32581 + Interview Questions in Mathematics

1.	Question 119 (xii) Write two integers, whose product is greater than both the integers.
Answer» Question 119 (xii) Write two integers, whose product is greater than both the integers.

1.

Question 119 (xii) Write two integers, whose product is greater than both the integers.

Answer»

Question 119 (xii)

Write two integers, whose product is greater than both the integers.

2.

The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet. Weight of sweet (gram) 0 - 250 250 - 500 500 - 750 750 - 1000 1000 - 1250 No. of customers 10 60 25 20 15

Answer» The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet.

Weight of sweet (gram)	0 - 250	250 - 500	500 - 750	750 - 1000	1000 - 1250
No. of customers	10	60	25	20	15

Discussion

3.	Which of the following expressions is used to determine the mode?
Answer» Which of the following expressions is used to determine the mode?

Discussion

4.	In Fig . 10.115, if PQR is the tangent to a circle at Q whose centre is O , AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to figure(a) 200 (b) 400 9c) 350 (d) 4500
Answer» In Fig . 10.115, if PQR is the tangent to a circle at Q whose centre is O , AB is a chord parallel to PR and $∠ B Q R = 70^{°}$ , then $∠ A Q B$ is equal to figure (a) 20⁰ (b) 40⁰ 9c) 35⁰ (d) 45⁰ 0

Discussion

5.	If (2p+1),13,(5p-3) are in AP, find the value of p.
Answer» If $(2 p + 1), 13, (5 p - 3)$ are in AP, find the value of p.

Discussion

6.	A circular pond is of diameter 17.5 m . It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per square metre Use π= 227
Answer» A circular pond is of diameter 17.5 m . It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per square metre $(U s e π = \frac{22}{7})$

Discussion

7.	Prove that (4-52) is an irrational number.
Answer» Prove that ( $4 - 5 \sqrt{2}$ ) is an irrational number.

Discussion

8.	Solve each of the following quadratic equations:3x−47+73x−4=52, x≠43
Answer» Solve each of the following quadratic equations: $\frac{3 x - 4}{7} + \frac{7}{3 x - 4} = \frac{5}{2}, x \neq \frac{4}{3}$

Discussion

9.	A circle of radius 5 cm has a chord of length 8 cm. Tangents drawn at the end points of the chord meet at a point. Find the perimeter of the triangle formed by the chord and the tangents.
Answer» A circle of radius 5 cm has a chord of length 8 cm. Tangents drawn at the end points of the chord meet at a point. Find the perimeter of the triangle formed by the chord and the tangents.

Discussion

10.	Some points are shown in the figure.With the help of it answer the following questions :(i)Write the co-ordinates of the points Q and R.(ii)Write the co-ordinates of the points T and M.(iii) Which point lies in the third quadrant ?(iv) Which are the points whose x and y co-ordinates are equal ?
Answer» Some points are shown in the figure.With the help of it answer the following questions : (i)Write the co-ordinates of the points Q and R. (ii)Write the co-ordinates of the points T and M. (iii) Which point lies in the third quadrant ? (iv) Which are the points whose x and y co-ordinates are equal ?

Discussion

11.	Find the value of cos(-1089 degree).
Answer» Find the value of cos(-1089 degree).

Discussion

12.	The dimensions of a cuboid are 35 cm × 30 cm × 25 cm. If Amit cuts a cube of greatest volume, then the volume of the cube is
Answer» The dimensions of a cuboid are 35 cm × 30 cm × 25 cm. If Amit cuts a cube of greatest volume, then the volume of the cube is

Discussion

13.	Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: 2x-3y+6=02x+3y-18=0
Answer» Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: $2 x - 3 y + 6 = 0 2 x + 3 y - 18 = 0$

Discussion

14.	If α and β are the zeros of the polynomial f(x)=x2−5x+k such that α−β=1, find the value of k.
Answer» If $α$ and $β$ are the zeros of the polynomial $f (x) = x^{2} - 5 x + k$ such that $α - β = 1$ , find the value of k.

Discussion

15.	Points P(4, 1), Q(6, 5) and R(2, 7) lie on a circle. What are the perpendicular distances of the chords PQ and QR from the centre, respectively?
Answer» Points P(4, 1), Q(6, 5) and R(2, 7) lie on a circle. What are the perpendicular distances of the chords PQ and QR from the centre, respectively?

Discussion

16.	Find the values of x and y that satisfy the below given pair of equations, where x≠0 & y≠0.2x+3y=135x−4y=−2
Answer» Find the values of $x$ and $y$ that satisfy the below given pair of equations, where $x \neq 0 & y \neq 0$ . $\frac{2}{x} + \frac{3}{y} = 13$ $\frac{5}{x} - \frac{4}{y} = - 2$

Discussion

17.	A corner point of a feasible region is a point in the region which is the __________ of two boundary lines.
Answer» A corner point of a feasible region is a point in the region which is the __________ of two boundary lines.

