24740 + Interview Questions in Mathematics Page 193 InterviewSolution

9601.	When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively(a) −2, −6(b) 2 and −6(c) −2 and 6(d) 2 and 6
Answer» When x³ − 2x² + ax − b is divided by x² − 2x − 3, the remainder is x − 6. The values of a and b are respectively (a) −2, −6 (b) 2 and −6 (c) −2 and 6 (d) 2 and 6

Discussion

9602.	Two parallel chords are drawn in a circle of diameter 30.0cm. The length of one chord is 24.0cm and the distance between the two chords is 21.0cm, find the length of the other chord.
Answer» Two parallel chords are drawn in a circle of diameter 30.0cm. The length of one chord is 24.0cm and the distance between the two chords is 21.0cm, find the length of the other chord.

Discussion

9603.	In the figure given above, what is the value of tan θ in terms of a, b and c?
Answer» In the figure given above, what is the value of $t a n θ$ in terms of a, b and c?

Discussion

9604.	Question 11On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Answer» Question 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

9604.

Question 11On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Answer»

Question 11

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Discussion

9605.	Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis?
Answer» Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis?

Discussion

9606.	In the figure given below, ∠BCD=60∘. Calcullate the measure of ∠BDA in degrees.
Answer» In the figure given below, $∠ B C D = 60^{\circ}$ . Calcullate the measure of $∠ B D A$ in degrees.

Discussion

9607.	Construct a parallelogram, ABCD with AB = 3.5 cm, BC = 4.5 cm and diagonal BD = 5.5 cm. [2 MARKS]
Answer» Construct a parallelogram, ABCD with AB = 3.5 cm, BC = 4.5 cm and diagonal BD = 5.5 cm. [2 MARKS]

Discussion

9608.	Write 3×a×a×2×b×b×b×c×c×c×c in the exponential form.
Answer» $Write 3 \times a \times a \times 2 \times b \times b \times b \times c \times c \times c \times c in the exponential form .$

Discussion

9609.	Mark the points A, B, C in the figure such that they satisfy all the three conditions.(i) A, B in the interior of ∠ DOF(ii) A, C in the exterior of ∠ EOF(iii) B on ∠ DOE
Answer» Mark the points A, B, C in the figure such that they satisfy all the three conditions. (i) A, B in the interior of $∠$ DOF (ii) A, C in the exterior of $∠$ EOF (iii) B on $∠$ DOE

Discussion

9610.	If x+1x=2, then x6+1x6= ______ .2
Answer» If $x + \frac{1}{x} = 2$ , then $x^{6} + \frac{1}{x^{6}} =$ ______ . 2

Discussion

9611.	Find the zeroes of the polynomial of p(x) = 2x2 - 1
Answer» Find the zeroes of the polynomial of p(x) = 2x² - 1

Discussion

9612.	Which of the following is irrational number?
Answer» Which of the following is irrational number?

Discussion

9613.	Answer the following questions :(i) If a = −52 then find the value of a3 (ii) Find the cube of 79
Answer» Answer the following questions : (i) If a = $\frac{- 5}{2}$ then find the value of a³ (ii) Find the cube of $\frac{7}{9}$

Discussion

9614.	Which of the following diagrams shows the construction of a 45° angle using only a compass and a ruler?
Answer» Which of the following diagrams shows the construction of a 45° angle using only a compass and a ruler?

Discussion

9615.	The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.
Answer» The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.

9615.

The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.

Answer»

The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon.

Find the angles of triangle ABC.

Discussion

9616.	The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.
Answer» The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

9616.

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

Answer»

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

Discussion

9617.	In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,
Answer» In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,

9617.

In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,

Answer»

In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,

Discussion

9618.	If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
Answer» If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?

Discussion

9619.	Question 4 (i)(i) How are prisms and cylinders alike?
Answer» Question 4 (i) (i) How are prisms and cylinders alike?

Discussion

9620.

The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table: Length (in mm) Number of leaves 118 − 126127 − 135136 − 144145 − 153154 − 162163 − 171172 − 180359 12542(i) Draw a histogram to represent the given data.(ii) Is there any other suitable graphical representation for the same data?(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

Answer»

The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:

Length (in mm)

Number of leaves

118 − 126

127 − 135

136 − 144

145 − 153

154 − 162

163 − 171

172 − 180

3

5

9

12

5

4

2

(i) Draw a histogram to represent the given data.

(ii) Is there any other suitable graphical representation for the same data?

(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

Discussion

9621.	Question 104 Rahim borrowed ₹1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.
Answer» Question 104 Rahim borrowed ₹1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.

9621.

Question 104 Rahim borrowed ₹1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.

Answer»

Question 104

Rahim borrowed ₹1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.

Discussion

9622.	12. I4.Find out the frequency of AabbCcDdee if parentsare AabbCCddEe and AabbccDdee (1) 0.78%.(3) 25%(2) 12.5%(4) 50%
Answer» 12. I4.Find out the frequency of AabbCcDdee if parentsare AabbCCddEe and AabbccDdee (1) 0.78%.(3) 25%(2) 12.5%(4) 50%

Discussion

9623.	A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ cm2.
Answer» A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ $c m^{2}$ .

