32581 + Interview Questions in Mathematics Page 212 InterviewSolution

10551.	A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23.Find the number of blue balls in the jar.
Answer» A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$ . Find the number of blue balls in the jar.

Discussion

10552.	Q: ABCD is a trapezium in which AB parallel to DC. If ar(triage ABD) = 24 cm^2 and AB = 8 cm, then height of triangle ABC is
Answer» Q: ABCD is a trapezium in which AB parallel to DC. If ar(triage ABD) = 24 cm^2 and AB = 8 cm, then height of triangle ABC is

Discussion

10553.	Question 3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically
Answer» Question 3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically

Discussion

10554.	Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.
Answer» Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

Discussion

10555.	There are (22x+1) number of houses in a village. Each house is involved in making of handmade paper bags. If profit of each house per month(in thousands) is given by the zeroes of the polynomial p(x)=x^2-2x-63. Find the number of houses in the village and the profit of a single house
Answer» There are (22x+1) number of houses in a village. Each house is involved in making of handmade paper bags. If profit of each house per month(in thousands) is given by the zeroes of the polynomial p(x)=x^2-2x-63. Find the number of houses in the village and the profit of a single house

Discussion

10556.	Question 177(ii) Find x. (25)2x+6×(25)3=(25)x+2
Answer» Question 177(ii) Find x. ${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$

10556.

Question 177(ii) Find x. (25)2x+6×(25)3=(25)x+2

Answer»

Question 177(ii)

Find x.
${(\frac{2}{5})}^{2 x + 6} \times {(\frac{2}{5})}^{3} = {(\frac{2}{5})}^{x + 2}$

Discussion

10557.	Prove the following trigonometric identities.sec6θ = tan6θ + 3 tan2θ sec2θ + 1
Answer» Prove the following trigonometric identities. sec⁶θ = tan⁶θ + 3 tan²θ sec²θ + 1

Discussion

10558.	Find the non-zero value of k for which the roots of the quadratic equation 9x2-3kx+k=0 are real and equal. [CBSE 2014]
Answer» Find the non-zero value of k for which the roots of the quadratic equation $9 x^{2} - 3 k x + k = 0$ are real and equal. [CBSE 2014]

Discussion

10559.	If sin alpha =1\2 Tan beta = 1\√3 Then find sin ( alpha + beta ) where alpha and beta are both acute angles
Answer» If sin alpha =1\2 Tan beta = 1\√3 Then find sin ( alpha + beta ) where alpha and beta are both acute angles

Discussion

10560.	one-fourth of a herd of elephants was seen in the forest. twice the square root of the herd had gone to mountain and the remaining 15 elephants were seen on the bank of the river.find the total number of elephants
Answer» one-fourth of a herd of elephants was seen in the forest. twice the square root of the herd had gone to mountain and the remaining 15 elephants were seen on the bank of the river.find the total number of elephants

Discussion

10561.	Prove that ABCD is a trapezium.Prove that the line joining the midpoints of two equal chords of a circle subtends equal angle with the chord.
Answer» Prove that ABCD is a trapezium.Prove that the line joining the midpoints of two equal chords of a circle subtends equal angle with the chord.

Discussion

10562.	Because of water resources away from the village the villagers built underground water canal to fill the well in which water flows with 2m/s and its width is 30 cm and length is 80 cm A how much time it will take to fill one well of radius 3 m and 21 m deep?
Answer» Because of water resources away from the village the villagers built underground water canal to fill the well in which water flows with 2m/s and its width is 30 cm and length is 80 cm A how much time it will take to fill one well of radius 3 m and 21 m deep?

Discussion

10563.	Solve each of the following quadratic equations:3x+1-12=23x-1, x≠-1, 13 [CBSE 2014]
Answer» Solve each of the following quadratic equations: $\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3 x - 1}, x \neq - 1, \frac{1}{3}$ [CBSE 2014]

Discussion

10564.	A truck covers a distance of 150 km at a certain average speed an then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance 5 hours, find the first speed of the truck.
Answer» A truck covers a distance of 150 km at a certain average speed an then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance 5 hours, find the first speed of the truck.

Discussion

10565.	Area bounded by the curve y = max{sinx cosx} and x-axis between the lines x = π/4 and x = 2π is equal toHow to solve such problems related to max and min.
Answer» Area bounded by the curve y = max{sinx cosx} and x-axis between the lines x = π/4 and x = 2π is equal to How to solve such problems related to max and min.