Discussion

18.	Write whether 245+32025on simplification gives a rational or an irrational number.
Answer» Write whether $\frac{2 \sqrt{45} + 3 \sqrt{20}}{2 \sqrt{5}}$ on simplification gives a rational or an irrational number.

Discussion

19.	Question 1If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.
Answer» Question 1 If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

Discussion

20.	Question 3 (ii)On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent.2x - 3y = 8 ; 4x - 6y = 9
Answer» Question 3 (ii) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent. 2x - 3y = 8 ; 4x - 6y = 9

Discussion

21.	For what value of n, the nth terms of the arithmetic progressions 63,65,67,...and 3, 10,17,... are equal?
Answer» For what value of n, the nth terms of the arithmetic progressions 63,65,67,...and 3, 10,17,... are equal?

Discussion

22.	The sum of a number and its reciprocal is 10/ 3. Find the number.
Answer» The sum of a number and its reciprocal is 10/ 3. Find the number.

Discussion

23.	Which of the following rational numbers is in the standard form?
Answer» Which of the following rational numbers is in the standard form?

Discussion

24.	Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………
Answer» Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………

24.

Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………

Answer»

Which of the following sequences form an AP?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11…….

(iii) -1, -1.25, -1.5, -1.75……

(iv) 1, -1, -3, -5…………

Discussion

25.	The seventh root of x divided by the eighth root of x is(a) x(b) x(c) x56(d) 1x56
Answer» The seventh root of x divided by the eighth root of x is (a) x (b) $\sqrt{x}$ (c) $\sqrt[56]{x}$ (d) $\frac{1}{\sqrt[56]{x}}$

Discussion

26.	P_1^{}(x) = ax^2-bx-c, P_2^{}(x) = bx^2-cx-a, P_3(x) = cx^2-ax-b be three quadritic polynomials . Suppose there exists a real number α such that P_1 (α) = P_2(α) = P_3(α). Prove that a =b= c
Answer» P_1^{}(x) = ax^2-bx-c, P_2^{}(x) = bx^2-cx-a, P_3(x) = cx^2-ax-b be three quadritic polynomials . Suppose there exists a real number α such that P_1 (α) = P_2(α) = P_3(α). Prove that a =b= c

Discussion

27.	Find the value of k if the quadratic equation x2+4x−k=0 has real and distinct roots.
Answer» Find the value of k if the quadratic equation $x^{2} + 4 x - k = 0$ has real and distinct roots.

Discussion

28.	Find the mode of the given data. Class Frequency 0−52005−1025010−1522515−2030020−2527518.75
Answer» Find the mode of the given data. $\begin{matrix} C l a s s & F r e q u e n c y 0 - 5 & 200 5 - 10 & 250 10 - 15 & 225 15 - 20 & 300 20 - 25 & 275 \end{matrix}$ 18.75

Discussion

29.	Prove that 3-427 is an irrational number, given that 2 is an irrational number.
Answer» Prove that $\frac{(3 - 4 \sqrt{2})}{7}$ is an irrational number, given that $\sqrt{2}$ is an irrational number.

Discussion

30.	Sec^2tan^-1root3+tan^2sec^-1root3
Answer» Sec^2tan^-1root3+tan^2sec^-1root3

Discussion

31.	One of the factors of x2−2x−15 is _____.
Answer» One of the factors of $x^{2} - 2 x - 15$ is _____.

Discussion

32.	Find the solution set of: \|x^2 - 2x - 3\| -\|4x - 2\| = \|x^2 + 2x -5\| (\|x\| represents modulus function)
Answer» Find the solution set of: \|x^2 - 2x - 3\| -\|4x - 2\| = \|x^2 + 2x -5\| (\|x\| represents modulus function)

Discussion

33.	In triangle ABC P is the mid point of AB &PQ is drawn parallel to BC.IF AP=3.5 AQ=4.5 PQ=6 Then the perimeter of ABC is
Answer» In triangle ABC P is the mid point of AB &PQ is drawn parallel to BC.IF AP=3.5 AQ=4.5 PQ=6 Then the perimeter of ABC is

Discussion

34.	The first term of an A.P. is 5, the common difference is 3 and the last term is 80;
Answer» The first term of an A.P. is 5, the common difference is 3 and the last term is 80;

Discussion

35.	Find the value of sin233° + sin257°.
Answer» Find the value of sin²33° + sin²57°.

Discussion

36.	Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20
Answer» Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20

36.

