32581 + Interview Questions in Mathematics

1.	Find the mean age of 100 residents of a town from the following data. Age equal and above (in years)010203040506070Number of persons100907550251550
Answer» Find the mean age of 100 residents of a town from the following data. $\begin{matrix} A g e e q u a l a n d a b o v e (i n y e a r s) & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 N u m b e r o f p e r s o n s & 100 & 90 & 75 & 50 & 25 & 15 & 5 & 0 \end{matrix}$

Discussion

2.	Solve the following quadratic equation by factorization. x−ax−b+x−bx−a=ab+ba
Answer» Solve the following quadratic equation by factorization. $\frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a}$

Discussion

3.	When a die is thrown, what is the probability of getting a number greater than 5?
Answer» When a die is thrown, what is the probability of getting a number greater than 5?

Discussion

4.	Solve each of the following systems of equations by using the method of cross multiplication: 6x−5y−16=0,7x−13y+10=0.
Answer» Solve each of the following systems of equations by using the method of cross multiplication: $6 x - 5 y - 16 = 0, 7 x - 13 y + 10 = 0.$

4.

Solve each of the following systems of equations by using the method of cross multiplication: 6x−5y−16=0,7x−13y+10=0.

Answer»

Solve each of the following systems of equations by using the method of cross multiplication:

$6 x - 5 y - 16 = 0, 7 x - 13 y + 10 = 0.$

Discussion

5.	A data has 25 observations arranged in a ascending order.Which observation represents the median?
Answer» A data has 25 observations arranged in a ascending order.Which observation represents the median?

Discussion

6.	IF the nth term of an AP is (2n +1) then the sum of its first three terms is (a) 6n +3 (b) 15 (c) 12 (d) 21
Answer» IF the nth term of an AP is (2n +1) then the sum of its first three terms is (a) 6n +3 (b) 15 (c) 12 (d) 21

Discussion

7.	Question 37(ii) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square?
Answer» Question 37(ii) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square?

Discussion

8.	Find the equation of the line, whose : (i) x-intercept = 5 and y-intercept = 3 (ii) x-intercept = -4 and y-intercept = 6 (iii) x-intercept = -8 and y-intercept = -4
Answer» Find the equation of the line, whose : (i) x-intercept = 5 and y-intercept = 3 (ii) x-intercept = -4 and y-intercept = 6 (iii) x-intercept = -8 and y-intercept = -4

8.

Find the equation of the line, whose : (i) x-intercept = 5 and y-intercept = 3 (ii) x-intercept = -4 and y-intercept = 6 (iii) x-intercept = -8 and y-intercept = -4

Answer»

Find the equation of the line, whose :

(i) x-intercept = 5 and y-intercept = 3

(ii) x-intercept = -4 and y-intercept = 6

(iii) x-intercept = -8 and y-intercept = -4

Discussion

9.	Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is (i) a prime number less than 10 (ii) a number which is a perfect square.
Answer» Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is (i) a prime number less than 10 (ii) a number which is a perfect square.

Discussion

10.	Find the values of k for which the quadratic equation 9xsquare-3x+k =0 has equal roots.
Answer» Find the values of k for which the quadratic equation 9xsquare-3x+k =0 has equal roots.

Discussion

11.	Question 29 Encircle the odd one of the following: (a) (−100)÷5 (b) (−81)÷9 (c) (−75)÷5 (d) (−32)÷9
Answer» Question 29 Encircle the odd one of the following: (a) $(- 100) \div 5$ (b) $(- 81) \div 9$ (c) $(- 75) \div 5$ (d) $(- 32) \div 9$

11.

Question 29 Encircle the odd one of the following: (a) (−100)÷5 (b) (−81)÷9 (c) (−75)÷5 (d) (−32)÷9

Answer»

Question 29

Encircle the odd one of the following:

(a) $(- 100) \div 5$
(b) $(- 81) \div 9$
(c) $(- 75) \div 5$
(d) $(- 32) \div 9$

Discussion

12.	3 bags and 4 pens together cost Rs. 257 whereas 4 bags and 3 pens together cost Rs.324.Find the total cost of 1 bag and 10 pens.
Answer» 3 bags and 4 pens together cost Rs. 257 whereas 4 bags and 3 pens together cost Rs.324.Find the total cost of 1 bag and 10 pens.

