32581 + Interview Questions in Mathematics Page 264 InterviewSolution

13151.	Solve the following quadratic equations by factorization:x+3x+2=3x-72x-3
Answer» Solve the following quadratic equations by factorization: $\frac{x + 3}{x + 2} = \frac{3 x - 7}{2 x - 3}$

Discussion

13152.	Solve each of the following quadratic equations:3x2-2x-1=0
Answer» Solve each of the following quadratic equations: $3 x^{2} - 2 x - 1 = 0$

Discussion

13153.	From a point P outside the circle, with centre O, tangents PA and PB are drawn.Then ∠AOP is equal to
Answer» From a point P outside the circle, with centre O, tangents PA and PB are drawn.Then ∠AOP is equal to

Discussion

13154.	If the mean of the data is 60, find the value of p. Class markfrequency25−351235−451645−55p55−651565−75875−851985−951317
Answer» If the mean of the data is 60, find the value of $p .$ $\begin{matrix} C l a s s m a r k & f r e q u e n c y 25 - 35 & 12 35 - 45 & 16 45 - 55 & p 55 - 65 & 15 65 - 75 & 8 75 - 85 & 19 85 - 95 & 13 \end{matrix}$ 17

Discussion

13155.	In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
Answer» In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.

Discussion

13156.	Let a and b be positive integers show that √2 always lies between a/b and a+2b/ a+b Please give an easier explanation of this question as it's solution is very complicated in RD Sharma
Answer» Let a and b be positive integers show that √2 always lies between a/b and a+2b/ a+b Please give an easier explanation of this question as it's solution is very complicated in RD Sharma

13156.

Let a and b be positive integers show that √2 always lies between a/b and a+2b/ a+b Please give an easier explanation of this question as it's solution is very complicated in RD Sharma

Answer»

Let a and b be positive integers show that √2 always lies between a/b and a+2b/ a+b

Please give an easier explanation of this question as it's solution is very complicated in RD Sharma

Discussion

13157.	Which of the following rational numbers is expressible as a terminating decimal ? (a) 124165 (b) 13130 (c) 2027625 (d)1625462
Answer» Which of the following rational numbers is expressible as a terminating decimal ? $(a) \frac{124}{165} (b) \frac{131}{30} (c) \frac{2027}{625} (d) \frac{1625}{462}$

13157.

Which of the following rational numbers is expressible as a terminating decimal ? (a) 124165 (b) 13130 (c) 2027625 (d)1625462

Answer»

Which of the following rational numbers is expressible as a terminating decimal ?

$(a) \frac{124}{165} (b) \frac{131}{30} (c) \frac{2027}{625} (d) \frac{1625}{462}$

Discussion

13158.	if A = { x : x is a multiple of 7 } and B = { x : x is a multiple of 11 }, then A-B is
Answer» if A = { x : x is a multiple of 7 } and B = { x : x is a multiple of 11 }, then A-B is

Discussion

13159.	Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)
Answer» Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

Discussion

13160.	In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is
Answer» In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

13160.

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

Answer»

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

Discussion

13161.	Let (x-1)^3 divides (p(x) +1) and (x+1)^{3 }divides (p(x) -1). Find the polynomial p(x) of degree 5.
Answer» Let (x-1)^3 divides (p(x) +1) and (x+1)^{3 }divides (p(x) -1). Find the polynomial p(x) of degree 5.

Discussion

13162.	If the points A (a, −11), B (5, b), C(2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Answer» If the points A (a, −11), B (5, b), C(2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.

Discussion

13163.	Three equal circles, each of radius 6cm, touch one another as shown in the figure. Find the area enclosed between them. [ Take π=3.14and√3 = 1.732.]
Answer» Three equal circles, each of radius $6 c m$ , touch one another as shown in the figure. Find the area enclosed between them. [ Take $π = 3.14 a n d \sqrt{3}$ = 1.732.]

13163.

Three equal circles, each of radius 6cm, touch one another as shown in the figure. Find the area enclosed between them. [ Take π=3.14and√3 = 1.732.]

Answer»

Three equal circles, each of radius $6 c m$ , touch one another as shown in the figure. Find the area enclosed between them.

[ Take $π = 3.14 a n d \sqrt{3}$ = 1.732.]

