32581 + Interview Questions in Mathematics

1.	A point P divides the line segment joining the points A(3,−5) and B(−4,8) such that APBP=K1. If P lies on the line x+y=0, then fine the value of K.
Answer» A point P divides the line segment joining the points $A (3, - 5)$ and $B (- 4, 8)$ such that $\frac{A P}{B P} = \frac{K}{1}$ . If P lies on the line $x + y = 0,$ then fine the value of K.

Discussion

2.	3x + 2y = 12, x – y + 1 = 0
Answer» 3x + 2y = 12, x – y + 1 = 0

Discussion

3.	If px=x2-4x+3, then p2-p-1+p12=_____________.
Answer» If $p (x) = x^{2} - 4 x + 3, then p (2) - p (- 1) + p (\frac{1}{2}) =_____________.$

Discussion

4.	The tangents drawn, at the end-points of a diameter, to a circle are ___________.
Answer» The tangents drawn, at the end-points of a diameter, to a circle are ___________.

Discussion

5.	THE SPEED OF A MOTOR LAUNCH WITH RESPECT TO STILL WATER IS 18m PER SEC AND THE SPEED OF STREAM IS IS 4m PER SEC. WHEN THE LAUNCH BEGINS TRAVELLING UPSTREAMS A FLOAT WAS DROPPED FROM IT.THE LAUNCH TRAVELLED 4.8 Km UPSTREAM, TURNAD ABOUT AND CAUGHT UP WITH THE FLOAT. HOW LONG IS IT BEFORE THE LAUNCH REACHES THE FLOAT?
Answer» THE SPEED OF A MOTOR LAUNCH WITH RESPECT TO STILL WATER IS 18m PER SEC AND THE SPEED OF STREAM IS IS 4m PER SEC. WHEN THE LAUNCH BEGINS TRAVELLING UPSTREAMS A FLOAT WAS DROPPED FROM IT.THE LAUNCH TRAVELLED 4.8 Km UPSTREAM, TURNAD ABOUT AND CAUGHT UP WITH THE FLOAT. HOW LONG IS IT BEFORE THE LAUNCH REACHES THE FLOAT?

Discussion

6.	In a Δ ABC, if the sides are a = 3, b = 5 and c = 4, then sin B/2 + cos B/2 is equal to
Answer» In a $Δ$ ABC, if the sides are a = 3, b = 5 and c = 4, then sin B/2 + cos B/2 is equal to

Discussion

7.	Question 1 (iv)Complete the following statement:The sum of the probabilities of all the elementary events of an experiment is ___.
Answer» Question 1 (iv) Complete the following statement: The sum of the probabilities of all the elementary events of an experiment is ___.

Discussion

8.	A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?
Answer» A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?

Discussion

9.	Prove that if a pair of opposite angles of a quadrilateral are right, then a circle can be drawn through all four of its vertices.
Answer» Prove that if a pair of opposite angles of a quadrilateral are right, then a circle can be drawn through all four of its vertices.

Discussion

10.	Is x − 1 a factor of x101 − 1? What about x + 1?
Answer» Is x − 1 a factor of x¹⁰¹ − 1? What about x + 1?

Discussion

11.	Express 0.4¯ as a rational number in simplest form.
Answer» Express $0 . \bar{4}$ as a rational number in simplest form.

Discussion

12.	If a piece of wood having a total volume of 1.6 cubic metre and density of 800 kg per cubic metre floats on the water density 1000 kg per cubic metre. Calculate what part of the wood is in water?
Answer» If a piece of wood having a total volume of 1.6 cubic metre and density of 800 kg per cubic metre floats on the water density 1000 kg per cubic metre. Calculate what part of the wood is in water?

Discussion

13.	A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Answer» A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Discussion

14.	Show graphically that each of the following given systems of equations has infinitely many solutions: 2x+3y=6,4x+6y=12.
Answer» Show graphically that each of the following given systems of equations has infinitely many solutions: $2 x + 3 y = 6, 4 x + 6 y = 12.$

14.

Show graphically that each of the following given systems of equations has infinitely many solutions: 2x+3y=6,4x+6y=12.

Answer»

Show graphically that each of the following given systems of equations has infinitely many solutions:

$2 x + 3 y = 6, 4 x + 6 y = 12.$

Discussion

15.	But what if we nevery get remainder zero whilemail using euclid's division algorithm
Answer» But what if we nevery get remainder zero whilemail using euclid's division algorithm

Discussion

16.	Why in wavy curve method upper side of curve is positive and lower side is negative ?
Answer» Why in wavy curve method upper side of curve is positive and lower side is negative ?

