32581 + Interview Questions in Mathematics Page 282 InterviewSolution

14051.	You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ to each other. Refer the figure and select the option which would lead us to the required construction. d is the distance OE.
Answer» You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of $60^{\circ}$ to each other. Refer the figure and select the option which would lead us to the required construction. d is the distance OE.

14051.

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ to each other. Refer the figure and select the option which would lead us to the required construction. d is the distance OE.

Answer»

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of $60^{\circ}$ to each other. Refer the figure and select the option which would lead us to the required construction. d is the distance OE.

14052.	Question 10Write True or False and justify your answer :In the figure, if AOB is a diameter and ∠ADC=120∘, then ∠CAB=30∘.
Answer» Question 10 Write True or False and justify your answer : In the figure, if AOB is a diameter and $∠ A D C = 120^{\circ}, t h e n ∠ C A B = 30^{\circ}$ .

14053.	The polynomial P(x) = 4x3 + 7x2– 5x + t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.
Answer» The polynomial P(x) = 4 $x^{3}$ + 7 $x^{2}$ – 5x + t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.

14054.	A person move 30m north and then 20m towards east and finally 30root2 in south-west direction.the displacement of the person from the origin will be?
Answer» A person move 30m north and then 20m towards east and finally 30root2 in south-west direction.the displacement of the person from the origin will be?

14055.	Let in a series 2n observations, half of them are equal to a and remaining half are equal to −a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 ad 20, respectively. Then the value of a2+b2 is equal to
Answer» Let in a series $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $- a$ . Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ ad $20$ , respectively. Then the value of $a^{2} + b^{2}$ is equal to

14056.	How to draw the tangent of a curved line?
Answer» How to draw the tangent of a curved line?

14057.	Question 14 (iv) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.
Answer» Question 14 (iv) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.

14058.	Choose the correct answer of the following question:A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is(a) 1 : 2 (b) 1 : 4 (c) 1 : 6 (d) 1 : 8 [CBSE 2012]
Answer» Choose the correct answer of the following question: A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is (a) 1 : 2 (b) 1 : 4 (c) 1 : 6 (d) 1 : 8 [CBSE 2012]

14059.	If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when
Answer» If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) $\neq$ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when

14060.	The equation x2+4x+c=0 has real roots, then
Answer» The equation $x^{2} + 4 x + c = 0$ has real roots, then

14061.	Question 4P, 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.

14062.	Slope of the line ' y = -2x-3 ' is
Answer» Slope of the line ' y = -2x-3 ' is

14063.	Find the volume and surface area of a cuboid of ℓ = 10 cm, b = 8 cm and h = 6 cm.
Answer» Find the volume and surface area of a cuboid of $ℓ$ = 10 cm, b = 8 cm and h = 6 cm.

14065.	Question 16The angle of elevation of the top of a vertical tower from a point on the ground is 60∘. From another point 10m vertically above the first, its angle of elevation is 45∘. Find the height of the tower.
Answer» Question 16 The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$ . From another point 10m vertically above the first, its angle of elevation is $45^{\circ}$ . Find the height of the tower.

14066.	If A and B are (− 2, − 2) and (2, − 4), respectively, find the coordinates of P such that and P lies on the line segment AB.
Answer» If A and B are (− 2, − 2) and (2, − 4), respectively, find the coordinates of P such that and P lies on the line segment AB.

14067.	How many rhombuses can we draw with one diagonal 5 centimetres long and one angle 50°? What are their areas?
Answer» How many rhombuses can we draw with one diagonal 5 centimetres long and one angle 50°? What are their areas?

14068.	Mark the correct alternative in the following question:What must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?(a) 5 (b) 3 (c) 4 (d) 6
Answer» Mark the correct alternative in the following question: What must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3? (a) 5 (b) 3 (c) 4 (d) 6

14069.	A (7, -1), B (4, 1) and C (-3, 4) are the vertices of a triangle ABC. Find the equation of a line through the vertex B and the point P in AC; such that AP : CP = 2 : 3.
Answer» A (7, -1), B (4, 1) and C (-3, 4) are the vertices of a triangle ABC. Find the equation of a line through the vertex B and the point P in AC; such that AP : CP = 2 : 3.

14070.	Question 9 A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Answer» Question 9 A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

14071.	The distance between the orthocentre and circumcentre of the triangle whose vertices are at -12, 32, -12, -32 and (1, 0), is __________.
Answer» The distance between the orthocentre and circumcentre of the triangle whose vertices are at $(- \frac{1}{2}, \frac{\sqrt{3}}{2}), (- \frac{1}{2}, - \frac{\sqrt{3}}{2})$ and (1, 0), is __________.