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20

Answer»

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is

(i) an odd number (ii) a perfect square number

(iii) divisible by 5 (iv) a prime number less than 20

Discussion

37.	Solve the following system of linear equations in three variables. x+y+z=52x−y+z=9x−2y+3z=16
Answer» Solve the following system of linear equations in three variables. $x + y + z = 5 2 x - y + z = 9 x - 2 y + 3 z = 16$

Discussion

38.	A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of 113 cm3 for each toy and all toys needs to be packed.(Take π=227)788
Answer» A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of $\frac{11}{3}$ $c m^{3}$ for each toy and all toys needs to be packed.(Take $π = \frac{22}{7}$ ) 788

Discussion

39.	If sinA CosA and TanA are in G.P., Then Cot^6A-Cot^2A is a.4b.2C.3D.1
Answer» If sinA CosA and TanA are in G.P., Then Cot^6A-Cot^2A is a.4 b.2 C.3 D.1

Discussion

40.	From a pack of 52 playing cards Jacks, queens, Kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is(i) a black queen(ii) a red card(iii) a black jack(iv) a picture card (Jacks, queens and Kings are picture cards).
Answer» From a pack of 52 playing cards Jacks, queens, Kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is (i) a black queen (ii) a red card (iii) a black jack (iv) a picture card (Jacks, queens and Kings are picture cards).

Discussion

41.	Question 3For the polynomial x3+2x+15−72x2−x6, write(i) The degree of the polynomial(ii) The coefficient of x3(iii) The coefficient of x6(iv) The constant term
Answer» Question 3 For the polynomial $\frac{x^{3} + 2 x + 1}{5} - \frac{7}{2} x^{2} - x^{6}$ , write (i) The degree of the polynomial (ii) The coefficient of $x^{3}$ (iii) The coefficient of $x^{6}$ (iv) The constant term

Discussion

42.	Four bells tools at an interval of 8,12,15and 18 seconds respectively. All the four begin to toll together. After how many seconds will they toll together again
Answer» Four bells tools at an interval of 8,12,15and 18 seconds respectively. All the four begin to toll together. After how many seconds will they toll together again

Discussion

43.	How many three - digit natural numbers are divisible by 7?
Answer» How many three - digit natural numbers are divisible by 7?

Discussion

44.	Solve each of the following systems of equations graphically: x+2y+2=0,3x+2y−2=0.
Answer» Solve each of the following systems of equations graphically: $x + 2 y + 2 = 0, 3 x + 2 y - 2 = 0.$

44.

Solve each of the following systems of equations graphically: x+2y+2=0,3x+2y−2=0.

Answer»

Solve each of the following systems of equations graphically:

$x + 2 y + 2 = 0, 3 x + 2 y - 2 = 0.$

Discussion

45.	Question 9An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its 16part is left unfilled with ice – cream.
Answer» Question 9 An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its $\frac{1}{6}$ part is left unfilled with ice – cream.

Discussion

46.	15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15, 18, 20, 16, 18, 19.The mode of the given data is ______.
Answer» 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15, 18, 20, 16, 18, 19. The mode of the given data is ______.

Discussion

47.	Draw a line segment of length 10 cm and bisect it. Further bisect one of the equal parts and measure its length.
Answer» Draw a line segment of length 10 cm and bisect it. Further bisect one of the equal parts and measure its length.

Discussion

48.	Solve :217x +131y=913 131x+217y=827
Answer» Solve :217x +131y=913 131x+217y=827

48.

Solve :217x +131y=913 131x+217y=827

Answer»

Solve :217x +131y=913

131x+217y=827

Discussion

49.	If AB is a chord of length 53 cm of a circle with centre O and radius 5 cm, then area of sector OAB is(a) 3π8cm2(b) 8π3cm2(c) 25πcm2(d) 25π3cm2
Answer» If AB is a chord of length $5 \sqrt{3}$ cm of a circle with centre O and radius 5 cm, then area of sector OAB is (a) $\frac{3 π}{8} c m^{2}$ (b) $\frac{8 π}{3} c m^{2}$ (c) $25 {πcm}^{2}$ (d) $\frac{25 π}{3} c m^{2}$

Discussion

50.	When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.
Answer» When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 119 (xii) Write two integers, whose product is greater than both the integers.

The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet. Weight of sweet (gram) 0 - 250 250 - 500 500 - 750 750 - 1000 1000 - 1250 No. of customers 10 60 25 20 15

Which of the following expressions is used to determine the mode?

In Fig . 10.115, if PQR is the tangent to a circle at Q whose centre is O , AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to figure(a) 200 (b) 400 9c) 350 (d) 4500

If (2p+1),13,(5p-3) are in AP, find the value of p.

A circular pond is of diameter 17.5 m . It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per square metre Use π= 227

Prove that (4-52) is an irrational number.