Discussion

13.	From the following frequency distribution,prepare the 'more than' ogive. ScoreNumber of candidates400−4502450−50035500−55040550−60032600−65024650−70027700−75018750−80034Total212
Answer» From the following frequency distribution,prepare the 'more than' ogive. $\begin{matrix} S c o r e & N u m b e r o f c a n d i d a t e s 400 - 450 & 2 450 - 500 & 35 500 - 550 & 40 550 - 600 & 32 600 - 650 & 24 650 - 700 & 27 700 - 750 & 18 750 - 800 & 34 T o t a l & 212 \end{matrix}$

13.

From the following frequency distribution,prepare the 'more than' ogive. ScoreNumber of candidates400−4502450−50035500−55040550−60032600−65024650−70027700−75018750−80034Total212

Answer»

From the following frequency distribution,prepare the 'more than' ogive.

$\begin{matrix} S c o r e & N u m b e r o f c a n d i d a t e s 400 - 450 & 2 450 - 500 & 35 500 - 550 & 40 550 - 600 & 32 600 - 650 & 24 650 - 700 & 27 700 - 750 & 18 750 - 800 & 34 T o t a l & 212 \end{matrix}$

Discussion

14.	If tanA+cotA =2 then find the value of tan2A+cot2A
Answer» If tanA+cotA =2 then find the value of ${t a n}^{2} A + {c o t}^{2} A$

Discussion

15.	Question 1 (i) Which of the drawings from (a) to (d) shows: 2×15 a) b) c) d)
Answer» Question 1 (i) Which of the drawings from (a) to (d) shows: $2 \times \frac{1}{5}$ a) b) c) d)

Discussion

16.	Question 30 Encircle the odd one of the following: (a) (−1)×(−1) (b) (−1)×(−1)×(−1) (c) (−1)×(−1)×(−1)×(−1) (d) (−1)×(−1)×(−1)×(−1)×(−1)×(−1)
Answer» Question 30 Encircle the odd one of the following: (a) $(- 1) \times (- 1)$ (b) $(- 1) \times (- 1) \times (- 1)$ (c) $(- 1) \times (- 1) \times (- 1) \times (- 1)$ (d) $(- 1) \times (- 1) \times (- 1) \times (- 1) \times (- 1) \times (- 1)$

16.

Question 30 Encircle the odd one of the following: (a) (−1)×(−1) (b) (−1)×(−1)×(−1) (c) (−1)×(−1)×(−1)×(−1) (d) (−1)×(−1)×(−1)×(−1)×(−1)×(−1)

Answer»

Question 30

Encircle the odd one of the following:

(a) $(- 1) \times (- 1)$
(b) $(- 1) \times (- 1) \times (- 1)$
(c) $(- 1) \times (- 1) \times (- 1) \times (- 1)$
(d) $(- 1) \times (- 1) \times (- 1) \times (- 1) \times (- 1) \times (- 1)$

Discussion

17.	Which of the following is/are correct for an AP whose common difference is d.
Answer» Which of the following is/are correct for an AP whose common difference is d.

Discussion

18.	Question 6 If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60∘ , then OP = a √3.
Answer» Question 6 If angle between two tangents drawn from a point P to a circle of radius a and centre O is $60^{\circ}$ , then OP = a $\sqrt{3}$ .

Discussion

19.	Question 2(i) Represent the following situations in the form of quadratic equations. (i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Answer» Question 2(i) Represent the following situations in the form of quadratic equations. (i) The area of a rectangular plot is $528 m^{2}$ . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Discussion

20.	Question 7 In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ=30∘. A chord RS is drawn parallel to the tangent PQ. Find the ∠ RQS.
Answer» Question 7 In figure, tangents PQ and PR are drawn to a circle such that $∠ R P Q = 30^{\circ}$ . A chord RS is drawn parallel to the tangent PQ. Find the $∠$ RQS.

Discussion

21.	Question 86 State whether the statement is True or False. (−1)×(−2)×(−3)=1×2×3
Answer» Question 86 State whether the statement is True or False. $(- 1) \times (- 2) \times (- 3) = 1 \times 2 \times 3$

21.