Discussion

13164.	The two opposite vertices of a square as shown in the figure are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Answer» The two opposite vertices of a square as shown in the figure are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

Discussion

13165.	A particle describes a horizontal circle on the smooth surface of an inverted cone,the height of the plane of the circle above the vertex is 9.8 cm. Find the speed of the particle(g=9.8m/s2
Answer» A particle describes a horizontal circle on the smooth surface of an inverted cone,the height of the plane of the circle above the vertex is 9.8 cm. Find the speed of the particle(g=9.8m/s2

Discussion

13166.	To draw a pair f tangents to a circle which are inclined to each other at an angle of 100°, It is required to draw tangents at end points of those two radii of the circle, the angle between which should be:(a) 100°(b) 50°(c) 80°(d) 200°
Answer» To draw a pair f tangents to a circle which are inclined to each other at an angle of 100°, It is required to draw tangents at end points of those two radii of the circle, the angle between which should be: (a) 100° (b) 50° (c) 80° (d) 200°

Discussion

13167.	If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is (a) 20 cm (b) 12√5 cm (c) 8√13 cm (d) 16 cm
Answer» If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is (a) 20 cm (b) $12 \sqrt{5} c m$ (c) $8 \sqrt{13} c m$ (d) 16 cm

13167.

If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is (a) 20 cm (b) 12√5 cm (c) 8√13 cm (d) 16 cm

Answer»

If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is

(a) 20 cm (b) $12 \sqrt{5} c m$ (c) $8 \sqrt{13} c m$ (d) 16 cm

Discussion

13168.	Solve each of the following quadratic equations:3x2+10x+73=0
Answer» Solve each of the following quadratic equations: $\sqrt{3} x^{2} + 10 x + 7 \sqrt{3} = 0$

Discussion

13169.	In ΔABC, D and E lie on the line AB and AC respectively, as shown in the figure.∠AED is:40
Answer» In $Δ A B C$ , D and E lie on the line AB and AC respectively, as shown in the figure. $∠ A E D$ is: 40

Discussion

13170.	If the perimeter of each face of a cube is 32 cm, find its lateral surface area.
Answer» If the perimeter of each face of a cube is 32 cm, find its lateral surface area.

Discussion

13171.	Write all the integers between -11 and 17 which are divisible by 3 and 5 both.
Answer» Write all the integers between -11 and 17 which are divisible by 3 and 5 both.

Discussion

13172.	3tanθ+cotθ=5cosecθ. Solve for θ, 0≤θ≤90. ___ ∘
Answer» $3 t a n θ + c o t θ = 5 c o s e c θ$ . Solve for $θ$ , $0 \leq θ \leq 90$ . ___ $^{\circ}$

Discussion

13173.	Pair the congruent figures.
Answer» Pair the congruent figures.

Discussion

13174.	prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.
Answer» prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

Discussion

13175.	In the given triangle DE II BC, which of the following statements is true?
Answer» In the given triangle DE II BC, which of the following statements is true?

13175.

In the given triangle DE II BC, which of the following statements is true?

Answer»

In the given triangle DE II BC, which of the following statements is true?

Discussion

13176.	How many irrational nos lies between 2 and 3
Answer» How many irrational nos lies between 2 and 3

Discussion

13177.

Write the modal class for the following frequency distribution: Class-interval: 10−15 15−20 20−25 25−30 30−35 35−40 Frequency: 30 35 75 40 30 15

Answer» Write the modal class for the following frequency distribution:

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	35	75	40	30	15

Discussion

13178.	A man rowing at the rate of 5 km an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down. Find the rate at which the river flows.
Answer» A man rowing at the rate of 5 km an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down. Find the rate at which the river flows.

Discussion

13179.	You have budgeted Rs. 1000 a month to spend on music classes. Your music studio charges Rs. 100 per month membership fee, plus Rs. 50 per class attended. Find the possible number of classes you can’t attend in the month of September.
Answer» You have budgeted Rs. 1000 a month to spend on music classes. Your music studio charges Rs. 100 per month membership fee, plus Rs. 50 per class attended. Find the possible number of classes you can’t attend in the month of September.

Discussion

13180.	In ΔABC, D and E are the mid points of AB and AC. If the area of ΔABC = 60 sq. cm. Show that the area of ΔADE = 15 sq. cm.
Answer» In ΔABC, D and E are the mid points of AB and AC. If the area of ΔABC = 60 sq. cm. Show that the area of ΔADE = 15 sq. cm.

Discussion

13181.	Question 17Which term of the AP 53, 48, 43,…. Is the first negative term?
Answer» Question 17 Which term of the AP 53, 48, 43,…. Is the first negative term?

Discussion

13182.	If we join the points A and B then, linw segment AB is known as ______.
Answer» If we join the points A and B then, linw segment AB is known as ______.

Discussion

13183.	In the following figure, the area of the shaded region is(a) 3π cm2 (b) 6π cm2(c) 9π cm2(d) 7π cm2
Answer» In the following figure, the area of the shaded region is (a) 3π cm² (b) 6π cm² (c) 9π cm² (d) 7π cm²

Discussion

13184.	Prove that (5-23) is an irrational number.
Answer» Prove that ( $5 - 2 \sqrt{3}$ ) is an irrational number.

Discussion

13185.	Give the relation between circumference and diameter of a circle.
Answer» Give the relation between circumference and diameter of a circle.

