simplify and solve the following linear equation.0.25(4f−3)=0.05(10f−9)

In the given figure, point S is equidistant from the points A and K. If ∠ACS = (3x+33)° and ∠KCS = 45°, then find the value of x.

Pedal triangle of an obtuse angled triangle lies

Prove that √15 is an irrational number.

If the value of (6+√5)×(6−√5)=6x−5y then the value of x= and y=.

Question 5 ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

The following quadratic equation has the equal root of opposite sign. Find the value of k in term of a and b. x2−bxax−c=k−1k+1

Which of the following represents a line parallel to x-axis?

Question 17Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.

Expand the following, using suitable identities: 1)(−2x+3y+2z)2 2)(−2x+5y−3z)2. [4 MARKS]

Factorise: (i) x3−2x2−x+2(ii) x3−3x2−9x−5(iii) x3+13x2+32x+20(iv) 2y3+y2−2y−1

What is the value of (a + b) (a – b)?

A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.

If x2+1x2=23, find the value of x3+1x3 if x is a positive integer.

what does non integer rational number mean? is it fractions ?

Express the number 0.3178(bar on 178) in the form of rational number p/q

The perpendicular distance of the point P(3, 3,4) from the x-axis is(a) 32(b) 5(c) 3(d) 4

Can you find if the points of intersection of all the perpendicular bisectors for an obtuse triangle PQR with measurements as follows: PQ = 5 units, QR = 8 units, and PR = 9 units lies outside or inside the triangle?

What do you understand by the word statistics in (i) singular form, (ii) plural forms

Which of the following is not a natural number?

The value of machinery is Rs.10000. The value is depreciating by 15% every year. What will be the value of the machinery after 2 years?

Factorize:2. a(a+b)3 − 3a2b (a + b)

What is the value of y in 3x - 4y = 10 when x = 2?

In the given figure area of parallelogram ABCD is 160 cm2, then the area of Δ DAC is

If 3a - 7b = 26 and ab = 5, then the value of 9a2 + 49b2.

Question 3 (ii)Form the pair of linear equations for the following problems and find their solution by substitution method:The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Find the side of a cube (in cm) whose surface area is 1176 cm2. ___

If the value of K, of 1 M HCN is 105 then its degreeof dissociation in 0.1 M HCI will be (a

The numbers 52,53, 54, 54, (2x+1), 55, 55, 56,57 are arranged in ascending order and their median is 55. Find the mode of the given data.

The equations of the lines passing through the point (1, 0) and at a distance 32 from the origin are(a) 3x±y–3=0(b) 3x±y+3=0(c) x±3y–3=0(d) none of these

In the figure BD = DC and ∠DBC=25∘. What is the value of ∠BAC?

Write the class size and class limits in each of the following:(i) 104, 114, 124, 134, 144, 154 and 164(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?

The value of (12)×(12)+(12)(12)+(12)×(34) is ___.

Find the value of x in the given figure.

Which of these points does not lie on the graph of y = -x + 3?

Given below is the concentration of SO2 in air (in ppm = parts per million) in 30 localities:SO2 concentration (in ppm)Number of localities0.00−0.0440.04−0.0890.08−0.1290.12−0.1620.16−0.2040.20−0.242Find the mean of SO2 concentration using assumed - mean method.0.099

What is Pythagoras theorm?

(b) Find the area bounded by the curves }4y=\vert x^2-4\vert and }y+\vert x\vert=7

The value of 50 and 40 (lower and upper limit resp][d theta/theta-theta not where theta not=30 C (a constant )is

If two circles are internally touching at point P. a line intersect those two circles at points A,B,C,D respectively.then prove that angleAPD=angleCPD.

In the given figure, if D and E are the mid points of sides AB and AC, respectively, and DE is produced to F such that E is the mid point of FD, which of the following options is correct?

Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and obtain the range of monthly household expenditure on food.

Which of the following points lies on the line 3x + 2y = 6?