Solve each of the following quadratic equations:3x−47+73x−4=52, x≠43

A circle of radius 5 cm has a chord of length 8 cm. Tangents drawn at the end points of the chord meet at a point. Find the perimeter of the triangle formed by the chord and the tangents.

Some points are shown in the figure.With the help of it answer the following questions :(i)Write the co-ordinates of the points Q and R.(ii)Write the co-ordinates of the points T and M.(iii) Which point lies in the third quadrant ?(iv) Which are the points whose x and y co-ordinates are equal ?

Find the value of cos(-1089 degree).

The dimensions of a cuboid are 35 cm × 30 cm × 25 cm. If Amit cuts a cube of greatest volume, then the volume of the cube is

Solve the following system of equations graphically and find the vertices and area of the ​triangle formed by these lines and the y-axis: 2x-3y+6=02x+3y-18=0

If α and β are the zeros of the polynomial f(x)=x2−5x+k such that α−β=1, find the value of k.

Points P(4, 1), Q(6, 5) and R(2, 7) lie on a circle. What are the perpendicular distances of the chords PQ and QR from the centre, respectively?

Find the values of x and y that satisfy the below given pair of equations, where x≠0 &amp; y≠0.2x+3y=135x−4y=−2

A corner point of a feasible region is a point in the region which is the __________ of two boundary lines.

Write whether 245+32025on simplification gives a rational or an irrational number.

Question 1If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

Question 3 (ii)On comparing the ratios a1a2, b1b2 and c1c2 find out whether the following pair of linear equations are consistent, or inconsistent.2x - 3y = 8 ; 4x - 6y = 9

For what value of n, the nth terms of the arithmetic progressions 63,65,67,...and 3, 10,17,... are equal?

The sum of a number and its reciprocal is 10/ 3. Find the number.

Which of the following rational numbers is in the standard form?

Which of the following sequences form an AP?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….(iii) -1, -1.25, -1.5, -1.75……(iv) 1, -1, -3, -5…………

The seventh root of x divided by the eighth root of x is(a) x(b) x(c) x56(d) 1x56

P_1^{}(x) = ax^2-bx-c, P_2^{}(x) = bx^2-cx-a, P_3(x) = cx^2-ax-b be three quadritic polynomials . Suppose there exists a real number α such that P_1 (α) = P_2(α) = P_3(α). Prove that a =b= c

Find the value of k if the quadratic equation x2+4x−k=0 has real and distinct roots.

Find the mode of the given data. Class Frequency 0−52005−1025010−1522515−2030020−2527518.75

Prove that 3-427 is an irrational number, given that 2 is an irrational number.

Sec^2tan^-1root3+tan^2sec^-1root3

One of the factors of x2−2x−15 is _____.

Find the solution set of: |x^2 - 2x - 3| -|4x - 2| = |x^2 + 2x -5| (|x| represents modulus function)

In triangle ABC P is the mid point of AB &PQ is drawn parallel to BC.IF AP=3.5 AQ=4.5 PQ=6 Then the perimeter of ABC is

The first term of an A.P. is 5, the common difference is 3 and the last term is 80;

Find the value of sin233° + sin257°.

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20

Solve the following system of linear equations in three variables. x+y+z=52x−y+z=9x−2y+3z=16

If sinA CosA and TanA are in G.P., Then Cot^6A-Cot^2A is a.4b.2C.3D.1

From a pack of 52 playing cards Jacks, queens, Kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is(i) a black queen(ii) a red card(iii) a black jack(iv) a picture card (Jacks, queens and Kings are picture cards).

Question 3For the polynomial x3+2x+15−72x2−x6, write(i) The degree of the polynomial(ii) The coefficient of x3(iii) The coefficient of x6(iv) The constant term

Four bells tools at an interval of 8,12,15and 18 seconds respectively. All the four begin to toll together. After how many seconds will they toll together again

How many three - digit natural numbers are divisible by 7?

Solve each of the following systems of equations graphically: x+2y+2=0,3x+2y−2=0.

Question 9An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its 16part is left unfilled with ice – cream.

15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15, 18, 20, 16, 18, 19.The mode of the given data is ______.

Draw a line segment of length 10 cm and bisect it. Further bisect one of the equal parts and measure its length.

Solve :217x +131y=913 131x+217y=827

If AB is a chord of length 53 cm of a circle with centre O and radius 5 cm, then area of sector OAB is(a) 3π8cm2(b) 8π3cm2(c) 25πcm2(d) 25π3cm2

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: 2x-3y+6=02x+3y-18=0

Find the values of x and y that satisfy the below given pair of equations, where x≠0 & y≠0.2x+3y=135x−4y=−2