32581 + Interview Questions in Mathematics Page 43 InterviewSolution

2101.

The daily expenses of 40 families has been shown by the following frequency distribution: Expenses (in ₹) 500 − 700 700 − 900 900 − 1100 1100 − 1300 1300 − 1500 Number of families 6 8 10 9 7 Find the mean daily expenses.

Answer» The daily expenses of 40 families has been shown by the following frequency distribution:

Expenses (in ₹)	500 − 700	700 − 900	900 − 1100	1100 − 1300	1300 − 1500
Number of families	6	8	10	9	7

Find the mean daily expenses.

Discussion

2102.	In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]
Answer» In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

2102.

In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

Answer»

In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

Discussion

2103.	find the value of x \|x - 3\| + \|4 - x\| = 1
Answer» find the value of x \|x - 3\| + \|4 - x\| = 1

Discussion

2104.	From Bangalore bus stand, if we buy 2 tickets to Malleshwaram and 3 tickets to Yeshwanthpur, the total cost is ₹ 46; but if we buy 3 tickets to Malleshwaram and 5 tickets to Yeshwanthpur, then the total cost is ₹ 74. Find the fares from Bangalore bus stand to Malleshwaram and to Yeshwanthpur respectively.
Answer» From Bangalore bus stand, if we buy 2 tickets to Malleshwaram and 3 tickets to Yeshwanthpur, the total cost is ₹ 46; but if we buy 3 tickets to Malleshwaram and 5 tickets to Yeshwanthpur, then the total cost is ₹ 74. Find the fares from Bangalore bus stand to Malleshwaram and to Yeshwanthpur respectively.

Discussion

2105.	How many terms of the AP 9, 17, 25, ... must be taken so that their sum is 636?
Answer» How many terms of the AP 9, 17, 25, ... must be taken so that their sum is 636?

Discussion

2106.	If sin(B+C)=√32 and sin A=12, find B+C and A.
Answer» $I f s i n (B + C) = \frac{\sqrt{3}}{2} a n d s i n A = \frac{1}{2}$ , find $B + C a n d A$ .

Discussion

2107.	Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.
Answer» Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.

Discussion

2108.	Find the mean, median and mode of: 3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4
Answer» Find the mean, median and mode of: 3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4

2108.

Find the mean, median and mode of: 3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4

Answer»

Find the mean, median and mode of:

3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4

Discussion

2109.	The quadratic polynomial in x whose zeros are −a, 2a is:
Answer» The quadratic polynomial in $x$ whose zeros are $- a, 2 a$ is:

Discussion

2110.	Question 25In an AP, if Sn=3n2+5n and ak=164 , then find the value of k.
Answer» Question 25 In an AP, if $S_{n} = 3 n^{2} + 5 n$ and $a_{k} = 164$ , then find the value of $k$ .

Discussion

2111.	Find the values of k for which the quadratic equation 3k+1x2+2k+1x+1=0 has equal roots. Also, find the roots.
Answer» Find the values of k for which the quadratic equation $(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0$ has equal roots. Also, find the roots.

Discussion

2112.	If the product of zeros of the quadratic polynomial f(x) = x2 − 4x + k is 3, find the value of k.
Answer» If the product of zeros of the quadratic polynomial f(x) = x² − 4x + k is 3, find the value of k.

Discussion

2113.	Q1-in a seminar the number of participants in hindi, English and mathematics are 60,84 and 108, respectively. The minimum number of rooms, required if in each room the same number of participants at to be seated and all of them being in the same subject?
Answer» Q1-in a seminar the number of participants in hindi, English and mathematics are 60,84 and 108, respectively. The minimum number of rooms, required if in each room the same number of participants at to be seated and all of them being in the same subject?

Discussion

2114.	Calculate the difference between the part of container filled with paper and plastic wastes.
Answer» Calculate the difference between the part of container filled with paper and plastic wastes.

Discussion

2115.	19.Given f(x+1) = 3x + 5, find f(x).
Answer» 19.Given f(x+1) = 3x + 5, find f(x).

Discussion

2116.	The product of three consecutive positive integers is divisible by 6 Justify whether the statement is true or false
Answer» The product of three consecutive positive integers is divisible by 6 Justify whether the statement is true or false

2116.