Discussion

17.	Tangents PQ and PR are drawn to the circle from an external point P. If PQ = 9 cm, and . Find the length of the chord QR.
Answer» Tangents PQ and PR are drawn to the circle from an external point P. If PQ = 9 cm, and . Find the length of the chord QR.

Discussion

18.	Question 5Draw a ΔABC in which AB = 5 cm , BC = 6 cm and ∠ABC=60∘. Construct a triangle similar to ABC with scale factor 57. Justify the construction.
Answer» Question 5 Draw a $Δ A B C$ in which AB = 5 cm , BC = 6 cm and $∠ A B C = 60^{\circ}$ . Construct a triangle similar to ABC with scale factor $\frac{5}{7}$ . Justify the construction.

Discussion

19.	A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 21 per litre.(Use π=227)
Answer» A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 21 per litre. (Use $π = \frac{22}{7}$ )

Discussion

20.	If 'n' is any positive integer then by Euclid algorithm. Show that n can be expressed in the form of 3m or 3m+1 ; where 'm' is some integer.
Answer» If 'n' is any positive integer then by Euclid algorithm. Show that n can be expressed in the form of 3m or 3m+1 ; where 'm' is some integer.

Discussion

21.

Say these words aloud. Then match them with the pictures by drawing lines. bag tin hen pen tap axe ant fox cap cot Disclaimer: Kindly refer the textbook for the images.Fill in the blanks from the words given above. b _ g h _ n t _ p c _ p t _ n c _ t _ nt p _ n f _ x _ xe

Answer» Say these words aloud. Then match them with the pictures by drawing lines.

bag

tin

hen

pen

tap

axe

ant

fox

cap

cot

Disclaimer: Kindly refer the textbook for the images.

Fill in the blanks from the words given above.

b ___ g	h ___ n	t ___ p	c ___ p	t ___ n
c ___ t	___ nt	p ___ n	f ___ x	___ xe

Discussion

22.	evaluate \lim_{x→5} e^x-e^5÷ x-5
Answer» evaluate \lim_{x→5} e^x-e^5÷ x-5

Discussion

23.	Which of the following options are equal to tan2A+cot2A+2?
Answer» Which of the following options are equal to $t a n^{2} A + c o t^{2} A + 2$ ?

Discussion

24.	A Circle of radius 2 unit lies in the first quadrant and touches both the axes of coordinates equation of circle with the centre 6,5 and touching the above circle externally i
Answer» A Circle of radius 2 unit lies in the first quadrant and touches both the axes of coordinates equation of circle with the centre 6,5 and touching the above circle externally i

Discussion

25.	Look at the figure above. This is a staircase consisting of 5 steps. The height of each in-step(green area) is 6 cms.(i) What is the total length of the pink line if the breadth of each step is 32 cms.(ii) Write the ratio of the height of the instep to its total length of the pink line in the form of a fraction.(iii) What fraction is the ratio of the area of the surface facing each step to the total area of the surface facing steps of the staircase in the fraction form.
Answer» Look at the figure above. This is a staircase consisting of 5 steps. The height of each in-step(green area) is 6 cms. (i) What is the total length of the pink line if the breadth of each step is 32 cms. (ii) Write the ratio of the height of the instep to its total length of the pink line in the form of a fraction. (iii) What fraction is the ratio of the area of the surface facing each step to the total area of the surface facing steps of the staircase in the fraction form.

Discussion

26.	Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm , 90 cm and 30 cm respectively. How many balls were melted to make the tube?
Answer» Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm , 90 cm and 30 cm respectively. How many balls were melted to make the tube?

Discussion

27.	What is the area of a square inscribed in a circle of diameter p cm ?
Answer» What is the area of a square inscribed in a circle of diameter p cm ?

Discussion

28.	The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is 30∘ than when it is 60∘. Find the length of the shadow at 30∘.
Answer» The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is $30^{\circ}$ than when it is $60^{\circ}$ . Find the length of the shadow at $30^{\circ}$ .

Discussion

29.	27 spherical drops of same capacitance C are merged to form big drop. Capacitance of bigger drop is?
Answer» 27 spherical drops of same capacitance C are merged to form big drop. Capacitance of bigger drop is?

Discussion

30.	Find the roots of 2x2+x–6=0 by factorisation.
Answer» Find the roots of $2 x^{2} + x - 6 = 0$ by factorisation.

Discussion

31.

