32581 + Interview Questions in Mathematics

1.	Solve for x and y. x+y=a+b ax-by=a^2-b^2 Solve by substitution and elimination method.
Answer» Solve for x and y. x+y=a+b ax-by=a^2-b^2 Solve by substitution and elimination method.

1.

Solve for x and y. x+y=a+b ax-by=a^2-b^2 Solve by substitution and elimination method.

Answer»

Solve for x and y.

x+y=a+b

ax-by=a^2-b^2

Solve by substitution and elimination method.

2.	A company declares a dividend of 11.2% to all its share-holders. If its Rs 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company. in order to have an annual income of Rs 1,680?
Answer» A company declares a dividend of 11.2% to all its share-holders. If its Rs 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company. in order to have an annual income of Rs 1,680?

Discussion

3.	Modes of transport of 1700 students of NIT Warangal is shown in the graph below. Which of the following options are correct?
Answer» Modes of transport of 1700 students of NIT Warangal is shown in the graph below. Which of the following options are correct?

Discussion

4.	The cost of a pair of shoes at a shop was Rs. 1450. The sales tax charged was 8%. Find the bill amount.
Answer» The cost of a pair of shoes at a shop was Rs. 1450. The sales tax charged was 8%. Find the bill amount.

Discussion

5.	Find the value of k if the lines given by 3x+2ky=2 ; 2x+5y=12 are parallel
Answer» Find the value of k if the lines given by 3x+2ky=2 ; 2x+5y=12 are parallel

Discussion

6.	The sum of first 7terms of an A.P. is 10and that of next 7terms is 17 Find the arithemetic progression.
Answer» The sum of first 7terms of an A.P. is 10and that of next 7terms is 17 Find the arithemetic progression.

Discussion

7.	Use real number line to find the range of values of x for which : (i) x>3 and 0<x<6. (ii) x<0 and −3≤x<1. (iii) −1<x≤6 and −2≤x≤3
Answer» Use real number line to find the range of values of x for which : (i) $x > 3 a n d 0 < x < 6.$ (ii) $x < 0 a n d - 3 \leq x < 1.$ (iii) $- 1 < x \leq 6 a n d - 2 \leq x \leq 3$

7.

Use real number line to find the range of values of x for which : (i) x>3 and 0<x<6. (ii) x<0 and −3≤x<1. (iii) −1<x≤6 and −2≤x≤3

Answer»

Use real number line to find the range of values of x for which :

(i) $x > 3 a n d 0 < x < 6.$

(ii) $x < 0 a n d - 3 \leq x < 1.$

(iii) $- 1 < x \leq 6 a n d - 2 \leq x \leq 3$

Discussion

8.	If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.
Answer» If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

Discussion

9.	The sum S of n successive odd numbers starting from 3 is given by the relation : S = n (n + 2). Determine n, if the sum is 168.
Answer» The sum S of n successive odd numbers starting from 3 is given by the relation : S = n (n + 2). Determine n, if the sum is 168.

Discussion

10.	If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate..
Answer» If the simple interest on a sum of money at 5 $%$ per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate..

Discussion

11.	In a circle of radius 7cm, tangent PT is drawn from point P such that PT= 24cm. If O is the centre of the circle, then the length of OP is:
Answer» In a circle of radius 7cm, tangent PT is drawn from point P such that PT= 24cm. If O is the centre of the circle, then the length of OP is:

Discussion

12.	Rakhi purchases a dress for Rs. 3199, which includes two successive discounts of 20% and 5% respectively on the marked price and then 8% sales tax on the remaining price. Find the marked price.
Answer» Rakhi purchases a dress for Rs. 3199, which includes two successive discounts of 20% and 5% respectively on the marked price and then 8% sales tax on the remaining price. Find the marked price.

Discussion

13.	A circle touches all the four sides of a quadrilateral ABCD with AB=10cm, BC=8cm and CD=6cm.Find AD.
Answer» A circle touches all the four sides of a quadrilateral ABCD with AB=10cm, BC=8cm and CD=6cm.Find AD.

13.

A circle touches all the four sides of a quadrilateral ABCD with AB=10cm, BC=8cm and CD=6cm.Find AD.

Answer»

A circle touches all the four sides of a quadrilateral ABCD with AB=10cm, BC=8cm and CD=6cm.Find AD.