Discussion

9624.	An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box ? The inside and outside surface of the box is to be painted with rust proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
Answer» An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box ? The inside and outside surface of the box is to be painted with rust proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?

Discussion

9625.	Question 7 Call all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
Answer» Question 7 Call all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Discussion

9626.	Factorize (a+b)3−8
Answer» Factorize $(a + b)^{3} - 8$

Discussion

9627.	There are 3 Apples, 4 Mangoes and 1 Watermelon available in a Fruit shop. What is the ratio of Apples to the total number of Fruits?
Answer» There are 3 Apples, 4 Mangoes and 1 Watermelon available in a Fruit shop. What is the ratio of Apples to the total number of Fruits?

Discussion

9628.	If 5√3−√2=a√3−b√2, then find the values of 'a' and 'b'.
Answer» If $\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$ , then find the values of 'a' and 'b'.

Discussion

9629.	Which of the following data is not necessary for construction of triangle ABC with base BC by the method of Triangle Construction 1?
Answer» Which of the following data is not necessary for construction of triangle ABC with base BC by the method of Triangle Construction 1?

Discussion

9630.	In figure, ‘S’ is any point on the side QR of △PQR.Prove that PQ+QR+RP>2PS.
Answer» $In figure, ‘S’ is any point on the side Q R of △ P Q R .$ Prove that $P Q + Q R + R P > 2 P S .$

Discussion

9631.	Question 2: In the given diagram, name the point(s) In the exterior of ∠EOF
Answer» Question 2: In the given diagram, name the point(s) In the exterior of $∠ E O F$

Discussion

9632.	In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD?
Answer» In a right angle triangle $Δ A B C$ , a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $Δ A B D$ and $Δ B C D$ ?

Discussion

9633.	A plastic hemisphere has a radius of curvature of 8 cm and a refractive index of 1.6. On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object O.The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately :
Answer» A plastic hemisphere has a radius of curvature of $8 cm$ and a refractive index of $1.6$ . On the axis halfway between the plane surface and the spherical one ( $4 cm$ from each) is a small object O. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately :

Discussion

9634.

On the basis of information given below, calculate the amount of medicines to be debited to the Income and Expenditure Account of Good Health Hospital for the year ended 31st March, 2019: Particulars 1st April, 2018 (₹) 31st March, 2019 (₹) Stock of Medicines 1,75,750 1,44,650 Creditors for Medicines 15,06,900 18,20,700 Medicines purchased during the year ended 31st March, 2019 were ₹ 60,80,700.

Answer» On the basis of information given below, calculate the amount of medicines to be debited to the Income and Expenditure Account of Good Health Hospital for the year ended 31st March, 2019:

Particulars	1st April, 2018 (₹)	31st March, 2019 (₹)
Stock of Medicines	1,75,750	1,44,650
Creditors for Medicines	15,06,900	18,20,700

Medicines purchased during the year ended 31st March, 2019 were ₹ 60,80,700.

Discussion

9635.	15. The circle of radius 2 units lies in the first quadrant and touches both the axes od coordinate ,Equation of circle with centre at (6,5) and touching the above circle externaly is
Answer» 15. The circle of radius 2 units lies in the first quadrant and touches both the axes od coordinate ,Equation of circle with centre at (6,5) and touching the above circle externaly is

Discussion

9636.	Find the value of x, where AB \|\| CD
Answer» Find the value of $x$ , where AB \|\| CD

Discussion

9637.	What is the probability of the least favoured graph? [3 MARKS]
Answer» What is the probability of the least favoured graph? [3 MARKS]

9637.

What is the probability of the least favoured graph? [3 MARKS]

Answer»

What is the probability of the least favoured graph? [3 MARKS]

Discussion

9638.	In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.
Answer» In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

9638.

In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

Answer»

In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

Discussion

9639.	Question 4 P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC⊥BD. Prove that PQRS is a rectangle.
Answer» Question 4 P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that $A C ⊥ B D$ . Prove that PQRS is a rectangle.

Discussion

9640.	For the division statement 65÷5=13, match the following terms with their respective values:
Answer» For the division statement $65 \div 5 = 13$ , match the following terms with their respective values:

Discussion

9641.	what will happen if- 1.Q=Keq 2.Q>Keq 3.Q
Answer» what will happen if- 1.Q=Keq 2.Q>Keq 3.Q

Discussion

9642.	The following observations are arranged in ascending order:26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.If the median is 65, find the value of x.
Answer» The following observations are arranged in ascending order: 26, 29, 42, 53, x, x + 2, 70, 75, 82, 93. If the median is 65, find the value of x.