14073.	PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then∠OPR:∠OPQ =.
Answer» PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then $∠ O P R : ∠ O P Q$ =.

14074.	Show that 23 is irrational.
Answer» Show that $\frac{\sqrt{2}}{3}$ is irrational.

14076.	The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.
Answer» The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

14077.	Sum of the area of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of two squares.
Answer» Sum of the area of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of two squares.

14078.	Who is the scientist behind linear equation in two variable?
Answer» Who is the scientist behind linear equation in two variable?

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You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ to each other. Refer the figure and select the option which would lead us to the required construction. d is the distance OE.

Question 10Write True or False and justify your answer :In the figure, if AOB is a diameter and ∠ADC=120∘, then ∠CAB=30∘.

The polynomial P(x) = 4x3 + 7x2– 5x + t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.

A person move 30m north and then 20m towards east and finally 30root2 in south-west direction.the displacement of the person from the origin will be?

Let in a series 2n observations, half of them are equal to a and remaining half are equal to −a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 ad 20, respectively. Then the value of a2+b2 is equal to

How to draw the tangent of a curved line?

Question 14 (iv) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting the jack of heart.

Choose the correct answer of the following question:A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is(a) 1 : 2 (b) 1 : 4 (c) 1 : 6 (d) 1 : 8 [CBSE 2012]

If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when

The equation x2+4x+c=0 has real roots, then

Question 4P, 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.

Slope of the line ' y = -2x-3 ' is

Find the volume and surface area of a cuboid of ℓ = 10 cm, b = 8 cm and h = 6 cm.

Question 16The angle of elevation of the top of a vertical tower from a point on the ground is 60∘. From another point 10m vertically above the first, its angle of elevation is 45∘. Find the height of the tower.

If A and B are (− 2, − 2) and (2, − 4), respectively, find the coordinates of P such that and P lies on the line segment AB.

How many rhombuses can we draw with one diagonal 5 centimetres long and one angle 50°? What are their areas?

Mark the correct alternative in the following question:What must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?(a) 5 (b) 3 (c) 4 (d) 6

A (7, -1), B (4, 1) and C (-3, 4) are the vertices of a triangle ABC. Find the equation of a line through the vertex B and the point P in AC; such that AP : CP = 2 : 3.

Question 9 A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

The distance between the orthocentre and circumcentre of the triangle whose vertices are at -12, 32, -12, -32 and (1, 0), is __________.

In the given circle, with AB as a diameter, find the value of x.

PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then∠OPR:∠OPQ =.

Show that 23 is irrational.

The given figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

Sum of the area of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of two squares.

Who is the scientist behind linear equation in two variable?

Solve equation, given below, using factorisation method: x(x−5)=24

If a and b are the zeroes of quadratic polynomial f(t)=t^2-5t+3, then find the value of (a^4*b^3)+(a^3*b^4).

Find the perimeter of a semicircular protractor whose diameter is 14 cm. [CBSE 2009]

In Fig. 7.247, ∠ABC = 90°, AB : BD : DC = 3 : 1 : 3. If AC = 20 cm, then AD = __________.

Two unbiased coins are tossed simultaneously. Find the probability of getting a) no heads b) at most one tail.

The shape formed by joining the points (5, - 2), (6, 4) and (7, - 2) is ___​​​​​​​

Match the quadratic equations with their roots.

Question 2 (i) Find the LCM and HCF of 26, 91 and verify that LCM × HCF = product of the two numbers.

Find the area bounded between y=e^(-x^2 ) and x=1 and x axis and y axis . Provethat area is less than (1/under root 2 ) +( 1/under root e )[1- 1/ under root 2]

7. The largest possible area of a sphere can be cut off from the cube of side 5cm. Now what will be the volume of the sphere.

Refer to the following figure. If we were given the coordinates of A, E and B and the lengths of ED, DC and BC, how would you go about finding the area of this figure, pick the easiest way.

Solve the following quadratic equations by factorization:7x+3x=3535

Harish wants to make a cover for the cube having side 5 cm which covers the sides but not the top and bottom. The area of cover he will be needing is

In the following alphabetical series, a combination of two alphabets is missing, denoted by the question marks (??). Choose the missing term from the given options. HH, IG, KE, NB, ??

