32581 + Interview Questions in Mathematics Page 285 InterviewSolution

14201.	If an integer a is greater than 7, then \|7 − a\| =(a) 7 − a (b) a − 7 (c) 7 + a (d) − 7 − a
Answer» If an integer a is greater than 7, then \|7 − a\| = (a) 7 − a (b) a − 7 (c) 7 + a (d) − 7 − a

Discussion

14202.	If the HCF of 408 and 1032 is expressed in the form of 1032 m - 408 × 5. Find m.
Answer» If the HCF of 408 and 1032 is expressed in the form of 1032 m - 408 × 5. Find m.

Discussion

14203.	Find the area of the shaded region. (Use π=3.14)
Answer» Find the area of the shaded region. (Use $π = 3.14$ )

14203.

Find the area of the shaded region. (Use π=3.14)

Answer»

Find the area of the shaded region. (Use $π = 3.14$ )

Discussion

14204.	If tan θ=34, then cos2 θ − sin2 θ =(a) 725(b) 1(c) -725(d) 425
Answer» If $\tan θ = \frac{3}{4}$ , then cos² θ − sin² θ = (a) $\frac{7}{25}$ (b) 1 (c) $\frac{- 7}{25}$ (d) $\frac{4}{25}$

Discussion

14205.	Find the coordinates of the point at which the line represented by the equation 2x+3y = 8 intersects the x-axis.
Answer» Find the coordinates of the point at which the line represented by the equation 2x+3y = 8 intersects the x-axis.

Discussion

14206.	How to find 5 rational number between 1 and 2
Answer» How to find 5 rational number between 1 and 2

Discussion

14207.	Equations x+y=2, 2x+2y=3 will have
Answer» Equations x+y=2, 2x+2y=3 will have

Discussion

14208.	In the given figure, DE \|\| BC. If AD = 6 cm, AB = 24 cm and DE = 5 cm, then find the value of BC.
Answer» In the given figure, DE \|\| BC. If AD = 6 cm, AB = 24 cm and DE = 5 cm, then find the value of BC.

Discussion

14209.	Question 1 (vi)Which of the following form an AP? Justify your answer.2,22,23,24,...
Answer» Question 1 (vi) Which of the following form an AP? Justify your answer. $2, 2^{2}, 2^{3}, 2^{4}, . . .$

Discussion

14210.	The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.
Answer» The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

Discussion

14211.	A box contains cards numbered 11 to 123. a card is drawn at random from the box find the probability that the number on the card is 1. is square number 2.a multiple of 7
Answer» A box contains cards numbered 11 to 123. a card is drawn at random from the box find the probability that the number on the card is 1. is square number 2.a multiple of 7

Discussion

14212.	A given circle x2 + y2 + 2gx + 2fy + c=0 touches the x-axis and intersects the y-axis at 2 points. How many values of x are possible for y = 0.
Answer» A given circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ touches the x-axis and intersects the y-axis at 2 points. How many values of x are possible for y = 0.

Discussion

14213.	Evaluate each of the followingtan2 60°+4 cos2 45°+3 sec2 30°+5 cos2 90°cosec 30°+sec 60°-cot2 30°
Answer» Evaluate each of the following $\frac{\tan^{2} 60 ° + 4 \cos^{2} 45 ° + 3 \sec^{2} 30 ° + 5 \cos^{2} 90 °}{cosec 30 ° + \sec 60 ° - \cot^{2} 30 °}$

Discussion

14214.	Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept.The name of the object/shape that exactly occupies this volume is ___.
Answer» Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept.The name of the object/shape that exactly occupies this volume is ___.

Discussion

14215.	In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If ∠ PAB = 67o, then the measure of ∠ AQB is (a) 73o (b) 64o (c) 53o (d) 44o
Answer» In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If $∠$ PAB = $67^{o}$ , then the measure of $∠$ AQB is (a) $73^{o}$ (b) $64^{o}$ (c) $53^{o}$ (d) $44^{o}$

14215.