Discussion

10566.	Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, −3). [CBSE 2014]
Answer» Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, −3). [CBSE 2014]

Discussion

10567.	Nita purchased an article marked at ₹ 2000 at a discount of 10 % . If the rate of sales tax is 15 % ; find the net amount paid by Nita for the article
Answer» Nita purchased an article marked at ₹ 2000 at a discount of 10 % . If the rate of sales tax is 15 % ; find the net amount paid by Nita for the article

Discussion

10568.	If three homogenous quantities a, b, c are in continued proportion such that ab=bc, then which of the following is true?
Answer» If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c}$ , then which of the following is true?

Discussion

10569.	If a matrix has 15 elements, how many possible orders can it have? ___
Answer» If a matrix has 15 elements, how many possible orders can it have? ___

Discussion

10570.	In a right angled triangle ABC in which ∠A = 90∘, If AD ⊥ BC.
Answer» In a right angled triangle ABC in which ∠A = $90^{\circ}$ , If AD $⊥$ BC.

10570.

In a right angled triangle ABC in which ∠A = 90∘, If AD ⊥ BC.

Answer»

In a right angled triangle ABC in which ∠A = $90^{\circ}$ , If AD $⊥$ BC.

Discussion

10571.	Question 1 (iii)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(iii) 4x2+4√3x+3=0
Answer» Question 1 (iii) Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iii) $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

10572.	The value of \|(3+4i)+ (5+6i)\| is
Answer» The value of \|(3+4i)+ (5+6i)\| is

Discussion

10573.	Which of the following arguments are correct and which are not correct? Give reasons for your answer.(i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.(ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.
Answer» Which of the following arguments are correct and which are not correct? Give reasons for your answer. (i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is. (ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.

10573.

Which of the following arguments are correct and which are not correct? Give reasons for your answer.(i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.(ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.

Answer»

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.

(ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.

Discussion

10574.	Find the value of p, when the mean of the following distribution is 20. x15171920+p23f2345p6
Answer» Find the value of p, when the mean of the following distribution is 20. $\begin{matrix} x & 15 & 17 & 19 & 20 + p & 23 f & 2 & 3 & 4 & 5 p & 6 \end{matrix}$

Discussion

10575.	12. Let ABC be a triangle having orthocentre & circumcentre at (9,5) and (0,0) respectively. If the equation of side BC is 2x-y=10,then find the possible coordinates of vertex A.
Answer» 12. Let ABC be a triangle having orthocentre & circumcentre at (9,5) and (0,0) respectively. If the equation of side BC is 2x-y=10,then find the possible coordinates of vertex A.

Discussion

10576.	If 0x-(x³/3!)(3) cosx>1-(x²/2!)
Answer» If 0x-(x³/3!) (3) cosx>1-(x²/2!)

Discussion

10577.	The minimum value of the expression 3x + 31 – x, x ∈ R, is __________.
Answer» The minimum value of the expression 3^x + 3^{1 – x}, x ∈ R, is __________.

Discussion

10578.	Inclination of a line parallel to x axis is _____.
Answer» Inclination of a line parallel to x axis is _____.

Discussion

10579.	A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m2, find the width of the footpath.
Answer» A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 $m^{2}$ , find the width of the footpath.

Discussion

10580.	In a lottery, there are 6 prizes and 24 blanks. What is the probability of not getting a prize? (a) 34 (b) 35 (b) 45 (d) 29
Answer» In a lottery, there are 6 prizes and 24 blanks. What is the probability of not getting a prize? (a) $\frac{3}{4}$ (b) $\frac{3}{5}$ (b) $\frac{4}{5}$ (d) $\frac{2}{9}$

Discussion

10581.	Find x if distance between points L(x, 7) and M(1, 15) is 10.
Answer» Find x if distance between points L(x, 7) and M(1, 15) is 10.

Discussion

10582.	On dividing by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x).
Answer» On dividing by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x).

Discussion

10583.

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution. Class Interval Frequency 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 8 3 15 12 8 4 N = 50

Answer»

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution.

Class Interval

Frequency

20 – 25

25 – 30

30 – 35

35 – 40

40 – 45

45 – 50

8

3

15

12

8

4

N = 50

Discussion

10584.	Question 1 (iv)Solve the following pairs of equations by reducing them to a pair of linear equations:5x−1+1y−2=26x−1−3y−2=1
Answer» Question 1 (iv) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{5}{x - 1} + \frac{1}{y - 2} = 2$ $\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

Discussion

10585.	On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.
Answer» On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.