In ΔPQR ≅ ΔEFD,(i) Which side of ΔPQR equals ED?(ii) Which angle of ΔPQR equals angle E?

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2 (Use π = 22/7).

cosec 30o + cot 45o in simplest form is

In a farm, a heap of paddy is in the form of a cone with a slant height of 13m and a height of 12m. What is the area of canvas needed to protect it from sun and rain?

If a and b are the zeroes of quadratic polynomial f(t)=t^2-5t+3, then find the value of (a^4b^3)+(a^3b^4).

The shape formed by joining the points (5, - 2), (6, 4) and (7, - 2) is ___

14080.	If a and b are the zeroes of quadratic polynomial f(t)=t^2-5t+3, then find the value of (a^4b^3)+(a^3b^4).
Answer» If a and b are the zeroes of quadratic polynomial f(t)=t^2-5t+3, then find the value of (a^4b^3)+(a^3b^4).

14081.	Find the perimeter of a semicircular protractor whose diameter is 14 cm. [CBSE 2009]
Answer» Find the perimeter of a semicircular protractor whose diameter is 14 cm. [CBSE 2009]

14082.	In Fig. 7.247, ∠ABC = 90°, AB : BD : DC = 3 : 1 : 3. If AC = 20 cm, then AD = __________.
Answer» In Fig. 7.247, ∠ABC = 90°, AB : BD : DC = 3 : 1 : 3. If AC = 20 cm, then AD = __________.

14084.	The monthly maximum temperature of a city is given in degree celcius in the following data. By taking suitable classes, prepare the grouped frequency distribution table 29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0, 30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4, 30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2From the table, answer the following questions.(i) For how many days the maximum temperature was less than 34oC ?(ii) For how many days the maximum temperature was 34oC or more than 34oC ?
Answer» The monthly maximum temperature of a city is given in degree celcius in the following data. By taking suitable classes, prepare the grouped frequency distribution table 29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0, 30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4, 30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2 From the table, answer the following questions. (i) For how many days the maximum temperature was less than 34^oC ? (ii) For how many days the maximum temperature was 34^oC or more than 34^oC ?

14085.	(a) A solid right circular copper cone of height 15 cm and radius 6 cm is melted and recast into smaller copper cones of height 3 cm and radius 2 cm. How many such smaller cones can be made? (b) Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. [6 MARKS]
Answer» (a) A solid right circular copper cone of height 15 cm and radius 6 cm is melted and recast into smaller copper cones of height 3 cm and radius 2 cm. How many such smaller cones can be made? (b) Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. [6 MARKS]

14086.	The shape formed by joining the points (5, - 2), (6, 4) and (7, - 2) is ___
Answer» The shape formed by joining the points (5, - 2), (6, 4) and (7, - 2) is ___

14087.	Match the quadratic equations with their roots.
Answer» Match the quadratic equations with their roots.

14088.	Question 2 (i) Find the LCM and HCF of 26, 91 and verify that LCM × HCF = product of the two numbers.
Answer» Question 2 (i) Find the LCM and HCF of 26, 91 and verify that LCM $\times$ HCF = product of the two numbers.

14090.	A Ramraj pencil box of dimensions 30cm × 5cm × 5cm consists of 10 sharpened cylindrical pencils placed in a vertical fashion each of length 20cm and diameter 1.4cm and having a conical surmount whose slant height is 2.5m. There are 2 rows of 5 pencils each. Find available volume in the box. Can a sharpener and an eraser in shape of a cube each of side 5cm be placed on top of the pencils such that sharpener is placed on top of the eraser.
Answer» A Ramraj pencil box of dimensions 30cm × 5cm × 5cm consists of 10 sharpened cylindrical pencils placed in a vertical fashion each of length 20cm and diameter 1.4cm and having a conical surmount whose slant height is 2.5m. There are 2 rows of 5 pencils each. Find available volume in the box. Can a sharpener and an eraser in shape of a cube each of side 5cm be placed on top of the pencils such that sharpener is placed on top of the eraser.

14091.	Find the area bounded between y=e^(-x^2 ) and x=1 and x axis and y axis . Provethat area is less than (1/under root 2 ) +( 1/under root e )[1- 1/ under root 2]
Answer» Find the area bounded between y=e^(-x^2 ) and x=1 and x axis and y axis . Provethat area is less than (1/under root 2 ) +( 1/under root e )[1- 1/ under root 2]