Discussion

14.	The sum of the series 452−432+442−422+432−412+422−402+⋯15 terms is
Answer» The sum of the series $45^{2} - 43^{2} + 44^{2} - 42^{2} + 43^{2} - 41^{2} + 42^{2} - 40^{2} + \dots 15 t e r m s$ is

Discussion

15.	Question 1 (i) Fill in the blanks using the correct word in the given bracket. (i) All circles are___. (congruent, similar)
Answer» Question 1 (i) Fill in the blanks using the correct word in the given bracket. (i) All circles are___. (congruent, similar)

Discussion

16.	Find the mode of the following frequency distribution: Marks10−2020−3030−4040−5050−60Frequency1235452513
Answer» Find the mode of the following frequency distribution: $\begin{matrix} Marks & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Frequency & 12 & 35 & 45 & 25 & 13 \end{matrix}$

Discussion

17.	A right circular cone is divided into three parts by trisecting its height by two planes drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio 1 : 7 : 19.
Answer» A right circular cone is divided into three parts by trisecting its height by two planes drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio 1 : 7 : 19.

Discussion

18.	Solve each of the following quadratic equations: a2b2x2+b2x−a2x−1=0
Answer» Solve each of the following quadratic equations: $a^{2} b^{2} x^{2} + b^{2} x - a^{2} x - 1 = 0$

Discussion

19.	The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students3413155
Answer» The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean using direct method. $\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$

19.

The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students3413155

Answer»

The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean using direct method.

$\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$

Discussion

20.	In figure, express x in terms of a,b and c.
Answer» In figure, express x in terms of a,b and c.

20.

In figure, express x in terms of a,b and c.

Answer»

In figure, express x in terms of a,b and c.

Discussion

21.	Verify that 5, -2 and 13 are the zeros of the cubic polynomial p(x)=3x3−10x2−27x+10 and verify the relation between its zeros and coefficients.
Answer» Verify that 5, -2 and $\frac{1}{3}$ are the zeros of the cubic polynomial $p (x) = 3 x^{3} - 10 x^{2} - 27 x + 10$ and verify the relation between its zeros and coefficients.

Discussion

22.	Define (i) rational numbers (ii) irrational numbers (iii) real numbers.
Answer» Define (i) rational numbers (ii) irrational numbers (iii) real numbers.

Discussion

23.	Derive the formula used to find the area of sector and length of arc of sector. [2 MARKS]
Answer» Derive the formula used to find the area of sector and length of arc of sector. [2 MARKS]

Discussion

24.	In a frequency distribution table with 12 classes,the class-width is 2.5 and the lowest class boundary is 8.1,then what is the upper class boundary of the highest class?
Answer» In a frequency distribution table with 12 classes,the class-width is 2.5 and the lowest class boundary is 8.1,then what is the upper class boundary of the highest class?

Discussion

25.	In a △ABC=∠C=3∠B=2(∠A+∠B),then ∠B=?(a) 20∘(b) 40∘(c) 60∘(d) 80∘
Answer» $I n a △ A B C = ∠ C = 3 ∠ B = 2 (∠ A + ∠ B), t h e n ∠ B = ? (a) 20^{\circ} (b) 40^{\circ} (c) 60^{\circ} (d) 80^{\circ}$

25.

In a △ABC=∠C=3∠B=2(∠A+∠B),then ∠B=?(a) 20∘(b) 40∘(c) 60∘(d) 80∘

Answer»

$I n a △ A B C = ∠ C = 3 ∠ B = 2 (∠ A + ∠ B), t h e n ∠ B = ? (a) 20^{\circ} (b) 40^{\circ} (c) 60^{\circ} (d) 80^{\circ}$

Discussion

26.	In a square matrix of order 3×3, which of the following can be a leading diagonal element?
Answer» In a square matrix of order 3×3, which of the following can be a leading diagonal element?

Discussion

27.	How many silver coins(cylindrical), 1.75 cm in diameter and of thickness 2 mm, can be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Answer» How many silver coins(cylindrical), 1.75 cm in diameter and of thickness 2 mm, can be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

Discussion

28.	Question 32 The sum of the prime factors of 1729 is (A) 13 (B) 19 (C) 32 (D) 39
Answer» Question 32 The sum of the prime factors of 1729 is (A) 13 (B) 19 (C) 32 (D) 39

Discussion

29.	Question 39 In the following question, fill in the blanks to make the statements true. The expression for 8−2 as a power with the base 2 is ___.
Answer» Question 39 In the following question, fill in the blanks to make the statements true. The expression for $8^{- 2}$ as a power with the base 2 is ___.

29.

Question 39 In the following question, fill in the blanks to make the statements true. The expression for 8−2 as a power with the base 2 is ___.