Discussion

9643.	Two circles of radii10 cm and 8 cm intersect and the length of the common chord is 12 cm. The distance between their centres is
Answer» Two circles of radii10 cm and 8 cm intersect and the length of the common chord is 12 cm. The distance between their centres is

Discussion

9644.	The graph of the sol�tion of the form y=mx is line which always passes through_____. Explain how
Answer» The graph of the sol�tion of the form y=mx is line which always passes through_____. Explain how

9644.

The graph of the sol�tion of the form y=mx is line which always passes through_____. Explain how

Answer»

The graph of the sol�tion of the form y=mx is line which always passes through_____.

Explain how

Discussion

9645.	Question 25Using suitable identity, evaluate the following(i) 1033(ii) 101×102(iii) 9992
Answer» Question 25 Using suitable identity, evaluate the following (i) $103^{3}$ (ii) $101 \times 102$ (iii) $999^{2}$

Discussion

9646.	The area of the trapezium having parallel side as 27 cm and 13 cm and distance between them as 8 cm is
Answer» The area of the trapezium having parallel side as 27 cm and 13 cm and distance between them as 8 cm is

Discussion

9647.	An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.
Answer» An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.

Discussion

9648.	Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.(1,2), (2,4), (3,6), (4,8)
Answer» Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order. (1,2), (2,4), (3,6), (4,8)

Discussion

9649.	The nature of roots of x2−3x+2=0 will be:
Answer» The nature of roots of $x^{2} - 3 x + 2 = 0$ will be:

Discussion

9650.	The number of sides of a polygon whose number of diagonals is 14 is
Answer» The number of sides of a polygon whose number of diagonals is 14 is

Discussion

Explore topic-wise InterviewSolutions in .

When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively(a) −2, −6(b) 2 and −6(c) −2 and 6(d) 2 and 6

Two parallel chords are drawn in a circle of diameter 30.0cm. The length of one chord is 24.0cm and the distance between the two chords is 21.0cm, find the length of the other chord.

In the figure given above, what is the value of tan θ in terms of a, b and c?

Question 11On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis?

In the figure given below, ∠BCD=60∘. Calcullate the measure of ∠BDA in degrees.

Construct a parallelogram, ABCD with AB = 3.5 cm, BC = 4.5 cm and diagonal BD = 5.5 cm. [2 MARKS]

Write 3×a×a×2×b×b×b×c×c×c×c in the exponential form.

Mark the points A, B, C in the figure such that they satisfy all the three conditions.(i) A, B in the interior of ∠ DOF(ii) A, C in the exterior of ∠ EOF(iii) B on ∠ DOE

If x+1x=2, then x6+1x6= ______ .2

Find the zeroes of the polynomial of p(x) = 2x2 - 1

Which of the following is irrational number?

Answer the following questions :(i) If a = −52 then find the value of a3 (ii) Find the cube of 79

Which of the following diagrams shows the construction of a 45° angle using only a compass and a ruler?

The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,

If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?

Question 4 (i)(i) How are prisms and cylinders alike?

Question 104 Rahim borrowed ₹1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.

12. I4.Find out the frequency of AabbCcDdee if parentsare AabbCCddEe and AabbccDdee (1) 0.78%.(3) 25%(2) 12.5%(4) 50%

A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ cm2.

Question 7 Call all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Factorize (a+b)3−8

There are 3 Apples, 4 Mangoes and 1 Watermelon available in a Fruit shop. What is the ratio of Apples to the total number of Fruits?

If 5√3−√2=a√3−b√2, then find the values of 'a' and 'b'.

Which of the following data is not necessary for construction of triangle ABC with base BC by the method of Triangle Construction 1?

In figure, ‘S’ is any point on the side QR of △PQR.Prove that PQ+QR+RP&gt;2PS.

Question 2: In the given diagram, name the point(s) In the exterior of ∠EOF

In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD?

15. The circle of radius 2 units lies in the first quadrant and touches both the axes od coordinate ,Equation of circle with centre at (6,5) and touching the above circle externaly is

Find the value of x, where AB || CD

What is the probability of the least favoured graph? [3 MARKS]

In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

Question 4 P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC⊥BD. Prove that PQRS is a rectangle.

For the division statement 65÷5=13, match the following terms with their respective values:

what will happen if- 1.Q=Keq 2.Q>Keq 3.Q

The following observations are arranged in ascending order:26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.If the median is 65, find the value of x.

Two circles of radii10 cm and 8 cm intersect and the length of the common chord is 12 cm. The distance between their centres is

The graph of the sol�tion of the form y=mx is line which always passes through_____. Explain how

Question 25Using suitable identity, evaluate the following(i) 1033(ii) 101×102(iii) 9992

The area of the trapezium having parallel side as 27 cm and 13 cm and distance between them as 8 cm is

An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.

Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.(1,2), (2,4), (3,6), (4,8)

The nature of roots of x2−3x+2=0 will be:

The number of sides of a polygon whose number of diagonals is 14 is

In figure, ‘S’ is any point on the side QR of △PQR.Prove that PQ+QR+RP>2PS.