32581 + Interview Questions in Mathematics

1.	An article costs ₹ 1450. The rate of sales tax is 8%. Find the bill amount.
Answer» An article costs ₹ 1450. The rate of sales tax is 8%. Find the bill amount.

Discussion

2.	x-2 is the factor of ___
Answer» x-2 is the factor of ___

Discussion

3.	16 kg oxygen gas expands at STP (1 atm) isobarically to occupy double of its original volume. The work done during the process is nearby
Answer» 16 kg oxygen gas expands at STP (1 atm) isobarically to occupy double of its original volume. The work done during the process is nearby

Discussion

4.	100 % as a decimal is ___
Answer» 100 % as a decimal is ___

Discussion

5.	Solve each of the following systems of equations by the method of cross-multiplication :ax+by=a+b23x+5y=4
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $a x + b y = \frac{a + b}{2} 3 x + 5 y = 4$

Discussion

6.	If a & b are the zeroes of polynomial px^2+ qx+ r,then find the value of a^2+b^2 ?
Answer» If a & b are the zeroes of polynomial px^2+ qx+ r,then find the value of a^2+b^2 ?

Discussion

7.	The sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550. Find the AP.
Answer» The sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550. Find the AP.

Discussion

8.	A body is thrown from ground at angle 60\ast above horizontal If θ is angle between its velocity and acceleration, then- (1) 30≤θ≤60 (2)60≤θ≤90 (3) 30≤θ≤ 150 (4) 60≤θ≤150
Answer» A body is thrown from ground at angle 60\ast above horizontal If θ is angle between its velocity and acceleration, then- (1) 30≤θ≤60 (2)60≤θ≤90 (3) 30≤θ≤ 150 (4) 60≤θ≤150

Discussion

9.	Two squares have side x cm and (x + 4) cm. The sum of their areas is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
Answer» Two squares have side x cm and (x + 4) cm. The sum of their areas is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.

Discussion

10.	Find 2 Rational Numbers between 1/3 and 2/5
Answer» Find 2 Rational Numbers between 1/3 and 2/5

Discussion

11.	[\|x\|]+[\|y\|]=2 then area bounded by them
Answer» [\|x\|]+[\|y\|]=2 then area bounded by them

Discussion

12.	Solve for x and y: 2(3x+2y)+3(3x−2y)=175,5(3x+2y)+1(3x−2y)=2.
Answer» Solve for x and y: $\frac{2}{(3 x + 2 y)} + \frac{3}{(3 x - 2 y)} = \frac{17}{5}, \frac{5}{(3 x + 2 y)} + \frac{1}{(3 x - 2 y)} = 2.$

12.

Solve for x and y: 2(3x+2y)+3(3x−2y)=175,5(3x+2y)+1(3x−2y)=2.

Answer»

Solve for x and y:

$\frac{2}{(3 x + 2 y)} + \frac{3}{(3 x - 2 y)} = \frac{17}{5}, \frac{5}{(3 x + 2 y)} + \frac{1}{(3 x - 2 y)} = 2.$

Discussion

13.	A ball is projected from the ground at angle60 from the ground if ball just clears a wall 5m from the point of projection & falls on the ground 15m away from it on other side, then the height of the wall is nearly equal to1] 5.8m2] 6.5m3] 7.9m4] 9.8m
Answer» A ball is projected from the ground at angle60 from the ground if ball just clears a wall 5m from the point of projection & falls on the ground 15m away from it on other side, then the height of the wall is nearly equal to 1] 5.8m 2] 6.5m 3] 7.9m 4] 9.8m

Discussion

14.	Question 1 (v)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.t2−15
Answer» Question 1 (v) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. $t^{2} - 15$

14.

Question 1 (v)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.t2−15

Answer»

Question 1 (v)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$t^{2} - 15$

Discussion

15.	Solve the following systems of equations: 2x+3y=9xy 4x+9y=21xy
Answer» Solve the following systems of equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{x y}$ $\frac{4}{x} + \frac{9}{y} = \frac{21}{x y}$

15.