Answer»

Question 39

In the following question, fill in the blanks to make the statements true.

The expression for $8^{- 2}$ as a power with the base 2 is ___.

Discussion

30.	Question 11 In the following question, out of the four options, only one is correct. Write the correct answer: The multiplicative inverse of (−59)−99 is: (a) (−59)99 (b) (59)99 (c) (−9−5)99 (d) (−95)99
Answer» Question 11 In the following question, out of the four options, only one is correct. Write the correct answer: The multiplicative inverse of ${(- \frac{5}{9})}^{- 99}$ is: (a) ${(- \frac{5}{9})}^{99}$ (b) ${(\frac{5}{9})}^{99}$ (c) ${(- \frac{9}{- 5})}^{99}$ (d) ${(- \frac{9}{5})}^{99}$

30.

Question 11 In the following question, out of the four options, only one is correct. Write the correct answer: The multiplicative inverse of (−59)−99 is: (a) (−59)99 (b) (59)99 (c) (−9−5)99 (d) (−95)99

Answer»

Question 11

In the following question, out of the four options, only one is correct. Write the correct answer:

The multiplicative inverse of ${(- \frac{5}{9})}^{- 99}$ is:
(a) ${(- \frac{5}{9})}^{99}$
(b) ${(\frac{5}{9})}^{99}$
(c) ${(- \frac{9}{- 5})}^{99}$
(d) ${(- \frac{9}{5})}^{99}$

Discussion

31.	In Δ ABC, AB=15 cm, ∠ A=30∘, ∠ B=130∘. The area of the triangle will be equal to [Tan 30∘=0.57Tan 50∘=1.2]
Answer» In $Δ A B C, A B = 15 c m, ∠ A = 30^{\circ}, ∠ B = 130^{\circ} .$ The area of the triangle will be equal to $[\begin{matrix} T a n 30^{\circ} = 0.57 T a n 50^{\circ} = 1.2 \end{matrix}]$

31.

In Δ ABC, AB=15 cm, ∠ A=30∘, ∠ B=130∘. The area of the triangle will be equal to [Tan 30∘=0.57Tan 50∘=1.2]

Answer»

In $Δ A B C, A B = 15 c m, ∠ A = 30^{\circ}, ∠ B = 130^{\circ} .$ The area of the triangle will be equal to $[\begin{matrix} T a n 30^{\circ} = 0.57 T a n 50^{\circ} = 1.2 \end{matrix}]$

Discussion

32.	In fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre. (Use π=227)
Answer» In fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre. (Use $π = \frac{22}{7}$ )

Discussion

33.	Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in lvel of water in the tank in half an hour.
Answer» Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in lvel of water in the tank in half an hour.

Discussion

34.	In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?
Answer» In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?

Discussion

35.	Question 6 Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.
Answer» Question 6 Is 0.2 a root of the equation $x^{2}$ – 0.4 = 0? Justify your answer.

Discussion

36.	A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 423 cm and height 3 cm. Find the number of cones so formed.
Answer» A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter $4 \frac{2}{3}$ cm and height 3 cm. Find the number of cones so formed.

Discussion

37.	A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in m2 ___
Answer» A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in $m^{2}$ ___

37.

A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in m2 ___

Answer»

A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in $m^{2}$

___

Discussion

38.	Which of the following are a quadratic polynomial in x whose zeros are (-a, 2a)?
Answer» Which of the following are a quadratic polynomial in x whose zeros are (-a, 2a)?

Discussion

39.	Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week , her weekly savings become Rs 20.75, find n.
Answer» Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the $n^{t h}$ week , her weekly savings become Rs 20.75, find n.

Discussion

40.	One says," give me a 100, friend! I shall then become twice as rich as you". The other replies, "If you give me 10, I shall be six times as rich as you." Tell me what is the amount of their capital?
Answer» One says," give me a 100, friend! I shall then become twice as rich as you". The other replies, "If you give me 10, I shall be six times as rich as you." Tell me what is the amount of their capital?

Discussion

41.	How can we identify which side of the right angled triangle is base and which side is perpendicular if both the theta of triangle are equal?
Answer» How can we identify which side of the right angled triangle is base and which side is perpendicular if both the theta of triangle are equal?

Discussion

42.	A model of a ship is made to a scale 1 : 300. (i) The length of the model of the ship is 2 m. Calculate the length of the ship. (ii) The area of the deck of the ship is 180,000 m2. Calculate the area of the deck of the model. (iii) The volume of the model is 6.5 m3. Calculate the volume of the ship.
Answer» A model of a ship is made to a scale 1 : 300. (i) The length of the model of the ship is 2 m. Calculate the length of the ship. (ii) The area of the deck of the ship is 180,000 $m^{2}$ . Calculate the area of the deck of the model. (iii) The volume of the model is 6.5 $m^{3}$ . Calculate the volume of the ship.