The product of three consecutive positive integers is divisible by 6 Justify whether the statement is true or false

Answer»

The product of three consecutive positive integers is divisible by 6

Justify whether the statement is true or false

Discussion

2117.	Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.(Use π=227)
Answer» Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____. $(U s e π = \frac{22}{7})$

Discussion

2118.	Solve the following quadratic equations by factorization:x+1x-1+x-2x+2=4-2x+3x-2; x≠1,-2, 2
Answer» Solve the following quadratic equations by factorization: $\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2 x + 3}{x - 2}; x \neq 1, - 2, 2$

Discussion

2119.	A person invested 20%, 30% and 25% of his savings in buying shares of three different companies X, Y and Z which declared dividends of 10%, 12% and 15% respectively. If the total income on account of dividends be Rs 2,337.50, find his savings and the amount which he invested in buying shares of each company. [4 MARKS]
Answer» A person invested $20 %, 30 %$ and $25 %$ of his savings in buying shares of three different companies X, Y and Z which declared dividends of $10 %, 12 %$ and $15 %$ respectively. If the total income on account of dividends be Rs 2,337.50, find his savings and the amount which he invested in buying shares of each company. [4 MARKS]

Discussion

2120.	A shopkeeper sells a refrigerator at cost price of Rs 15000 with a profit of 20%. Find the price at which customer has purchased it. Also find profit gained by the shopkeeper.
Answer» A shopkeeper sells a refrigerator at cost price of Rs 15000 with a profit of 20%. Find the price at which customer has purchased it. Also find profit gained by the shopkeeper.

Discussion

2121.	tan2 θ(sec θ−1)2=
Answer» $\frac{{tan}^{2} θ}{(sec θ - 1)^{2}} =$

Discussion

2122.	A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for 6 days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and charge for each extra day.
Answer» A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for 6 days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and charge for each extra day.

Discussion

2123.	The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.Based on the above information, answer the following questions. If α and β are the zeros of polynomialx2+3x−2, find 1(α)3+1(β)3.
Answer» The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. Based on the above information, answer the following questions. If $α$ and $β$ are the zeros of polynomial $x^{2} + 3 x - 2$ , find $\frac{1}{(α)^{3}} + \frac{1}{(β)^{3}}$ .

Discussion

2124.	Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .
Answer» Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

Discussion

2125.	If 3+5+7+.....to n terms5+8+11+...to 10 terms=7, then n is equal to
Answer» If $\frac{3 + 5 + 7 + . . . . . t o n t e r m s}{5 + 8 + 11 + . . . t o 10 t e r m s} = 7,$ then n is equal to

Discussion

2126.	Question 25 In an AP, if Sn=3n2+5n and ak=164 , then find the value of k.
Answer» Question 25 In an AP, if $S_{n} = 3 n^{2} + 5 n$ and $a_{k} = 164$ , then find the value of $k$ .

Discussion

2127.	Question 111 (i)What will happen to the volume of the cube, if its edge is tripled?
Answer» Question 111 (i) What will happen to the volume of the cube, if its edge is tripled?

2127.

Question 111 (i)What will happen to the volume of the cube, if its edge is tripled?

Answer»

Question 111 (i)

What will happen to the volume of the cube, if its edge is tripled?

Discussion

2128.	Given ∆ABC ~ ∆PQR, if ABPQ=13, then find Area ∆ABCArea ∆PQR.
Answer» Given $∆ A B C ~ ∆ P Q R, if \frac{A B}{P Q} = \frac{1}{3}, then find \frac{Area (∆ A B C)}{Area (∆ P Q R)}$ .

Discussion

2129.	Which of the following can’t be represented in standard form ax+by+c=0 of a linear equation?
Answer» Which of the following can’t be represented in standard form $a x + b y + c = 0$ of a linear equation?

Discussion

2130.	Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Answer» Find the sum of all natural numbers between 1 and 100, which are divisible by 3.

Discussion

2131.	State the type of the conditional clause in the sentence. I wouldn’t have spoken like that if I had known that she was listening.
Answer» State the type of the conditional clause in the sentence. I wouldn’t have spoken like that if I had known that she was listening.

2131.

State the type of the conditional clause in the sentence. I wouldn’t have spoken like that if I had known that she was listening.

Answer»

State the type of the conditional clause in the sentence.