Discussion

13186.	In ∆ABC, point M is the midpoint of side BC.If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Answer» In ∆ABC, point M is the midpoint of side BC. If, AB²+ AC²= 290 cm², AM = 8 cm, find BC.

Discussion

13187.	The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β. Prove that the height of the cloud is h(tanβ+tanα)(tanβ−tanα) metres
Answer» The angle of elevation of a cloud from a point h metres above a lake is $α$ and the angle of depression of its reflection in the lake is $β$ . Prove that the height of the cloud is $\frac{h (t a n β + t a n α)}{(t a n β - t a n α)} m e t r e s$

Discussion

13188.	The constant ratio between circumference and diameter is denoted by which Greek symbol?
Answer» The constant ratio between circumference and diameter is denoted by which Greek symbol?

Discussion

13189.	AA criteria
Answer» AA criteria

Discussion

13190.	Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d=Sn–kSn–1+Sn–2, then k=?
Answer» Let $S_{n}$ denote the sum of $n$ terms of an A.P. whose first term is $a$ . If the common difference $d$ is given by $d = S_{n} - k S_{n} - 1 + S_{n - 2}$ , then $k = ?$

Discussion

13191.	In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Answer» In an A.P. the 10^th term is 46 sum of the 5^th and 7^th term is 52. Find the A.P.

Discussion

13192.

Find the missing frequency (p) for the following distribution whose mean is 7.68. x: 3 5 7 9 11 13 f: 6 8 15 p 8 4

Answer» Find the missing frequency (p) for the following distribution whose mean is 7.68.

x:	3	5	7	9	11	13
f:	6	8	15	p	8	4

Discussion

13193.	In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region.[Use π = 3.14.]
Answer» In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. [Use $π$ = 3.14.]

Discussion

13194.	If the equation 9x2+6kx+4=0 has equal roots, then find the value of k =
Answer» If the equation $9 x^{2} + 6 k x + 4 = 0$ has equal roots, then find the value of k =

Discussion

13195.	7 coupons are numbered 1 to 7. Four are drawn one by one with replacement. If the probability of 'any selected coupon is greater than or equal to 5′ is (ab)p, then a+b−p=(where a,b are relative prime)
Answer» $7$ coupons are numbered $1$ to $7.$ Four are drawn one by one with replacement. If the probability of 'any selected coupon is greater than or equal to $5^{'}$ is ${(\frac{a}{b})}^{p},$ then $a + b - p =$ (where $a, b$ are relative prime)

Discussion

13196.	Write the degree of each of the following polynomials:(i) 5x3+4x2+7x(ii) 4−y2
Answer» Write the degree of each of the following polynomials: (i) $5 x^{3} + 4 x^{2} + 7 x$ (ii) $4 - y^{2}$

Discussion

13197.	Three balls are drawn from a bag containing 4 red, 3 black and 5 white balls. The probability of drawing 2 balls of same colour and one of different colour is
Answer» Three balls are drawn from a bag containing $4$ red, $3$ black and $5$ white balls. The probability of drawing $2$ balls of same colour and one of different colour is

Discussion

13198.	a) Find the value of 'K' for which x = 3 is a solution of the quadratic equation. (K+2)x2−Kx+6=0. b) Thus find the other root of the equation. [6 MARKS]
Answer» a) Find the value of 'K' for which $x$ = 3 is a solution of the quadratic equation. $(K + 2) x^{2} - K x + 6 = 0.$ b) Thus find the other root of the equation. [6 MARKS]

Discussion

13199.	In the following, determine the set values of k for which the given quadratic equation has real roots:(i) 2x2+3x+k=0(ii) 2x2+kx+3=0(iii) 2x2-5x-k=0(iv) kx2+6x+1=0(v) x2-kx+9=0(vi) 2x2+kx+2=0(vii) 3x2+2x+k=0(viii) 4x2-3kx+1=0(ix) 2x2+kx-4=0
Answer» In the following, determine the set values of k for which the given quadratic equation has real roots: (i) $2 x^{2} + 3 x + k = 0$ (ii) $2 x^{2} + k x + 3 = 0$ (iii) $2 x^{2} - 5 x - k = 0$ (iv) $k x^{2} + 6 x + 1 = 0$ (v) $x^{2} - k x + 9 = 0$ (vi) $2 x^{2} + k x + 2 = 0$ (vii) $3 x^{2} + 2 x + k = 0$ (viii) $4 x^{2} - 3 k x + 1 = 0$ (ix) $2 x^{2} + k x - 4 = 0$

Discussion

13200.	If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that
Answer» If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that

Discussion

Explore topic-wise InterviewSolutions in .