Discussion

43.	From the given Frequency distribution table, find the Average Class Mark. Class InternalFrequency0−10210−20820−301230−40740−50950−60460−705
Answer» From the given Frequency distribution table, find the Average Class Mark. $\begin{matrix} Class Internal & Frequency 0 - 10 & 2 10 - 20 & 8 20 - 30 & 12 30 - 40 & 7 40 - 50 & 9 50 - 60 & 4 60 - 70 & 5 \end{matrix}$

43.

From the given Frequency distribution table, find the Average Class Mark. Class InternalFrequency0−10210−20820−301230−40740−50950−60460−705

Answer»

From the given Frequency distribution table, find the Average Class Mark.

$\begin{matrix} Class Internal & Frequency 0 - 10 & 2 10 - 20 & 8 20 - 30 & 12 30 - 40 & 7 40 - 50 & 9 50 - 60 & 4 60 - 70 & 5 \end{matrix}$

Discussion

44.	Question 2(f) Find the product by suitable arrangement: 125×40×8×25
Answer» Question 2(f) Find the product by suitable arrangement: $125 \times 40 \times 8 \times 25$

44.

Question 2(f) Find the product by suitable arrangement: 125×40×8×25

Answer»

Question 2(f)

Find the product by suitable arrangement:

$125 \times 40 \times 8 \times 25$

Discussion

45.	The reflection of the point (1,2) in y - axis is
Answer» The reflection of the point $(1, 2)$ in y - axis is

Discussion

46.	Prove that (tanA-tanB)2 + (1+tanAtanB)2 is equal to sec square A*sec squareB
Answer» Prove that (tanA-tanB)²+ (1+tanAtanB)^{2 is equal to sec square A*sec squareB}

Discussion

47.	A company with 15,000 shares of ₹ 100 each declares an annual dividend of 5%. What is the total dividend paid by the company?
Answer» A company with 15,000 shares of ₹ 100 each declares an annual dividend of $5 %$ . What is the total dividend paid by the company?

Discussion

48.	Find the value of 1.22+2.32+3.42+−−−−−−−n terms12.+22.3+32.4+−−−−−−−n terms.
Answer» Find the value of $\frac{{1.2}^{2} + {2.3}^{2} + {3.4}^{2} + - - - - - - - n t e r m s}{1^{2} . + 2^{2} .3 + 3^{2} .4 + - - - - - - - n t e r m s}$ .

Discussion

49.	A hemispherical bowl of internal diameter 30 cm contains a liquid. The liquid is to be filled in cylindrical bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl are
Answer» A hemispherical bowl of internal diameter 30 cm contains a liquid. The liquid is to be filled in cylindrical bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl are

Discussion

50.	ax2+2hxy+by2=0 always represents a pair of straight lines passing through the origin. If Column 1 Column 2 a. h2>ab 1. Lines are coincident b. h2=ab 2. Lines are real and distinct c. h2<ab 3. Lines are imaginary with real point of intersection i.e. (0,0)
Answer» $a x^{2} + 2 h x y + b y^{2} = 0$ always represents a pair of straight lines passing through the origin. If Column 1 Column 2 a. $h^{2}$ >ab 1. Lines are coincident b. $h^{2}$ =ab 2. Lines are real and distinct c. $h^{2}$ <ab 3. Lines are imaginary with real point of intersection i.e. (0,0)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve for x and y. x+y=a+b ax-by=a^2-b^2 Solve by substitution and elimination method.

A company declares a dividend of 11.2% to all its share-holders. If its Rs 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company. in order to have an annual income of Rs 1,680?

Modes of transport of 1700 students of NIT Warangal is shown in the graph below. Which of the following options are correct?

The cost of a pair of shoes at a shop was Rs. 1450. The sales tax charged was 8%. Find the bill amount.

Find the value of k if the lines given by 3x+2ky=2 ; 2x+5y=12 are parallel

The sum of first 7terms of an A.P. is 10and that of next 7terms is 17 Find the arithemetic progression.

Use real number line to find the range of values of x for which : (i) x&gt;3 and 0&lt;x&lt;6. (ii) x&lt;0 and −3≤x&lt;1. (iii) −1&lt;x≤6 and −2≤x≤3

If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

The sum S of n successive odd numbers starting from 3 is given by the relation : S = n (n + 2). Determine n, if the sum is 168.