The following table shows the income of farmers in a grape season. Find the mean of their income. Income (Thousand Rupees) 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Farmers 10 11 15 16 18 14

Answer» The following table shows the income of farmers in a grape season. Find the mean of their income.

Income (Thousand Rupees)	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Farmers	10	11	15	16	18	14

Discussion

32.	The total surface area of a cube is 96 cm2. The volume of the cube is:
Answer» The total surface area of a cube is $96 c m^{2}$ . The volume of the cube is:

Discussion

33.	Find A2−5A+6I, if A=⎡⎢⎣2012131−10⎤⎥⎦
Answer» Find $A^{2} - 5 A + 6 I,$ if $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 1 2 & 1 & 3 1 & - 1 & 0 \end{matrix} ⎤ ⎥ ⎦$

Discussion

34.	In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is
Answer» In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is

Discussion

35.	Using the properties of proportion, solve the following equation for x. x3+3x3x2+1=3419111
Answer» Using the properties of proportion, solve the following equation for $x .$ $\frac{x^{3} + 3 x}{3 x^{2} + 1} = \frac{341}{91}$ 11

Discussion

36.	Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.
Answer» Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.

Discussion

37.	A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m ×16 m find the area of the field in which the cow can graze?
Answer» A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m ×16 m find the area of the field in which the cow can graze?

Discussion

38.	From a well-shuffled pack of 52 cards, a card is drawn at random. The probability that it is a face card is:
Answer» From a well-shuffled pack of 52 cards, a card is drawn at random. The probability that it is a face card is:

Discussion

39.	Solve the following quadratic equations by factorization:33x-12x+3-22x+33x-1=5; x≠13, -32
Answer» Solve the following quadratic equations by factorization: $3 (\frac{3 x - 1}{2 x + 3}) - 2 (\frac{2 x + 3}{3 x - 1}) = 5; x \neq \frac{1}{3}, - \frac{3}{2}$

Discussion

40.	If x = a, y = b is the solution of the systems of equations x - y = 2 and x + y = 4 , then the values of a and b are, respectively(a) 3 and 1 (b) 3 and 5 (c) 5 and 3 (d) - 1 and -3
Answer» If $x = a, y = b$ is the solution of the systems of equations $x - y = 2$ and $x + y = 4$ , then the values of $a$ and $b$ are, respectively (a) 3 and 1 (b) 3 and 5 (c) 5 and 3 (d) $-$ 1 and $-$ 3

Discussion

41.	If a:b = 7:10 and x:y = 3:4 find out (3ay-2bx) : (5ay-bx)
Answer» If a:b = 7:10 and x:y = 3:4 find out (3ay-2bx) : (5ay-bx)

Discussion

42.	Solve the following systems of equations:x+y=2xyx-yxy=6x ≠ 0, y ≠ 0
Answer» Solve the following systems of equations: $x + y = 2 x y \frac{x - y}{x y} = 6$ x ≠ 0, y ≠ 0

Discussion

43.	let y= (x)3+x then what in minimum value of y ?
Answer» let y= (x)3+x then what in minimum value of y ?

Discussion

44.	In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?
Answer» In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?

Discussion

45.	Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor 35.5
Answer» Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor $\frac{3}{5}$ . 5

Discussion

46.	the area of region bounded by the equation x+2y=3,x=0,y=0 is equal t
Answer» the area of region bounded by the equation x+2y=3,x=0,y=0 is equal t

Discussion

47.	In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]
Answer» In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]

47.

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]

Answer»

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]

Discussion

48.	Find the value of k for which each of the following system of equations have no solution :3x − 4y + 7 = 0kx + 3y − 5 = 0
Answer» Find the value of k for which each of the following system of equations have no solution : 3x − 4y + 7 = 0 kx + 3y − 5 = 0

Discussion

49.	If the minimum value of x2 + 2x + 3 is m and maximum value of -x2 + 4x + 6 is M then the value of m + M is
Answer» If the minimum value of x2 + 2x + 3 is m and maximum value of -x2 + 4x + 6 is M then the value of m + M is

Discussion

50.	tanx/1-cotx + cotx/1-tanx = sec x. cosec x +1
Answer» tanx/1-cotx + cotx/1-tanx = sec x. cosec x +1

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A point P divides the line segment joining the points A(3,−5) and B(−4,8) such that APBP=K1. If P lies on the line x+y=0, then fine the value of K.

3x + 2y = 12, x – y + 1 = 0

If px=x2-4x+3, then p2-p-1+p12=_____________.