Question 86 State whether the statement is True or False. (−1)×(−2)×(−3)=1×2×3

Answer»

Question 86

State whether the statement is True or False.

$(- 1) \times (- 2) \times (- 3) = 1 \times 2 \times 3$

Discussion

22.	Find the sum to n terms od A.P. whose kth term is 5k + 1.
Answer» Find the sum to n terms od A.P. whose kth term is 5k + 1.

Discussion

23.	Question 1(iii) Check whether the following are quadratic equations: (iii)(x−2)(x+1)=(x−1)(x+3)
Answer» Question 1(iii) Check whether the following are quadratic equations: $(i i i) (x - 2) (x + 1) = (x - 1) (x + 3)$

Discussion

24.	The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the larger one is
Answer» The areas of two similar triangles are $12 c m^{2}$ and $48 c m^{2}$ . If the height of the smaller one is 2.1 cm, then the corresponding height of the larger one is

Discussion

25.	The figure shows a circle with centre O and radius 4cm. ∠ BOD = 72∘. A point is selected at random inside the circle. Find the probability that point lies inside the sector.
Answer» The figure shows a circle with centre O and radius 4cm. $∠$ BOD = $72^{\circ}$ . A point is selected at random inside the circle. Find the probability that point lies inside the sector.

Discussion

26.	If α, β are the zeros of the polynomial f(x)=2x2+5x+k satisfying the relation α2+β2+αβ=214, then find the value of k for this condition to be true. [3 MARKS]
Answer» If $α$ , $β$ are the zeros of the polynomial $f (x) = 2 x^{2} + 5 x + k$ satisfying the relation $α^{2} + β^{2} + α β = \frac{21}{4}$ , then find the value of k for this condition to be true. [3 MARKS]

Discussion

27.	Aarush used to solve 4 questions in 16 minutes. After much practice, he is now able to solve 6 questions in 18 minutes. What is the percentage decrease in the time he has achieved to solve each question? [3 MARKS]
Answer» Aarush used to solve 4 questions in 16 minutes. After much practice, he is now able to solve 6 questions in 18 minutes. What is the percentage decrease in the time he has achieved to solve each question? [3 MARKS]

27.

Aarush used to solve 4 questions in 16 minutes. After much practice, he is now able to solve 6 questions in 18 minutes. What is the percentage decrease in the time he has achieved to solve each question? [3 MARKS]

Answer»

Aarush used to solve 4 questions in 16 minutes. After much practice, he is now able to solve 6 questions in 18 minutes. What is the percentage decrease in the time he has achieved to solve each question?
[3 MARKS]

Discussion

28.	Triangle ABC is similar to triangle DEF and their areas are respectively 64 cm2 and 121 cm2. If EF= 15.4 cm, then BC=
Answer» Triangle ABC is similar to triangle DEF and their areas are respectively 64 cm² and 121 cm². If EF= 15.4 cm, then BC=

Discussion

29.	If y = 12 (3x+7) is rewritten in the form ax+by+c=0, what are the values of a, b and c?
Answer» If y = $\frac{1}{2}$ (3x+7) is rewritten in the form $a x + b y + c = 0$ , what are the values of a, b and c?

Discussion

30.	Find the number nearest to 24001 and between 24001 and 25000 divisible by 16,24,40
Answer» Find the number nearest to 24001 and between 24001 and 25000 divisible by 16,24,40

Discussion

31.	In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of ∠BAC−∠OBC.
Answer» In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of $∠ B A C - ∠ O B C$ .

Discussion

32.	The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2. Find the cost of ploughing the field in Rupees. (Take π=227). [3 MARKS]
Answer» The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per $m^{2}$ . Find the cost of ploughing the field in Rupees. (Take $π = \frac{22}{7}$ ). [3 MARKS]

Discussion

33.	Two players X and O play a game of “noughts and crosses” on a 3 × 3 grid. The purposeof the game is for a player to get 3 symbols belonging to the player in a straight line(vertically, horizontally or diagonally). Each player marks one symbol on his or her turn.After two moves (1 turn each), the grid looks as follows with X to play next. Where should X put his symbol next so that he will always win this game finally regardless of how well O plays?
Answer» Two players X and O play a game of “noughts and crosses” on a 3 $\times$ 3 grid. The purposeof the game is for a player to get 3 symbols belonging to the player in a straight line(vertically, horizontally or diagonally). Each player marks one symbol on his or her turn.After two moves (1 turn each), the grid looks as follows with X to play next. Where should X put his symbol next so that he will always win this game finally regardless of how well O plays?

