32581 + Interview Questions in Mathematics Page 246 InterviewSolution

12251.

Find the mean of each of the following frequency distributions : Class interval: 0−8 8−16 16−24 24−32 32−40 Frequency: 5 6 4 3 2

Answer» Find the mean of each of the following frequency distributions :

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	5	6	4	3	2

Discussion

12252.

Enter the following transactions in the Journal of Sahil Bros. : 2018 ₹ October 1 Purchased goods from Anil for Cash 40,000 3 Purchased goods from Atul 75,000 6 Returned goods to Atul 3,000 8 Paid cash to Atul 50,000 10 Sold goods to Charu 1,00,000 12 Charu returned 20% of goods 15 Paid rent 2,000 20 Sahil withdrew for personal use 10,000

Answer» Enter the following transactions in the Journal of Sahil Bros. :

2018			₹
October	1	Purchased goods from Anil for Cash	40,000
	3	Purchased goods from Atul	75,000
	6	Returned goods to Atul	3,000
	8	Paid cash to Atul	50,000
	10	Sold goods to Charu	1,00,000
	12	Charu returned 20% of goods
	15	Paid rent	2,000
	20	Sahil withdrew for personal use	10,000

Discussion

12253.	A steel wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of steel to be 8.88 g per cm3
Answer» A steel wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of steel to be 8.88 g per cm3

Discussion

12254.	Question 1 (vi)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(vi) 4x2+5√2x−3
Answer» Question 1 (vi) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (vi) $4 x^{2} + 5 \sqrt{2} x - 3$

Discussion

12255.	The distance between the points (a cos25∘,0) and (0,a cos65∘) is ___.
Answer» The distance between the points $(a c o s 25^{\circ}, 0)$ and $(0, a c o s 65^{\circ})$ is ___.

Discussion

12256.	, IF sina-cosa 1/2.then find the value of 1/ sina+cosa
Answer» , IF sina-cosa 1/2.then find the value of 1/ sina+cosa

Discussion

12257.	The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is __________.
Answer» The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is __________.

Discussion

12258.	Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way.Class intervalFrequency(km/h)30−40340−50650−602560−706570−805080−902890−10014Draw a histogram and frequency polygon representing the data above.
Answer» Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way. $\begin{matrix} Class interval & Frequency (km/h) 30 - 40 & 3 40 - 50 & 6 50 - 60 & 25 60 - 70 & 65 70 - 80 & 50 80 - 90 & 28 90 - 100 & 14 \end{matrix}$ Draw a histogram and frequency polygon representing the data above.

Discussion

12259.	If α and β are the zeroes of the polynomial f(x)=x2 -p(x+1)-c,then (α+1)(β+1) is equal to?
Answer» If α and β are the zeroes of the polynomial f(x)=x²-p(x+1)-c,then (α+1)(β+1) is equal to?

Discussion

12260.	Question 5 An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.
Answer» Question 5 An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

Discussion

12261.	The denominator of a fraction is 5 more than its numerator. If the numerator is decreased by 1 and the denominator is increased by 2, the resulting fraction is 15. Find the original fraction.
Answer» The denominator of a fraction is $5$ more than its numerator. If the numerator is decreased by $1$ and the denominator is increased by $2$ , the resulting fraction is $\frac{1}{5}$ . Find the original fraction.

Discussion

12262.	Let Cl : x^2+y^2 = 1; C2: (x-10)^2+y^2=1, C3:x^2+y^2-10x-42y + 457 =0 be three circles. A cirele C hasbeen drawn to touch circles C1 and C2 externally andC3 internally. Now circles C1, C2 and C3 start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formedby joining the centres of rolling circles C1, C2and C3lies on
Answer» Let Cl : x^2+y^2 = 1; C2: (x-10)^2+y^2=1, C3:x^2+y^2-10x-42y + 457 =0 be three circles. A cirele C hasbeen drawn to touch circles C1 and C2 externally andC3 internally. Now circles C1, C2 and C3 start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formedby joining the centres of rolling circles C1, C2and C3lies on

Discussion

12263.	there are two lamp posts L1 and L2 of equal height on either side of the road having width 100 m. I f angle of elevation of the lamp-posts from a point on the road are 30 degree and 45 degree , then the height of the lamp-post will be
Answer» there are two lamp posts L1 and L2 of equal height on either side of the road having width 100 m. I f angle of elevation of the lamp-posts from a point on the road are 30 degree and 45 degree , then the height of the lamp-post will be

Discussion

12264.	Evaluate : 2/3(cos30^4-sin45^4)-3(sin²60-sec²45)+1/4cot²30
Answer» Evaluate : 2/3(cos30^4-sin45^4)-3(sin²60-sec²45)+1/4cot²30

Discussion

12265.	Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, determine the area of the larger triangle.
Answer» Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², determine the area of the larger triangle.