Discussion

10586.	An appropriate substitution to solve the differential equation dxdy=x2logxy-x2xy logxy is ________________.
Answer» An appropriate substitution to solve the differential equation $\frac{d x}{d y} = \frac{x^{2} \log (\frac{x}{y}) - x^{2}}{x y \log (\frac{x}{y})}$ is ________________.

Discussion

10587.	Without solving the following quadratic equation, find the value of p for which the roots are equal: px2−4x+3=0
Answer» Without solving the following quadratic equation, find the value of p for which the roots are equal: $p x^{2} - 4 x + 3 = 0$

Discussion

10588.	3. (i) Is 68 a term of the A.P. 7,10,13,...? (ii) Is 302 a term of the A.P. 3,8,13,...? (iii) Is -150 a term of the A.P. 11,8,5,2?
Answer» 3. (i) Is 68 a term of the A.P. 7,10,13,...? (ii) Is 302 a term of the A.P. 3,8,13,...? (iii) Is -150 a term of the A.P. 11,8,5,2?

10588.

3. (i) Is 68 a term of the A.P. 7,10,13,...? (ii) Is 302 a term of the A.P. 3,8,13,...? (iii) Is -150 a term of the A.P. 11,8,5,2?

Answer»

3.

(i) Is 68 a term of the A.P. 7,10,13,...?
(ii) Is 302 a term of the A.P. 3,8,13,...?
(iii) Is -150 a term of the A.P. 11,8,5,2?

Discussion

10589.	A quadratic polynomial whose zeroes are 34 and 12 is
Answer» $A quadratic polynomial whose zeroes are \frac{3}{4} and \frac{1}{2} is$

Discussion

10590.	The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.
Answer» The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

Discussion

10591.	Question 15 If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is A) 0 B) 5 C) 6 D) 15
Answer» Question 15 If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is A) 0 B) 5 C) 6 D) 15

Discussion

10592.	40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.
Answer» 40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.

Discussion

10593.	A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm2. [Take π = 3.14]
Answer» A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm². [Take π = 3.14]

Discussion

10594.	7. IF A 4TH DEGREE POLYNOMIAL IS DIVIDED BY A QUADRATIC POLYNOMIAL ,THEN THE ATMOST DEGREE OF REMAINDER IS -------?
Answer» 7. IF A 4TH DEGREE POLYNOMIAL IS DIVIDED BY A QUADRATIC POLYNOMIAL ,THEN THE ATMOST DEGREE OF REMAINDER IS -------?

Discussion

10595.	Find the HCF and lcm of 8/9,10/27 AND 16/81
Answer» Find the HCF and lcm of 8/9,10/27 AND 16/81

Discussion

10596.	In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB=50∘. If AT is the tangent to the circle at the point A, then ∠ BAT is equal to
Answer» In figure, AB is a chord of the circle and AOC is its diameter such that $∠ A C B = 50^{\circ}$ . If AT is the tangent to the circle at the point A, then $∠$ BAT is equal to

Discussion

10597.	Find the zero ofx²-32x-105
Answer» Find the zero of x²-32x-105

Discussion

10598.	Find the value of k for which each of the following system of equations have infinitely many solutions :2x-3y=7k+2x-2k+1y=32k-1
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $2 x - 3 y = 7 (k + 2) x - (2 k + 1) y = 3 (2 k - 1)$

Discussion

10599.	If the mid-points of the sides AB, BC and CA of a ∆ABC are D (1, 2, –3), E (3, 0, 1) and F(–1, 1, –4) then the coordinates of the centroid of the triangle ABC are __________________.
Answer» If the mid-points of the sides AB, BC and CA of a ∆ABC are D (1, 2, –3), E (3, 0, 1) and F(–1, 1, –4) then the coordinates of the centroid of the triangle ABC are __________________.

Discussion

10600.	Mr Parekh invested Rs 52,000 on Rs 100 shares at a discount of Rs 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs 20. Find : (i) The annual dividend (ii) The profit earned including his dividend [4 MARKS]
Answer» Mr Parekh invested Rs 52,000 on Rs 100 shares at a discount of Rs 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs 20. Find : (i) The annual dividend (ii) The profit earned including his dividend [4 MARKS]

Discussion

Explore topic-wise InterviewSolutions in .

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23.Find the number of blue balls in the jar.