Solve the following systems of equations: 2x+3y=9xy 4x+9y=21xy

Answer»

Solve the following systems of equations:

$\frac{2}{x} + \frac{3}{y} = \frac{9}{x y}$

$\frac{4}{x} + \frac{9}{y} = \frac{21}{x y}$

Discussion

16.	How to draw a graph for 1/log\|x\|
Answer» How to draw a graph for 1/log\|x\|

Discussion

17.

To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Concentration of SO2 (in ppm) Frequency 0.00−0.04 0.04−0.08 0.08−0.12 0.12−0.16 0.16−0.20 0.20−0.24 4 9 9 2 4 2 Find the mean of concentration of SO2 in the air.

Answer» To find out the concentration of SO₂ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

Concentration of SO₂ (in ppm)	Frequency
0.00−0.04 0.04−0.08 0.08−0.12 0.12−0.16 0.16−0.20 0.20−0.24	4 9 9 2 4 2

Find the mean of concentration of SO₂ in the air.

Discussion

18.	The volume of a hemi-sphere is 242512 cm3. Find its curved surface area. (Use π = 22/7)
Answer» The volume of a hemi-sphere is 2425 $\frac{1}{2}$ cm³. Find its curved surface area. (Use π = 22/7)

Discussion

19.	If θ is any acute angle, what is the area of a square with adjacent sides sin θ and cosec θ?
Answer» If $θ$ is any acute angle, what is the area of a square with adjacent sides $s i n θ$ and $c o s e c θ$ ?

Discussion

20.	State the Pythagoras' theorem.
Answer» State the Pythagoras' theorem.

Discussion

21.	Slope of a line whose inclination is 60∘ is ____.
Answer» Slope of a line whose inclination is $60^{\circ}$ is ____.

Discussion

22.	{Q7/30 If }A=(a_{ij}) be a square matrix of order }n and }a_{ij}=(-1)^in_{C_i}x_i}{{}^nC_j, if }n is odd, then trace of }A is equal to
Answer» {Q7/30 If }A=(a_{ij}) be a square matrix of order }n and }a_{ij}=(-1)^in_{C_i}x_i}{{}^nC_j, if }n is odd, then trace of }A is equal to

Discussion

23.	A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is
Answer» A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is

23.

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is

Answer»

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is

Discussion

24.	For a frequency distribution, mean, median and mode are connected by the relation(a) Mode = 3 Mean − 2 Median(b) Mode = 2 Median − 3 Mean(c) Mode = 3 Median − 2 Mean(d) Mode = 3 Median + 2 Mean
Answer» For a frequency distribution, mean, median and mode are connected by the relation (a) Mode = 3 Mean − 2 Median (b) Mode = 2 Median − 3 Mean (c) Mode = 3 Median − 2 Mean (d) Mode = 3 Median + 2 Mean

Discussion

25.	If (x−3)(x−2) is the HCF of the polynomials x2−2x−3)(2x2+ax−2) and (x2+x−2)(3x2+bx−3), then a & b is
Answer» If $(x - 3) (x - 2)$ is the HCF of the polynomials $x^{2} - 2 x - 3) (2 x^{2} + a x - 2)$ and $(x^{2} + x - 2) (3 x^{2} + b x - 3)$ , then $a & b$ is

Discussion

26.	Prove that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.
Answer» Prove that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.

Discussion

27.	The angles of a polygon are in A.P. with common difference 5∘. If the smallest angle is 120∘, find the number of sides of the polygon.
Answer» The angles of a polygon are in A.P. with common difference $5^{\circ}$ . If the smallest angle is $120^{\circ}$ , find the number of sides of the polygon.