Discussion

12266.	The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle. [Use π = 22/7 and 3 = 1.73]
Answer» The area of a circle inscribed in an equilateral triangle is 154 cm². Find the perimeter of the triangle. [Use π = 22/7 and $\sqrt{3}$ = 1.73]

Discussion

12267.	Find the area of the shaded region in the given figure, if ABCD is a square of side 20 m and APD and BPC are semicircle.
Answer» Find the area of the shaded region in the given figure, if ABCD is a square of side 20 m and APD and BPC are semicircle.

Discussion

12268.	How many coins of radius 1 cm and thickness 0.28 CM should be melted to form a solid cylinder of height 7 cm and diameter 8 cm
Answer» How many coins of radius 1 cm and thickness 0.28 CM should be melted to form a solid cylinder of height 7 cm and diameter 8 cm

Discussion

12269.	In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF and the quad. FDCE is -
Answer» In the given figure, AE and BD are two medians of a $△$ ABC meeting at F. The ratio of the area of $△$ ABF and the quad. FDCE is -

12269.

In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF and the quad. FDCE is -

Answer»

In the given figure, AE and BD are two medians of a $△$ ABC meeting at F. The ratio of the area of $△$ ABF and the quad. FDCE is -

Discussion

12270.	42. If sum of first n terms of two AS are in ratio (7n+2):(n+4).find the ratio of 5th term.Explai each step
Answer» 42. If sum of first n terms of two AS are in ratio (7n+2):(n+4).find the ratio of 5th term.Explai each step

Discussion

12271.	Solve by factorisation (quadratic equations) 1/2a+b+2x = 1/2a+ 1/b +1/2x
Answer» Solve by factorisation (quadratic equations) 1/2a+b+2x = 1/2a+ 1/b +1/2x

12271.

Solve by factorisation (quadratic equations) 1/2a+b+2x = 1/2a+ 1/b +1/2x

Answer»

Solve by factorisation (quadratic equations)

1/2a+b+2x = 1/2a+ 1/b +1/2x

Discussion

12272.	The difference between the semi perimeter and the side of a △ ABC are 8 cm , 7cm & 5 cm respectively.Find the area of triang
Answer» The difference between the semi perimeter and the side of a △ ABC are 8 cm , 7cm & 5 cm respectively.Find the area of triang

Discussion

12273.	If y is inversely proportional to x, then yx is always
Answer» If y is inversely proportional to x, then yx is always

Discussion

12274.	In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.
Answer» In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.

Discussion

12275.	A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 12 such matchboxes?
Answer» A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 12 such matchboxes?

Discussion

12276.	Solve each of the following systems of eqautions by the method of cross-multiplication: ax+by=a2 bx+ay=b2
Answer» Solve each of the following systems of eqautions by the method of cross-multiplication: $a x + b y = a^{2}$ $b x + a y = b^{2}$

12276.

Solve each of the following systems of eqautions by the method of cross-multiplication: ax+by=a2 bx+ay=b2

Answer»

Solve each of the following systems of eqautions by the method of cross-multiplication:

$a x + b y = a^{2}$

$b x + a y = b^{2}$

Discussion

12277.	Answer the questions with the help of a given figure.(i) State the points which are equidistant from point B.(ii) Write a pair of points equidistant from point Q.(iii) Find d(U,V), d(P,C), d(V,B),d(U, L).
Answer» Answer the questions with the help of a given figure. (i) State the points which are equidistant from point B. (ii) Write a pair of points equidistant from point Q. (iii) Find d(U,V), d(P,C), d(V,B),d(U, L).

Discussion

12278.	Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is(a) a4(b) a2(c) a2(d) a22
Answer» Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is (a) $\frac{a}{4}$ (b) $\frac{a}{\sqrt{2}}$ (c) $a \sqrt{2}$ (d) $\frac{a}{2 \sqrt{2}}$

Discussion

12279.	Determine the 10th term from the end of the A.P. 4, 9, 14, ........, 254.
Answer» Determine the $10^{t h}$ term from the end of the A.P. 4, 9, 14, ........, 254.

Discussion

12280.	Question 2 Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC=40∘.
Answer» Question 2 Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $∠ A O C = 40^{\circ}$ .