I wouldn’t have spoken like that if I had known that she was listening.

Discussion

2132.	A roller having radius 35 cm and length 1 m takes 200 complete revolutions to move once on a play ground. What us the area of the playground?
Answer» A roller having radius 35 cm and length 1 m takes 200 complete revolutions to move once on a play ground. What us the area of the playground?

Discussion

2133.	By using the method of completing the square, show that the equation 2x2+x+4=0 has no real roots.
Answer» By using the method of completing the square, show that the equation $2 x^{2} + x + 4 = 0$ has no real roots.

Discussion

2134.	All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a black face card (ii) a red card. [CBSE 2014]
Answer» All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a black face card (ii) a red card. [CBSE 2014]

Discussion

2135.	Question 10Find the solution of the pair of equations x10+y5−1=0 and x8+y6=15 find λ, if y=λx+5
Answer» Question 10 Find the solution of the pair of equations $\frac{x}{10} + \frac{y}{5} - 1 = 0 a n d \frac{x}{8} + \frac{y}{6} = 15 f i n d λ, i f y = λ x + 5$

Discussion

2136.	Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is(a) 2a metres(b) a22metres(c) a2 metres(d) 2a metres
Answer» Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is (a) $\sqrt{2} a m e t r e s$ (b) $\frac{a}{2 \sqrt{2}} m e t r e s$ (c) $\frac{a}{\sqrt{2}} m e t r e s$ (d) 2a metres

Discussion

2137.	Find the values of a and b for which the following system of linear equations has an infinite number of solutions:2x+3y=7a+bx+2a-by=21 [CBSE 2001]
Answer» Find the values of a and b for which the following system of linear equations has an infinite number of solutions: $2 x + 3 y = 7 (a + b) x + (2 a - b) y = 21$ [CBSE 2001]

Discussion

2138.	The vertices of △ ABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.
Answer» The vertices of $△$ ABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.

Discussion

2139.	The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is(a) x3 − 3x2 + 3x − 5(b) −x3 − 3x2 − 3x − 5(c) −x3 + 3x2 − 3x + 5(d) x3 − 3x2 − 3x + 5
Answer» The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is (a) x³ − 3x² + 3x − 5 (b) −x³ − 3x² − 3x − 5 (c) −x³ + 3x² − 3x + 5 (d) x³ − 3x² − 3x + 5

Discussion

2140.	The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.
Answer» The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

2140.

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

Answer»

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

Discussion

2141.	11. The eccentricity of an ellipse whose focii are (2,4) &(14,9)and touches x axis is. p/313 then value of p is
Answer» 11. The eccentricity of an ellipse whose focii are (2,4) &(14,9)and touches x axis is. p/313 then value of p is

Discussion

2142.	The number 1.2.3.4.5.6......25 has _______ number of zeroes in the end.
Answer» The number 1.2.3.4.5.6......25 has _______ number of zeroes in the end.

Discussion

2143.	In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.
Answer» In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

Discussion

2144.

In an annual examination, marks (out of 90) obtained by students of class X in mathematics are given below: Marks obtained 0−15 15−30 30−45 45−60 60−75 75−90 Number of students 2 4 5 20 9 10 Find the mean marks.

Answer» In an annual examination, marks (out of 90) obtained by students of class X in mathematics are given below:

Marks obtained	0−15	15−30	30−45	45−60	60−75	75−90
Number of students	2	4	5	20	9	10

Find the mean marks.

Discussion

2145.	The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 655 cm², find the length of the parallel sides.
Answer» The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 655 cm², find the length of the parallel sides.

Discussion

2146.	A park is in the form of a rectangle 120 m × 100 m. At the centre of the park there is a circular lawn, The area of park excluding lawn is 8700 m2. Find the radius of the circular lawn. (Use π = 22/7).
Answer» A park is in the form of a rectangle 120 m × 100 m. At the centre of the park there is a circular lawn, The area of park excluding lawn is 8700 m². Find the radius of the circular lawn. (Use π = 22/7).

Discussion

2147.	Q73. A couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
Answer» Q73. A couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

Discussion

2148.	A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting (i) three heads, (ii) at least 2 tails.
Answer» A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting (i) three heads, (ii) at least 2 tails.