The tangents drawn, at the end-points of a diameter, to a circle are ___________.

In a Δ ABC, if the sides are a = 3, b = 5 and c = 4, then sin B/2 + cos B/2 is equal to

Question 1 (iv)Complete the following statement:The sum of the probabilities of all the elementary events of an experiment is ___.

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?

Prove that if a pair of opposite angles of a quadrilateral are right, then a circle can be drawn through all four of its vertices.

Is x − 1 a factor of x101 − 1? What about x + 1?

Express 0.4¯ as a rational number in simplest form.

If a piece of wood having a total volume of 1.6 cubic metre and density of 800 kg per cubic metre floats on the water density 1000 kg per cubic metre. Calculate what part of the wood is in water?

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Show graphically that each of the following given systems of equations has infinitely many solutions: 2x+3y=6,4x+6y=12.

But what if we nevery get remainder zero whilemail using euclid's division algorithm

Why in wavy curve method upper side of curve is positive and lower side is negative ?

Tangents PQ and PR are drawn to the circle from an external point P. If PQ = 9 cm, and . Find the length of the chord QR.

Question 5Draw a ΔABC in which AB = 5 cm , BC = 6 cm and ∠ABC=60∘. Construct a triangle similar to ABC with scale factor 57. Justify the construction.

A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 21 per litre.(Use π=227)

If 'n' is any positive integer then by Euclid algorithm. Show that n can be expressed in the form of 3m or 3m+1 ; where 'm' is some integer.

Say these words aloud. Then match them with the pictures by drawing lines. bag tin hen pen tap axe ant fox cap cot Disclaimer: Kindly refer the textbook for the images.Fill in the blanks from the words given above. b ___ g h ___ n t ___ p c ___ p t ___ n c ___ t ___ nt p ___ n f ___ x ___ xe

evaluate \lim_{x→5} e^x-e^5÷ x-5

Which of the following options are equal to tan2A+cot2A+2?

A Circle of radius 2 unit lies in the first quadrant and touches both the axes of coordinates equation of circle with the centre 6,5 and touching the above circle externally i

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm , 90 cm and 30 cm respectively. How many balls were melted to make the tube?

What is the area of a square inscribed in a circle of diameter p cm ?

The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is 30∘ than when it is 60∘. Find the length of the shadow at 30∘.

27 spherical drops of same capacitance C are merged to form big drop. Capacitance of bigger drop is?

Find the roots of 2x2+x–6=0 by factorisation.

The following table shows the income of farmers in a grape season. Find the mean of their income. Income (Thousand Rupees) 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Farmers 10 11 15 16 18 14

The total surface area of a cube is 96 cm2. The volume of the cube is:

Find A2−5A+6I, if A=⎡⎢⎣2012131−10⎤⎥⎦

In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is

Using the properties of proportion, solve the following equation for x. x3+3x3x2+1=3419111

Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m ×16 m find the area of the field in which the cow can graze?

From a well-shuffled pack of 52 cards, a card is drawn at random. The probability that it is a face card is:

Solve the following quadratic equations by factorization:33x-12x+3-22x+33x-1=5; x≠13, -32

If x = a, y = b is the solution of the systems of equations x - y = 2 and x + y = 4 , then the values of a and b are, respectively(a) 3 and 1 (b) 3 and 5 (c) 5 and 3 (d) - 1 and -3

If a:b = 7:10 and x:y = 3:4 find out (3ay-2bx) : (5ay-bx)

Solve the following systems of equations:x+y=2xyx-yxy=6x ≠ 0, y ≠ 0

let y= (x)3+x then what in minimum value of y ?

In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?

Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor 35.5

the area of region bounded by the equation x+2y=3,x=0,y=0 is equal t

In the given pentagon ABCDE, prove that 2CD &lt; Perimeter (ABCDE). [4 MARKS]

Find the value of k for which each of the following system of equations have no solution :3x − 4y + 7 = 0kx + 3y − 5 = 0

If the minimum value of x2 + 2x + 3 is m and maximum value of -x2 + 4x + 6 is M then the value of m + M is

tanx/1-cotx + cotx/1-tanx = sec x. cosec x +1

Say these words aloud. Then match them with the pictures by drawing lines. bag tin hen pen tap axe ant fox cap cot Disclaimer: Kindly refer the textbook for the images.Fill in the blanks from the words given above. b _ g h _ n t _ p c _ p t _ n c _ t _ nt p _ n f _ x _ xe

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]