Discussion

28.	What is the sum of the infinite series 7+77+777+...n terms
Answer» What is the sum of the infinite series 7+77+777+...n terms

Discussion

29.	what should be the volume of the milk (in m3) which measures 5L
Answer» what should be the volume of the milk (in m3) which measures 5L

Discussion

30.	Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(i)A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.(ii)A fraction becomeswhen 1 is subtracted from the numerator and it becomeswhen 8 is added to its denominator. Find the fraction.(iii)Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?(v)The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Answer» Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: (i)A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day. (ii)A fraction becomeswhen 1 is subtracted from the numerator and it becomeswhen 8 is added to its denominator. Find the fraction. (iii)Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? (iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? (v)The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

30.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(i)A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.(ii)A fraction becomeswhen 1 is subtracted from the numerator and it becomeswhen 8 is added to its denominator. Find the fraction.(iii)Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?(v)The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Answer»

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

(i)A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.

(ii)A fraction becomeswhen 1 is subtracted from the numerator and it becomeswhen 8 is added to its denominator. Find the fraction.

(iii)Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

(v)The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Discussion

31.	If sec θ=135, show that 2 sin θ-3 cos θ4 sin θ- 9 cos θ=3.
Answer» If $\sec θ = \frac{13}{5}$ , show that $\frac{2 \sin θ - 3 \cos θ}{4 \sin θ - 9 \cos θ} = 3$ .

Discussion

32.	The arithmetic mean of the following data is 14. Find the value of k. xi : 5 10 15 20 25 fi : 7 k 8 4 5.
Answer» The arithmetic mean of the following data is 14. Find the value of k. $x_{i}$ : 5 10 15 20 25 $f_{i}$ : 7 k 8 4 5.

Discussion

33.	A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3 . Find the number .
Answer» A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3 . Find the number .

Discussion

34.	Choose the option which represents the simplest form of the fraction of shaded portion.
Answer» Choose the option which represents the simplest form of the fraction of shaded portion.

Discussion

35.	Question 2The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose and are to be painted silver.Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black.Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
Answer» Question 2 The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise $p e r c m^{2}$ and black paint costs 5 paise $p e r c m^{2}$ .

Discussion

36.	Software Ltd. company with registered capital of ₹ 5,00,000 in shares of ₹ 10 each issued 20,000 of such shares payable ₹ 2 on application, ₹ 4 on allotment, ₹ 2 on first call ₹ 2 on final call. All the money payable on allotment was duly received but on the first call being made, one shareholder paid the entire balance on his holding of 300 shares and five shareholders with a total holding of 1,000 shares failed to pay their dues on the first call. These shares were forfeited for non-payment of first call money. Final call was made and all the money due was received. Later on, forfeited shares were reissued ₹ 6 per share as fully paid-up.Record the above in the company's Journal and prepare the Balance Sheet.
Answer» Software Ltd. company with registered capital of ₹ 5,00,000 in shares of ₹ 10 each issued 20,000 of such shares payable ₹ 2 on application, ₹ 4 on allotment, ₹ 2 on first call ₹ 2 on final call. All the money payable on allotment was duly received but on the first call being made, one shareholder paid the entire balance on his holding of 300 shares and five shareholders with a total holding of 1,000 shares failed to pay their dues on the first call. These shares were forfeited for non-payment of first call money. Final call was made and all the money due was received. Later on, forfeited shares were reissued ₹ 6 per share as fully paid-up. Record the above in the company's Journal and prepare the Balance Sheet.

Discussion

37.	The median class for the following data is MarksBelow 10Below 20Below 30Below 40Below 50 No. of students 510233140
Answer» The median class for the following data is $\begin{matrix} Marks & B e l o w 10 & B e l o w 20 & B e l o w 30 & B e l o w 40 & B e l o w 50 No. of students & 5 & 10 & 23 & 31 & 40 \end{matrix}$

Discussion

38.	For a circle of radius r=10π cm.Angle subtended by arc θ =12∘ .What is the length of the arc in cm?
Answer» For a circle of radius $r = \frac{10}{π}$ cm. Angle subtended by arc $θ = 12^{\circ}$ . What is the length of the arc in cm?