Discussion

2149.	A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327. What is the basic first class full fare and what is the reservation charge?
Answer» A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327. What is the basic first class full fare and what is the reservation charge?

Discussion

2150.	A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire. [CBSE 2012]
Answer» A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire. [CBSE 2012]

Discussion

Explore topic-wise InterviewSolutions in .

The daily expenses of 40 families has been shown by the following frequency distribution: Expenses (in ₹) 500 − 700 700 − 900 900 − 1100 1100 − 1300 1300 − 1500 Number of families 6 8 10 9 7 Find the mean daily expenses.

In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

find the value of x |x - 3| + |4 - x| = 1

How many terms of the AP 9, 17, 25, ... must be taken so that their sum is 636?

If sin(B+C)=√32 and sin A=12, find B+C and A.

Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.

Find the mean, median and mode of: 3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4

The quadratic polynomial in x whose zeros are −a, 2a is:

Question 25In an AP, if Sn=3n2+5n and ak=164 , then find the value of k.

Find the values of k for which the quadratic equation 3k+1x2+2k+1x+1=0 has equal roots. Also, find the roots.

If the product of zeros of the quadratic polynomial f(x) = x2 − 4x + k is 3, find the value of k.

Q1-in a seminar the number of participants in hindi, English and mathematics are 60,84 and 108, respectively. The minimum number of rooms, required if in each room the same number of participants at to be seated and all of them being in the same subject?

Calculate the difference between the part of container filled with paper and plastic wastes.

19.Given f(x+1) = 3x + 5, find f(x).

The product of three consecutive positive integers is divisible by 6 Justify whether the statement is true or false

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.(Use π=227)

Solve the following quadratic equations by factorization:x+1x-1+x-2x+2=4-2x+3x-2; x≠1,-2, 2

A shopkeeper sells a refrigerator at cost price of Rs 15000 with a profit of 20%. Find the price at which customer has purchased it. Also find profit gained by the shopkeeper.

tan2 θ(sec θ−1)2=

Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

If 3+5+7+.....to n terms5+8+11+...to 10 terms=7, then n is equal to

Question 25 In an AP, if Sn=3n2+5n and ak=164 , then find the value of k.

Question 111 (i)What will happen to the volume of the cube, if its edge is tripled?

Given ∆ABC ~ ∆PQR, if ABPQ=13, then find Area ∆ABCArea ∆PQR.

Which of the following can’t be represented in standard form ax+by+c=0 of a linear equation?

Find the sum of all natural numbers between 1 and 100, which are divisible by 3.

State the type of the conditional clause in the sentence. I wouldn’t have spoken like that if I had known that she was listening.

A roller having radius 35 cm and length 1 m takes 200 complete revolutions to move once on a play ground. What us the area of the playground?

By using the method of completing the square, show that the equation 2x2+x+4=0 has no real roots.

All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a black face card (ii) a red card. [CBSE 2014]

Question 10Find the solution of the pair of equations x10+y5−1=0 and x8+y6=15 find λ, if y=λx+5

Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is(a) 2a metres(b) a22metres(c) a2 metres(d) 2a metres

Find the values of a and b for which the following system of linear equations has an infinite number of solutions:2x+3y=7a+bx+2a-by=21 [CBSE 2001]

The vertices of △ ABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.

The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is(a) x3 − 3x2 + 3x − 5(b) −x3 − 3x2 − 3x − 5(c) −x3 + 3x2 − 3x + 5(d) x3 − 3x2 − 3x + 5

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

11. The eccentricity of an ellipse whose focii are (2,4) &(14,9)and touches x axis is. p/313 then value of p is

The number 1.2.3.4.5.6......25 has _______ number of zeroes in the end.

In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

In an annual examination, marks (out of 90) obtained by students of class X in mathematics are given below: Marks obtained 0−15 15−30 30−45 45−60 60−75 75−90 Number of students 2 4 5 20 9 10 Find the mean marks.

The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 655 cm², find the length of the parallel sides.

A park is in the form of a rectangle 120 m × 100 m. At the centre of the park there is a circular lawn, The area of park excluding lawn is 8700 m2. Find the radius of the circular lawn. (Use π = 22/7).

Q73. A couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting (i) three heads, (ii) at least 2 tails.

A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire. [CBSE 2012]