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If ∠ PAB = 67o, then the measure of ∠ AQB is (a) 73o (b) 64o (c) 53o (d) 44o

Answer»

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If $∠$ PAB = $67^{o}$ , then the measure of $∠$ AQB is

(a) $73^{o}$ (b) $64^{o}$ (c) $53^{o}$ (d) $44^{o}$

Discussion

14216.	If (x+2) and (x-1) are factors of x3−(a+1)x2−(b+2)x+10=0, find the values of a and b
Answer» If (x+2) and (x-1) are factors of $x^{3} - (a + 1) x^{2} - (b + 2) x + 10 = 0$ , find the values of a and b

Discussion

14217.	Solve for x: √3x2−2√2x−2√3=0
Answer» Solve for x: $\sqrt{3} x^{2} - 2 \sqrt{2} x - 2 \sqrt{3} = 0$

Discussion

14218.	1 + cot2A= cosec2A is valid for
Answer» 1 + $c o t^{2} A$ = $c o s e c^{2} A$ is valid for

Discussion

14219.	find zeroes of the polynomial:- q(x)=3x^2-x
Answer» find zeroes of the polynomial:- q(x)=3x^2-x

Discussion

14220.	In the figure is a tangent to a circle. and are two points on the circle. If BTP = 720 and ATB = 430 find ABT.
Answer» In the figure is a tangent to a circle. and are two points on the circle. If BTP = $72^{0}$ and ATB = $43^{0}$ find ABT.

14220.

In the figure is a tangent to a circle. and are two points on the circle. If BTP = 720 and ATB = 430 find ABT.

Answer»

In the figure is a tangent to a circle. and are two points on

the circle. If BTP = $72^{0}$ and ATB = $43^{0}$ find ABT.

Discussion

14221.	The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Answer» The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

Discussion

14222.	The minimum value of XY+√YZ+3√ZX for all positive real numbers x, y, z is
Answer» The minimum value of $\frac{X}{Y} + \sqrt{\frac{Y}{Z}} + \sqrt[3]{\frac{Z}{X}}$ for all positive real numbers x, y, z is

Discussion

14223.	A vertical tower stands on the horizontal ground and is surmounted by a vertical flagstaff of height 'h' metre. At a point on the ground, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. Find the height of the tower.
Answer» A vertical tower stands on the horizontal ground and is surmounted by a vertical flagstaff of height 'h' metre. At a point on the ground, the angle of elevation of the bottom of the flagstaff is $α$ and that of the top of the flagstaff is $β$ . Find the height of the tower.

Discussion

14224.	A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?
Answer» A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

Discussion

14225.	If sinθ : a = cosα : 1 and tanθ : b = cotα : 1, then the value of (asinα) : b equals
Answer» If sinθ : a = cosα : 1 and tanθ : b = cotα : 1, then the value of (asinα) : b equals

Discussion

14226.	The graphical representation of Linear equation is
Answer» The graphical representation of Linear equation is

Discussion

14227.	How many square metres of a canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?
Answer» How many square metres of a canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

Discussion

14228.	In the given figure, DE and DF are two tangents drawn from an external point D to a circle with centre A. If DE = 5 cm. and DE ⊥ DF then the radius of the circle is [CBSE 2013](a) 3 cm(b) 4 cm(c) 5 cm(d) 6 cm
Answer» In the given figure, DE and DF are two tangents drawn from an external point D to a circle with centre A. If DE = 5 cm. and DE ⊥ DF then the radius of the circle is [CBSE 2013] (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Discussion

14229.	A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. The surface area of the cylinder is ___
Answer» A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. The surface area of the cylinder is ___

Discussion

14230.	The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 223 cm, find the diameter of the cylinder.
Answer» The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2 \frac{2}{3}$ cm, find the diameter of the cylinder.

Discussion

14231.	Construct an isosceles triangle ABC such that AB=6 cm, BC=AC=4 cm.Bisect ∠ C internally and mark a point P on this bisector such that CP=5 cm.Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
Answer» Construct an isosceles triangle ABC such that AB=6 cm, BC=AC=4 cm.Bisect $∠ C$ internally and mark a point P on this bisector such that CP=5 cm.Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.