Discussion

39.	Solve the following systems of equations:15x+16y=1213x-37y=8, x≠0, y≠0
Answer» Solve the following systems of equations: $\frac{1}{5 x} + \frac{1}{6 y} = 12 \frac{1}{3 x} - \frac{3}{7 y} = 8, x \neq 0, y \neq 0$

Discussion

40.	In the figure given above, what is the value of tan θ in terms of a,b and c?
Answer» In the figure given above, what is the value of $t a n θ$ in terms of a,b and c?

Discussion

41.	Question 29 80 bulbs are selected at random from a lot and their life time ( in hours) is recorded in the form of a frequency table given below: Lifetime (in hours)3005007009001100Frequency1012232510 One bulb is selected at random from the lot. The probability that its life is 1150 h, is: A) 180 B) 716 C) 0 D) 1
Answer» Question 29 80 bulbs are selected at random from a lot and their life time ( in hours) is recorded in the form of a frequency table given below: $\begin{matrix} Lifetime (in hours) & 300 & 500 & 700 & 900 & 1100 Frequency & 10 & 12 & 23 & 25 & 10 \end{matrix}$ One bulb is selected at random from the lot. The probability that its life is 1150 h, is: A) $\frac{1}{80}$ B) $\frac{7}{16}$ C) 0 D) 1

Discussion

42.	9. If a and b are the zeros of the quadritic polynomial f(t) = t2-5t+3 , then the value of a4b3+a3b4 is
Answer» 9. If a and b are the zeros of the quadritic polynomial f(t) = t2-5t+3 , then the value of a4b3+a3b4 is

Discussion

43.	A train 150m long is running at 72 km/hr. It crosses a bridge in 13 sec. Find the length of the bridge.
Answer» A train $150 m$ long is running at $72$ km/hr. It crosses a bridge in $13$ sec. Find the length of the bridge.

Discussion

44.	Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is ________.
Answer» Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is ________.

Discussion

45.	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

46.	Find the sum of all the multiplies of 9 lying between 405 and 805.
Answer» Find the sum of all the multiplies of 9 lying between 405 and 805.

Discussion

47.	The histogram for the following Class Marks2535455565Frequency71518128
Answer» The histogram for the following $\begin{matrix} Class Marks & 25 & 35 & 45 & 55 & 65 Frequency & 7 & 15 & 18 & 12 & 8 \end{matrix}$

47.

The histogram for the following Class Marks2535455565Frequency71518128

Answer»

The histogram for the following

$\begin{matrix} Class Marks & 25 & 35 & 45 & 55 & 65 Frequency & 7 & 15 & 18 & 12 & 8 \end{matrix}$

Discussion

48.	A die is weighted such that the probability of rolling the face numbered n is proportional to n2(n=1,2,3,4,5,6). The die is rolled twice, yielding the number a and b. The probability that a<b is P. Then the value of [2P] is where [.] represent the greatest integer function
Answer» A die is weighted such that the probability of rolling the face numbered $n$ is proportional to $n^{2} (n = 1, 2, 3, 4, 5, 6)$ . The die is rolled twice, yielding the number $a$ and $b$ . The probability that $a < b$ is $P$ . Then the value of $[\frac{2}{P}]$ is where [.] represent the greatest integer function

Discussion

49.	If a, b and c are all non-zero and a + b + c = 0, then prove that a2bc+b2ac+c2ab=3.
Answer» If a, b and c are all non-zero and a + b + c = 0, then prove that $\frac{a^{2}}{b c} + \frac{b^{2}}{a c} + \frac{c^{2}}{a b} = 3$ .

Discussion

50.	Find two rational numbers between √2 and √3
Answer» Find two rational numbers between √2 and √3

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

An article costs ₹ 1450. The rate of sales tax is 8%. Find the bill amount.

x-2 is the factor of ___

16 kg oxygen gas expands at STP (1 atm) isobarically to occupy double of its original volume. The work done during the process is nearby

100 % as a decimal is ___

Solve each of the following systems of equations by the method of cross-multiplication :ax+by=a+b23x+5y=4

If a & b are the zeroes of polynomial px^2+ qx+ r,then find the value of a^2+b^2 ?

The sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550. Find the AP.