33.

Two players X and O play a game of “noughts and crosses” on a 3 × 3 grid. The purposeof the game is for a player to get 3 symbols belonging to the player in a straight line(vertically, horizontally or diagonally). Each player marks one symbol on his or her turn.After two moves (1 turn each), the grid looks as follows with X to play next. Where should X put his symbol next so that he will always win this game finally regardless of how well O plays?

Answer»

Two players X and O play a game of “noughts and crosses” on a 3 $\times$ 3 grid. The purposeof the game is for a player to get 3 symbols belonging to the player in a straight line(vertically, horizontally or diagonally). Each player marks one symbol on his or her turn.After two moves (1 turn each), the grid looks as follows with X to play next. Where should X put his symbol next so that he will always win this game finally regardless of how well O plays?

Discussion

34.	Select the wrong number in the series: 6, 26, 62, 123, 214, 341
Answer» Select the wrong number in the series: 6, 26, 62, 123, 214, 341

34.

Select the wrong number in the series: 6, 26, 62, 123, 214, 341

Answer»

Select the wrong number in the series:

6, 26, 62, 123, 214, 341

Discussion

35.	Is 200 any term of the sequence 3, 7, 11, 15,...?
Answer» Is 200 any term of the sequence 3, 7, 11, 15,...?

Discussion

36.	Are all three at the same point on the road?
Answer» Are all three at the same point on the road?

36.

Are all three at the same point on the road?

Answer»

Are all three at the same point on the road?

Discussion

37.	Students who took all three subjects i.e. Physics, Chemistry and Maths Read the statements and choose the letters of the region which correctly represent the statement in Venn diagram.
Answer» Students who took all three subjects i.e. Physics, Chemistry and Maths Read the statements and choose the letters of the region which correctly represent the statement in Venn diagram.

37.

Students who took all three subjects i.e. Physics, Chemistry and Maths Read the statements and choose the letters of the region which correctly represent the statement in Venn diagram.

Answer»

Students who took all three subjects i.e. Physics, Chemistry and Maths

Read the statements and choose the letters of the region which correctly represent the statement in Venn diagram.

Discussion

38.	In ΔABC, E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.
Answer» In $Δ A B C$ , E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.

Discussion

39.	Question 8 Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?
Answer» Question 8 Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Discussion

40.	If the distances of P(x,y) from A(5, 1) and B (-1, 5)are equal, then prove that 3x = 2y.
Answer» If the distances of P(x,y) from A(5, 1) and B (-1, 5)are equal, then prove that 3x = 2y.

Discussion

41.	504 cones each of diameter 3.5 cm and height 3 cm are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.[π=227]
Answer» 504 cones each of diameter 3.5 cm and height 3 cm are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area. $[π = \frac{22}{7}]$

Discussion

42.	Question 5 Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Answer» Question 5 Is it possible to design a rectangular park of perimeter 80 and area 400 $m^{2}$ ? If so find its length and breadth.

Discussion

43.	A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as divident, find : (i) the number of shares he has in the company. (ii) the dividend percent per share.
Answer» A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as divident, find : (i) the number of shares he has in the company. (ii) the dividend percent per share.

43.

A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as divident, find : (i) the number of shares he has in the company. (ii) the dividend percent per share.

Answer»

A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as divident, find :

(i) the number of shares he has in the company.

(ii) the dividend percent per share.

Discussion

44.	Find the probability of getting the difference of two numbers obtained as a prime number, if a pair of dice are thrown simultaneously.
Answer» Find the probability of getting the difference of two numbers obtained as a prime number, if a pair of dice are thrown simultaneously.