Discussion

14232.	the class marks of a frequncy distribution are 6,10,14,18,22,26,30.Find its class size
Answer» the class marks of a frequncy distribution are 6,10,14,18,22,26,30.Find its class size

Discussion

14233.	How many cubes of side 2 cm can be fit into a cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively?
Answer» How many cubes of side 2 cm can be fit into a cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively?

Discussion

14234.	A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.
Answer» A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

14234.

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

Answer»

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

Discussion

14235.	What is Kb?
Answer» What is Kb?

Discussion

14236.	If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is
Answer» If A and B are two square matrices of order 3 $\times$ 3 which satisfy AB = A and BA = B then $(A + B)^{7}$ is

Discussion

14237.	ABC is a triangle with AB=10 cm, BC=8 cm, and AC=6 cm. Three circles are drawn touching each other with the vertices of the triangle as their centres. The radius of the smallest circle is:
Answer» $A B C$ is a triangle with $A B = 10 cm$ , $B C = 8 cm$ , and $A C = 6 cm$ . Three circles are drawn touching each other with the vertices of the triangle as their centres. The radius of the smallest circle is:

Discussion

14238.	State any two irrational numbers whose sum and product are rational numbers.
Answer» State any two irrational numbers whose sum and product are rational numbers.

Discussion

14239.	If area of a circle inscribed in an equilateral triangle is 48π square units, then perimeter of the triangle is(a) 173 units(b) 36 units(c) 72 units(d) 483 units
Answer» If area of a circle inscribed in an equilateral triangle is 48π square units, then perimeter of the triangle is (a) 17 $\sqrt{3}$ units (b) 36 units (c) 72 units (d) 48 $\sqrt{3}$ units

Discussion

14240.	If (3y − 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y. [CBSE 2014]
Answer» If (3y − 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y. [CBSE 2014]

Discussion

14241.	In Fig. 1, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is :
Answer» In Fig. 1, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is :

Discussion

14242.	The complete set of values of k, for which the quadratic equation x2−kx+k+2=0 has equal roots, consists of
Answer» The complete set of values of k, for which the quadratic equation $x^{2} - k x + k + 2 = 0$ has equal roots, consists of

Discussion

14243.	Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients3x2-x-4
Answer» Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients $3 x^{2} - x - 4$

Discussion

14244.	If x3+ax2+bx+6 has (x-2) as a factors and leaves a remainder 3 when divided(x-3). Find a and b
Answer» If x³+ax²+bx+6 has (x-2) as a factors and leaves a remainder 3 when divided(x-3). Find a and b

Discussion

14245.	In Fig. 13.113, ABCD is a square with side 22 cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)
Answer» In Fig. 13.113, ABCD is a square with side $2 \sqrt{2}$ cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)

Discussion

14246.	In the given figure, if AB = 8 cm and PE = 3 cm, then AE = (a) 11 cm(b) 7 cm(c) 5 cm(d) 3 cm
Answer» In the given figure, if AB = 8 cm and PE = 3 cm, then AE = (a) 11 cm (b) 7 cm (c) 5 cm (d) 3 cm

Discussion

14247.	Find the sum of each of the following arithmetic series:(i) 7+1012+14+...+84(ii) 34 + 32 + 30 + ... + 10(iii) (−5) + (−8) + (−11) + ... + (−230)
Answer» Find the sum of each of the following arithmetic series: (i) $7 + 10 \frac{1}{2} + 14 + . . . + 84$ (ii) 34 + 32 + 30 + ... + 10 (iii) (−5) + (−8) + (−11) + ... + (−230)

Discussion

14248.	If the pth term of an AP is (2p + 3). Find the AP
Answer» If the pth term of an AP is (2p + 3). Find the AP

Discussion

14249.	GST stands for ___
Answer» GST stands for ___

Discussion

14250.	Express 0.23¯ as a rational number in simplest form.
Answer» Express $0 . \bar{23}$ as a rational number in simplest form.

Discussion

Explore topic-wise InterviewSolutions in .

If an integer a is greater than 7, then |7 − a| =(a) 7 − a (b) a − 7 (c) 7 + a (d) − 7 − a

If the HCF of 408 and 1032 is expressed in the form of 1032 m - 408 × 5. Find m.