Discussion

12281.	_______ is the formula to find out the total surface area of a cylinder in which both sides are hemisphere
Answer» _______ is the formula to find out the total surface area of a cylinder in which both sides are hemisphere

Discussion

12282.	the sum of 5 and 6 term of an a p is 4k+20 and 9 term is 2k+17 find the first term and the common difference
Answer» the sum of 5 and 6 term of an a p is 4k+20 and 9 term is 2k+17 find the first term and the common difference

Discussion

12283.	If 2x+y=2x-y=8 then the value of y is(a) 12 (b) 32 (c) 0 (d) none of these
Answer» If $2^{x + y} = 2^{x - y} = \sqrt{8}$ then the value of y is (a) $\frac{1}{2}$ (b) $\frac{3}{2}$ (c) 0 (d) none of these

Discussion

12284.	One card is drawn from a well shuffled deck of 52 playing cards. What is the probability of getting a non-face card?
Answer» One card is drawn from a well shuffled deck of 52 playing cards. What is the probability of getting a non-face card?

Discussion

12285.	Question 5 (iv) Find 30.94 ÷ 0.7
Answer» Question 5 (iv) Find 30.94 $\div$ 0.7

Discussion

12286.	If a1,a2.....an be in AP of non zero terms then prove that 1/(a1a2 ) + 1/(a2a3)+........+1/(an-1an) = (n-1) /(a1an)
Answer» If a₁,a₂.....a_n be in AP of non zero terms then prove that 1/(a₁a₂) + 1/(a₂a₃)+........+1/(a_n-1a_n) = (n-1) /(a₁a_n)

Discussion

12287.	The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is (a) 361 cm2 (b) 125 cm2 (c) 236 cm2 (d) 486 cm2
Answer» The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5 $\sqrt{5}$ cm. Its surface area is (a) 361 $c m^{2}$ (b) 125 $c m^{2}$ (c) 236 $c m^{2}$ (d) 486 $c m^{2}$

12287.

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is (a) 361 cm2 (b) 125 cm2 (c) 236 cm2 (d) 486 cm2

Answer»

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5 $\sqrt{5}$ cm. Its surface area is

(a) 361 $c m^{2}$ (b) 125 $c m^{2}$ (c) 236 $c m^{2}$ (d) 486 $c m^{2}$

Discussion

12288.	___ is a line that intersects a circle at only one point, and ___ is a line that intersects the circle at two distinct points.
Answer» ___ is a line that intersects a circle at only one point, and ___ is a line that intersects the circle at two distinct points.

Discussion

12289.	The points (a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle.
Answer» The points $(a, a), (- a, - a)$ and $(- \sqrt{3} a, \sqrt{3} a)$ are the vertices of a/an _____ triangle.

Discussion

12290.	Find inverse of the function f(x)=5^(log x to the base e) where f: (0,infinty) to (0,infinity)
Answer» Find inverse of the function f(x)=5^(log x to the base e) where f: (0,infinty) to (0,infinity)

Discussion

12291.	Question 1 Find which of the variables x,y,z and u represent rational numbers and which irrational numbers: (i)x2=5(ii)y2=9(iii)z2=0.04(iv)u2=174
Answer» Question 1 Find which of the variables x,y,z and u represent rational numbers and which irrational numbers: $(i) x^{2} = 5 (i i) y^{2} = 9 (i i i) z^{2} = 0.04 (i v) u^{2} = \frac{17}{4}$

Discussion

12292.	∆ABC is an equilateral triangle. Point P is on base BC such that PC = 13 BC, if AB = 6 cm find AP.
Answer» ∆ABC is an equilateral triangle. Point P is on base BC such that PC = $\frac{1}{3}$ BC, if AB = 6 cm find AP.

Discussion

12293.	If P(a,b) divides B(h,k) and C(l,m) such that a = pl+qhp+q. Find the ratio in which P divides BC.
Answer» If P(a,b) divides B(h,k) and C(l,m) such that $a$ = $\frac{p l + q h}{p + q}$ . Find the ratio in which P divides BC.

Discussion

12294.	Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).
Answer» Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

Discussion

12295.	Question 1 For some integer m, every even integer is of the form A) m B) m + 1 C) 2m D) 2m + 1
Answer» Question 1 For some integer m, every even integer is of the form A) m B) m + 1 C) 2m D) 2m + 1

Discussion

12296.	What is the ratio ABBC for the line segment AB following the construction method below? Step 1: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2,...,A30 Step 2: A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and intersecting AB at C.
Answer» What is the ratio $\frac{A B}{B C}$ for the line segment AB following the construction method below? Step 1: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$ Step 2: A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ and intersecting AB at C.

Discussion

12297.	In the above figure, AB = 7 cm & BC = 9 cm. Find the length of CD.
Answer» In the above figure, AB = 7 cm & BC = 9 cm. Find the length of CD.

12297.

In the above figure, AB = 7 cm & BC = 9 cm. Find the length of CD.

Answer»

In the above figure, AB = 7 cm & BC = 9 cm. Find the length of CD.