Solve the following quadratic equations by factorization:x+3x+2=3x-72x-3

Solve each of the following quadratic equations:3x2-2x-1=0

From a point P outside the circle, with centre O, tangents PA and PB are drawn.Then ∠AOP is equal to

If the mean of the data is 60, find the value of p. Class markfrequency25−351235−451645−55p55−651565−75875−851985−951317

Let a and b be positive integers show that √2 always lies between a/b and a+2b/ a+b Please give an easier explanation of this question as it's solution is very complicated in RD Sharma

Which of the following rational numbers is expressible as a terminating decimal ? (a) 124165 (b) 13130 (c) 2027625 (d)1625462

if A = { x : x is a multiple of 7 } and B = { x : x is a multiple of 11 }, then A-B is

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

Let (x-1)^3 divides (p(x) +1) and (x+1)^{3 }divides (p(x) -1). Find the polynomial p(x) of degree 5.

If the points A (a, −11), B (5, b), C(2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.

Three equal circles, each of radius 6cm, touch one another as shown in the figure. Find the area enclosed between them. [ Take π=3.14and√3 = 1.732.]

The two opposite vertices of a square as shown in the figure are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

A particle describes a horizontal circle on the smooth surface of an inverted cone,the height of the plane of the circle above the vertex is 9.8 cm. Find the speed of the particle(g=9.8m/s2

To draw a pair f tangents to a circle which are inclined to each other at an angle of 100°, It is required to draw tangents at end points of those two radii of the circle, the angle between which should be:(a) 100°(b) 50°(c) 80°(d) 200°

If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm then its slant height is (a) 20 cm (b) 12√5 cm (c) 8√13 cm (d) 16 cm

Solve each of the following quadratic equations:3x2+10x+73=0

In ΔABC, D and E lie on the line AB and AC respectively, as shown in the figure.∠AED is:40

If the perimeter of each face of a cube is 32 cm, find its lateral surface area.

Write all the integers between -11 and 17 which are divisible by 3 and 5 both.

3tanθ+cotθ=5cosecθ. Solve for θ, 0≤θ≤90. ___ ∘

Pair the congruent figures.

prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

In the given triangle DE II BC, which of the following statements is true?

How many irrational nos lies between 2 and 3

Write the modal class for the following frequency distribution: Class-interval: 10−15 15−20 20−25 25−30 30−35 35−40 Frequency: 30 35 75 40 30 15

A man rowing at the rate of 5 km an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down. Find the rate at which the river flows.

You have budgeted Rs. 1000 a month to spend on music classes. Your music studio charges Rs. 100 per month membership fee, plus Rs. 50 per class attended. Find the possible number of classes you can’t attend in the month of September.

In ΔABC, D and E are the mid points of AB and AC. If the area of ΔABC = 60 sq. cm. Show that the area of ΔADE = 15 sq. cm.

Question 17Which term of the AP 53, 48, 43,…. Is the first negative term?

If we join the points A and B then, linw segment AB is known as ______.

In the following figure, the area of the shaded region is(a) 3π cm2 (b) 6π cm2(c) 9π cm2(d) 7π cm2

Prove that (5-23) is an irrational number.

Give the relation between circumference and diameter of a circle.

In ∆ABC, point M is the midpoint of side BC.If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.

The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β. Prove that the height of the cloud is h(tanβ+tanα)(tanβ−tanα) metres

The constant ratio between circumference and diameter is denoted by which Greek symbol?

AA criteria

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d=Sn–kSn–1+Sn–2, then k=?

In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.

Find the missing frequency (p) for the following distribution whose mean is 7.68. x: 3 5 7 9 11 13 f: 6 8 15 p 8 4

In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region.[Use π = 3.14.]

If the equation 9x2+6kx+4=0 has equal roots, then find the value of k =

7 coupons are numbered 1 to 7. Four are drawn one by one with replacement. If the probability of 'any selected coupon is greater than or equal to 5′ is (ab)p, then a+b−p=(where a,b are relative prime)

Write the degree of each of the following polynomials:(i) 5x3+4x2+7x(ii) 4−y2

Three balls are drawn from a bag containing 4 red, 3 black and 5 white balls. The probability of drawing 2 balls of same colour and one of different colour is

a) Find the value of 'K' for which x = 3 is a solution of the quadratic equation. (K+2)x2−Kx+6=0. b) Thus find the other root of the equation. [6 MARKS]

In the following, determine the set values of k for which the given quadratic equation has real roots:(i) 2x2+3x+k=0(ii) 2x2+kx+3=0(iii) 2x2-5x-k=0(iv) kx2+6x+1=0(v) x2-kx+9=0(vi) 2x2+kx+2=0(vii) 3x2+2x+k=0(viii) 4x2-3kx+1=0(ix) 2x2+kx-4=0

If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that