Q: ABCD is a trapezium in which AB parallel to DC. If ar(triage ABD) = 24 cm^2 and AB = 8 cm, then height of triangle ABC is

Question 3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically

Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

There are (22x+1) number of houses in a village. Each house is involved in making of handmade paper bags. If profit of each house per month(in thousands) is given by the zeroes of the polynomial p(x)=x^2-2x-63. Find the number of houses in the village and the profit of a single house

Question 177(ii) Find x. (25)2x+6×(25)3=(25)x+2

Prove the following trigonometric identities.sec6θ = tan6θ + 3 tan2θ sec2θ + 1

Find the non-zero value of k for which the roots of the quadratic equation 9x2-3kx+k=0 are real and equal. [CBSE 2014]

If sin alpha =1\2 Tan beta = 1\√3 Then find sin ( alpha + beta ) where alpha and beta are both acute angles

one-fourth of a herd of elephants was seen in the forest. twice the square root of the herd had gone to mountain and the remaining 15 elephants were seen on the bank of the river.find the total number of elephants

Prove that ABCD is a trapezium.Prove that the line joining the midpoints of two equal chords of a circle subtends equal angle with the chord.

Because of water resources away from the village the villagers built underground water canal to fill the well in which water flows with 2m/s and its width is 30 cm and length is 80 cm A how much time it will take to fill one well of radius 3 m and 21 m deep?

Solve each of the following quadratic equations:3x+1-12=23x-1, x≠-1, 13 [CBSE 2014]

A truck covers a distance of 150 km at a certain average speed an then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance 5 hours, find the first speed of the truck.

Area bounded by the curve y = max{sinx cosx} and x-axis between the lines x = π/4 and x = 2π is equal toHow to solve such problems related to max and min.

Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, −3). [CBSE 2014]

Nita purchased an article marked at ₹ 2000 at a discount of 10 % . If the rate of sales tax is 15 % ; find the net amount paid by Nita for the article

If three homogenous quantities a, b, c are in continued proportion such that ab=bc, then which of the following is true?

If a matrix has 15 elements, how many possible orders can it have? ___

In a right angled triangle ABC in which ∠A = 90∘, If AD ⊥ BC.

Question 1 (iii)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(iii) 4x2+4√3x+3=0

The value of |(3+4i)+ (5+6i)| is

Find the value of p, when the mean of the following distribution is 20. x15171920+p23f2345p6

12. Let ABC be a triangle having orthocentre & circumcentre at (9,5) and (0,0) respectively. If the equation of side BC is 2x-y=10,then find the possible coordinates of vertex A.

If 0x-(x³/3!)(3) cosx&gt;1-(x²/2!)

The minimum value of the expression 3x + 31 – x, x ∈ R, is __________.

Inclination of a line parallel to x axis is _____.

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m2, find the width of the footpath.

In a lottery, there are 6 prizes and 24 blanks. What is the probability of not getting a prize? (a) 34 (b) 35 (b) 45 (d) 29

Find x if distance between points L(x, 7) and M(1, 15) is 10.

On dividing by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x).

Calculation (i) Arithmetic Mean and (ii) Standard Deviation for the following frequency distribution. Class Interval Frequency 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 8 3 15 12 8 4 N = 50

Question 1 (iv)Solve the following pairs of equations by reducing them to a pair of linear equations:5x−1+1y−2=26x−1−3y−2=1

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.

An appropriate substitution to solve the differential equation dxdy=x2logxy-x2xy logxy is ________________.

Without solving the following quadratic equation, find the value of p for which the roots are equal: px2−4x+3=0

3. (i) Is 68 a term of the A.P. 7,10,13,...? (ii) Is 302 a term of the A.P. 3,8,13,...? (iii) Is -150 a term of the A.P. 11,8,5,2?

A quadratic polynomial whose zeroes are 34 and 12 is

The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

Question 15 If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is A) 0 B) 5 C) 6 D) 15

40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.

7. IF A 4TH DEGREE POLYNOMIAL IS DIVIDED BY A QUADRATIC POLYNOMIAL ,THEN THE ATMOST DEGREE OF REMAINDER IS -------?

Find the HCF and lcm of 8/9,10/27 AND 16/81

In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB=50∘. If AT is the tangent to the circle at the point A, then ∠ BAT is equal to

Find the zero ofx²-32x-105

Find the value of k for which each of the following system of equations have infinitely many solutions :2x-3y=7k+2x-2k+1y=32k-1

If the mid-points of the sides AB, BC and CA of a ∆ABC are D (1, 2, –3), E (3, 0, 1) and F(–1, 1, –4) then the coordinates of the centroid of the triangle ABC are __________________.

Mr Parekh invested Rs 52,000 on Rs 100 shares at a discount of Rs 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs 20. Find : (i) The annual dividend (ii) The profit earned including his dividend [4 MARKS]

If 0x-(x³/3!)(3) cosx>1-(x²/2!)