Discussion

12298.	When x3 - 3x2 + 5x - 3 is divided by x2 - k , the remainder is 7x + a . Then the value of k is_____
Answer» When x³ - 3x² + 5x - 3 is divided by x² - k , the remainder is 7x + a . Then the value of k is_____

Discussion

12299.	A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.
Answer» A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.

Discussion

12300.	If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.
Answer» If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

Discussion

Explore topic-wise InterviewSolutions in .

Find the mean of each of the following frequency distributions : Class interval: 0−8 8−16 16−24 24−32 32−40 Frequency: 5 6 4 3 2

A steel wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of steel to be 8.88 g per cm3

Question 1 (vi)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(vi) 4x2+5√2x−3

The distance between the points (a cos25∘,0) and (0,a cos65∘) is ___.

, IF sina-cosa 1/2.then find the value of 1/ sina+cosa

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is __________.

Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way.Class intervalFrequency(km/h)30−40340−50650−602560−706570−805080−902890−10014Draw a histogram and frequency polygon representing the data above.

If α and β are the zeroes of the polynomial f(x)=x2 -p(x+1)-c,then (α+1)(β+1) is equal to?

The denominator of a fraction is 5 more than its numerator. If the numerator is decreased by 1 and the denominator is increased by 2, the resulting fraction is 15. Find the original fraction.

there are two lamp posts L1 and L2 of equal height on either side of the road having width 100 m. I f angle of elevation of the lamp-posts from a point on the road are 30 degree and 45 degree , then the height of the lamp-post will be

Evaluate : 2/3(cos30^4-sin45^4)-3(sin²60-sec²45)+1/4cot²30

Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, determine the area of the larger triangle.

The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle. [Use π = 22/7 and 3 = 1.73]

Find the area of the shaded region in the given figure, if ABCD is a square of side 20 m and APD and BPC are semicircle.

How many coins of radius 1 cm and thickness 0.28 CM should be melted to form a solid cylinder of height 7 cm and diameter 8 cm

In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF and the quad. FDCE is -

42. If sum of first n terms of two AS are in ratio (7n+2):(n+4).find the ratio of 5th term.Explai each step

Solve by factorisation (quadratic equations) 1/2a+b+2x = 1/2a+ 1/b +1/2x

The difference between the semi perimeter and the side of a △ ABC are 8 cm , 7cm & 5 cm respectively.Find the area of triang

If y is inversely proportional to x, then yx is always

In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.

A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 12 such matchboxes?

Solve each of the following systems of eqautions by the method of cross-multiplication: ax+by=a2 bx+ay=b2

Answer the questions with the help of a given figure.(i) State the points which are equidistant from point B.(ii) Write a pair of points equidistant from point Q.(iii) Find d(U,V), d(P,C), d(V,B),d(U, L).

Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is(a) a4(b) a2(c) a2(d) a22

Determine the 10th term from the end of the A.P. 4, 9, 14, ........, 254.

Question 2 Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC=40∘.

_______ is the formula to find out the total surface area of a cylinder in which both sides are hemisphere

the sum of 5 and 6 term of an a p is 4k+20 and 9 term is 2k+17 find the first term and the common difference

If 2x+y=2x-y=8 then the value of y is(a) 12 (b) 32 (c) 0 (d) none of these

One card is drawn from a well shuffled deck of 52 playing cards. What is the probability of getting a non-face card?

Question 5 (iv) Find 30.94 ÷ 0.7

If a1,a2.....an be in AP of non zero terms then prove that 1/(a1a2 ) + 1/(a2a3)+........+1/(an-1an) = (n-1) /(a1an)

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is (a) 361 cm2 (b) 125 cm2 (c) 236 cm2 (d) 486 cm2

___ is a line that intersects a circle at only one point, and ___ is a line that intersects the circle at two distinct points.

The points (a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle.

Find inverse of the function f(x)=5^(log x to the base e) where f: (0,infinty) to (0,infinity)

Question 1 Find which of the variables x,y,z and u represent rational numbers and which irrational numbers: (i)x2=5(ii)y2=9(iii)z2=0.04(iv)u2=174

∆ABC is an equilateral triangle. Point P is on base BC such that PC = 13 BC, if AB = 6 cm find AP.

If P(a,b) divides B(h,k) and C(l,m) such that a = pl+qhp+q. Find the ratio in which P divides BC.

Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

Question 1 For some integer m, every even integer is of the form A) m B) m + 1 C) 2m D) 2m + 1

In the above figure, AB = 7 cm &amp; BC = 9 cm. Find the length of CD.

When x3 - 3x2 + 5x - 3 is divided by x2 - k , the remainder is 7x + a . Then the value of k is_____

A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

_ is a line that intersects a circle at only one point, and _ is a line that intersects the circle at two distinct points.

In the above figure, AB = 7 cm & BC = 9 cm. Find the length of CD.