A body is thrown from ground at angle 60\ast above horizontal If θ is angle between its velocity and acceleration, then- (1) 30≤θ≤60 (2)60≤θ≤90 (3) 30≤θ≤ 150 (4) 60≤θ≤150

Two squares have side x cm and (x + 4) cm. The sum of their areas is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.

Find 2 Rational Numbers between 1/3 and 2/5

[|x|]+[|y|]=2 then area bounded by them

Solve for x and y: 2(3x+2y)+3(3x−2y)=175,5(3x+2y)+1(3x−2y)=2.

A ball is projected from the ground at angle60 from the ground if ball just clears a wall 5m from the point of projection & falls on the ground 15m away from it on other side, then the height of the wall is nearly equal to1] 5.8m2] 6.5m3] 7.9m4] 9.8m

Question 1 (v)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.t2−15

Solve the following systems of equations: 2x+3y=9xy 4x+9y=21xy

How to draw a graph for 1/log|x|

The volume of a hemi-sphere is 242512 cm3. Find its curved surface area. (Use π = 22/7)

If θ is any acute angle, what is the area of a square with adjacent sides sin θ and cosec θ?

State the Pythagoras' theorem.

Slope of a line whose inclination is 60∘ is ____.

{Q7/30 If }A=(a_{ij}) be a square matrix of order }n and }a_{ij}=(-1)^in_{C_i}x_i}{{}^nC_j, if }n is odd, then trace of }A is equal to

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is

For a frequency distribution, mean, median and mode are connected by the relation(a) Mode = 3 Mean − 2 Median(b) Mode = 2 Median − 3 Mean(c) Mode = 3 Median − 2 Mean(d) Mode = 3 Median + 2 Mean

If (x−3)(x−2) is the HCF of the polynomials x2−2x−3)(2x2+ax−2) and (x2+x−2)(3x2+bx−3), then a &amp; b is

Prove that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.

The angles of a polygon are in A.P. with common difference 5∘. If the smallest angle is 120∘, find the number of sides of the polygon.

What is the sum of the infinite series 7+77+777+...n terms

what should be the volume of the milk (in m3) which measures 5L

If sec θ=135, show that 2 sin θ-3 cos θ4 sin θ- 9 cos θ=3.

The arithmetic mean of the following data is 14. Find the value of k. xi : 5 10 15 20 25 fi : 7 k 8 4 5.

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3 . Find the number .

Choose the option which represents the simplest form of the fraction of shaded portion.

The median class for the following data is MarksBelow 10Below 20Below 30Below 40Below 50 No. of students 510233140

For a circle of radius r=10π cm.Angle subtended by arc θ =12∘ .What is the length of the arc in cm?

Solve the following systems of equations:15x+16y=1213x-37y=8, x≠0, y≠0

In the figure given above, what is the value of tan θ in terms of a,b and c?

9. If a and b are the zeros of the quadritic polynomial f(t) = t2-5t+3 , then the value of a4b3+a3b4 is

A train 150m long is running at 72 km/hr. It crosses a bridge in 13 sec. Find the length of the bridge.

Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is ________.

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.

Find the sum of all the multiplies of 9 lying between 405 and 805.

The histogram for the following Class Marks2535455565Frequency71518128

A die is weighted such that the probability of rolling the face numbered n is proportional to n2(n=1,2,3,4,5,6). The die is rolled twice, yielding the number a and b. The probability that a&lt;b is P. Then the value of [2P] is where [.] represent the greatest integer function

If a, b and c are all non-zero and a + b + c = 0, then prove that a2bc+b2ac+c2ab=3.

Find two rational numbers between √2 and √3

If (x−3)(x−2) is the HCF of the polynomials x2−2x−3)(2x2+ax−2) and (x2+x−2)(3x2+bx−3), then a & b is

A die is weighted such that the probability of rolling the face numbered n is proportional to n2(n=1,2,3,4,5,6). The die is rolled twice, yielding the number a and b. The probability that a<b is P. Then the value of [2P] is where [.] represent the greatest integer function