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate..

In a circle of radius 7cm, tangent PT is drawn from point P such that PT= 24cm. If O is the centre of the circle, then the length of OP is:

Rakhi purchases a dress for Rs. 3199, which includes two successive discounts of 20% and 5% respectively on the marked price and then 8% sales tax on the remaining price. Find the marked price.

A circle touches all the four sides of a quadrilateral ABCD with AB=10cm, BC=8cm and CD=6cm.Find AD.

The sum of the series 452−432+442−422+432−412+422−402+⋯15 terms is

Question 1 (i) Fill in the blanks using the correct word in the given bracket. (i) All circles are___. (congruent, similar)

Find the mode of the following frequency distribution: Marks10−2020−3030−4040−5050−60Frequency1235452513

A right circular cone is divided into three parts by trisecting its height by two planes drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio 1 : 7 : 19.

Solve each of the following quadratic equations: a2b2x2+b2x−a2x−1=0

The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students3413155

In figure, express x in terms of a,b and c.

Verify that 5, -2 and 13 are the zeros of the cubic polynomial p(x)=3x3−10x2−27x+10 and verify the relation between its zeros and coefficients.

Define (i) rational numbers (ii) irrational numbers (iii) real numbers.

Derive the formula used to find the area of sector and length of arc of sector. [2 MARKS]

In a frequency distribution table with 12 classes,the class-width is 2.5 and the lowest class boundary is 8.1,then what is the upper class boundary of the highest class?

In a △ABC=∠C=3∠B=2(∠A+∠B),then ∠B=?(a) 20∘(b) 40∘(c) 60∘(d) 80∘

In a square matrix of order 3×3, which of the following can be a leading diagonal element?

How many silver coins(cylindrical), 1.75 cm in diameter and of thickness 2 mm, can be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

Question 32 The sum of the prime factors of 1729 is (A) 13 (B) 19 (C) 32 (D) 39

Question 39 In the following question, fill in the blanks to make the statements true. The expression for 8−2 as a power with the base 2 is ___.

Question 11 In the following question, out of the four options, only one is correct. Write the correct answer: The multiplicative inverse of (−59)−99 is: (a) (−59)99 (b) (59)99 (c) (−9−5)99 (d) (−95)99

In Δ ABC, AB=15 cm, ∠ A=30∘, ∠ B=130∘. The area of the triangle will be equal to [Tan 30∘=0.57Tan 50∘=1.2]

Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in lvel of water in the tank in half an hour.

In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?

Question 6 Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 423 cm and height 3 cm. Find the number of cones so formed.

A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in m2 ___

Which of the following are a quadratic polynomial in x whose zeros are (-a, 2a)?

Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week , her weekly savings become Rs 20.75, find n.

One says," give me a 100, friend! I shall then become twice as rich as you". The other replies, "If you give me 10, I shall be six times as rich as you." Tell me what is the amount of their capital?

How can we identify which side of the right angled triangle is base and which side is perpendicular if both the theta of triangle are equal?

From the given Frequency distribution table, find the Average Class Mark. Class InternalFrequency0−10210−20820−301230−40740−50950−60460−705

Question 2(f) Find the product by suitable arrangement: 125×40×8×25

The reflection of the point (1,2) in y - axis is

Prove that (tanA-tanB)2 + (1+tanAtanB)2 is equal to sec square A*sec squareB

A company with 15,000 shares of ₹ 100 each declares an annual dividend of 5%. What is the total dividend paid by the company?

Find the value of 1.22+2.32+3.42+−−−−−−−n terms12.+22.3+32.4+−−−−−−−n terms.

A hemispherical bowl of internal diameter 30 cm contains a liquid. The liquid is to be filled in cylindrical bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl are

ax2+2hxy+by2=0 always represents a pair of straight lines passing through the origin. If Column 1 Column 2 a. h2&gt;ab 1. Lines are coincident b. h2=ab 2. Lines are real and distinct c. h2&lt;ab 3. Lines are imaginary with real point of intersection i.e. (0,0)

Use real number line to find the range of values of x for which : (i) x>3 and 0<x<6. (ii) x<0 and −3≤x<1. (iii) −1<x≤6 and −2≤x≤3

ax2+2hxy+by2=0 always represents a pair of straight lines passing through the origin. If Column 1 Column 2 a. h2>ab 1. Lines are coincident b. h2=ab 2. Lines are real and distinct c. h2<ab 3. Lines are imaginary with real point of intersection i.e. (0,0)