Find the area of the shaded region. (Use π=3.14)

If tan θ=34, then cos2 θ − sin2 θ =(a) 725(b) 1(c) -725(d) 425

Find the coordinates of the point at which the line represented by the equation 2x+3y = 8 intersects the x-axis.

How to find 5 rational number between 1 and 2

Equations x+y=2, 2x+2y=3 will have

In the given figure, DE || BC. If AD = 6 cm, AB = 24 cm and DE = 5 cm, then find the value of BC.

Question 1 (vi)Which of the following form an AP? Justify your answer.2,22,23,24,...

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

A box contains cards numbered 11 to 123. a card is drawn at random from the box find the probability that the number on the card is 1. is square number 2.a multiple of 7

A given circle x2 + y2 + 2gx + 2fy + c=0 touches the x-axis and intersects the y-axis at 2 points. How many values of x are possible for y = 0.

Evaluate each of the followingtan2 60°+4 cos2 45°+3 sec2 30°+5 cos2 90°cosec 30°+sec 60°-cot2 30°

Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept.The name of the object/shape that exactly occupies this volume is ___.

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If ∠ PAB = 67o, then the measure of ∠ AQB is (a) 73o (b) 64o (c) 53o (d) 44o

If (x+2) and (x-1) are factors of x3−(a+1)x2−(b+2)x+10=0, find the values of a and b

Solve for x: √3x2−2√2x−2√3=0

1 + cot2A= cosec2A is valid for

find zeroes of the polynomial:- q(x)=3x^2-x

In the figure is a tangent to a circle. and are two points on the circle. If BTP = 720 and ATB = 430 find ABT.

The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

The minimum value of XY+√YZ+3√ZX for all positive real numbers x, y, z is

A vertical tower stands on the horizontal ground and is surmounted by a vertical flagstaff of height 'h' metre. At a point on the ground, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. Find the height of the tower.

If sinθ : a = cosα : 1 and tanθ : b = cotα : 1, then the value of (asinα) : b equals

The graphical representation of Linear equation is

How many square metres of a canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

In the given figure, DE and DF are two tangents drawn from an external point D to a circle with centre A. If DE = 5 cm. and DE ⊥ DF then the radius of the circle is [CBSE 2013](a) 3 cm(b) 4 cm(c) 5 cm(d) 6 cm

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. The surface area of the cylinder is ___

The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 223 cm, find the diameter of the cylinder.

Construct an isosceles triangle ABC such that AB=6 cm, BC=AC=4 cm.Bisect ∠ C internally and mark a point P on this bisector such that CP=5 cm.Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.

the class marks of a frequncy distribution are 6,10,14,18,22,26,30.Find its class size

How many cubes of side 2 cm can be fit into a cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively?

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

What is Kb?

If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is

ABC is a triangle with AB=10 cm, BC=8 cm, and AC=6 cm. Three circles are drawn touching each other with the vertices of the triangle as their centres. The radius of the smallest circle is:

State any two irrational numbers whose sum and product are rational numbers.

If area of a circle inscribed in an equilateral triangle is 48π square units, then perimeter of the triangle is(a) 173 units(b) 36 units(c) 72 units(d) 483 units

If (3y − 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y. [CBSE 2014]

In Fig. 1, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is :

The complete set of values of k, for which the quadratic equation x2−kx+k+2=0 has equal roots, consists of

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients3x2-x-4

If x3+ax2+bx+6 has (x-2) as a factors and leaves a remainder 3 when divided(x-3). Find a and b

In Fig. 13.113, ABCD is a square with side 22 cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)

In the given figure, if AB = 8 cm and PE = 3 cm, then AE = (a) 11 cm(b) 7 cm(c) 5 cm(d) 3 cm

Find the sum of each of the following arithmetic series:(i) 7+1012+14+...+84(ii) 34 + 32 + 30 + ... + 10(iii) (−5) + (−8) + (−11) + ... + (−230)

If the pth term of an AP is (2p + 3). Find the AP

GST stands for ___

Express 0.23¯ as a rational number in simplest form.