Discussion

45.	Question 1 Which of the following expressions are polynomials? Justify your answer. I. 8 II. √3x2−2x III. 1−√5x IV. 15x−2+5x+7 V. (x−2)(x−4)x VI. 1x+1 VII. 17a3−2√3a2+4a−7 VIII. 12x
Answer» Question 1 Which of the following expressions are polynomials? Justify your answer. I. $8$ II. $\sqrt{3} x^{2} - 2 x$ III. $1 - \sqrt{5 x}$ IV. $\frac{1}{5 x^{- 2}} + 5 x + 7$ V. $\frac{(x - 2) (x - 4)}{x}$ VI. $\frac{1}{x + 1}$ VII. $\frac{1}{7} a^{3} - \frac{2}{\sqrt{3}} a^{2} + 4 a - 7$ VIII. $\frac{1}{2 x}$

Discussion

46.	Question 2 State whether the following is true or false. To construct a triangle similar to a given ΔABC with its sides of 73 corresponding sides of ΔABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect of BC. The points B1,B2,...B7 are located at equal distances on BX, B3 joined to C and then a line segment B6C’ is drawn parallel to B3C where C’ lies on BC produced . Finally line segment A’C’ is drawn parallel to AC.
Answer» Question 2 State whether the following is true or false. To construct a triangle similar to a given $Δ$ ABC with its sides of $\frac{7}{3}$ corresponding sides of $Δ$ ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect of BC. The points $B_{1}, B_{2}, . . . B_{7}$ are located at equal distances on BX, $B_{3}$ joined to C and then a line segment $B_{6} C$ ’ is drawn parallel to $B_{3} C$ where C’ lies on BC produced . Finally line segment A’C’ is drawn parallel to AC.

Discussion

47.	Posted of concurrence of median is called.....& notation is.......
Answer» Posted of concurrence of median is called.....& notation is.......

Discussion

48.	In the following figure A, B, C are the midpoints of the sides of △PQR. If A, B and Q has the coordinates (3,3), (4,2) and (2,1) respectively, then the coordinates of P,C and R are
Answer» In the following figure A, B, C are the midpoints of the sides of $△ P Q R$ . If A, B and Q has the coordinates (3,3), (4,2) and (2,1) respectively, then the coordinates of P,C and R are

48.

In the following figure A, B, C are the midpoints of the sides of △PQR. If A, B and Q has the coordinates (3,3), (4,2) and (2,1) respectively, then the coordinates of P,C and R are

Answer»

In the following figure A, B, C are the midpoints of the sides of $△ P Q R$ . If A, B and Q has the coordinates (3,3), (4,2) and (2,1) respectively, then the coordinates of P,C and R are

Discussion

49.	There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?
Answer» There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

49.

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Answer»

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Discussion

50.	In the △PQR, find ∠PCQ where C is the circumcenter of △PQR.
Answer» In the $△$ PQR, find $∠$ PCQ where C is the circumcenter of $△$ PQR.

50.

In the △PQR, find ∠PCQ where C is the circumcenter of △PQR.

Answer»

In the $△$ PQR, find $∠$ PCQ where C is the circumcenter of $△$ PQR.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the mean age of 100 residents of a town from the following data. Age equal and above (in years)010203040506070Number of persons100907550251550

Solve the following quadratic equation by factorization. x−ax−b+x−bx−a=ab+ba

When a die is thrown, what is the probability of getting a number greater than 5?

Solve each of the following systems of equations by using the method of cross multiplication: 6x−5y−16=0,7x−13y+10=0.

A data has 25 observations arranged in a ascending order.Which observation represents the median?

IF the nth term of an AP is (2n +1) then the sum of its first three terms is (a) 6n +3 (b) 15 (c) 12 (d) 21

Question 37(ii) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square?

Find the equation of the line, whose : (i) x-intercept = 5 and y-intercept = 3 (ii) x-intercept = -4 and y-intercept = 6 (iii) x-intercept = -8 and y-intercept = -4

Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is (i) a prime number less than 10 (ii) a number which is a perfect square.

Find the values of k for which the quadratic equation 9xsquare-3x+k =0 has equal roots.

Question 29 Encircle the odd one of the following: (a) (−100)÷5 (b) (−81)÷9 (c) (−75)÷5 (d) (−32)÷9

3 bags and 4 pens together cost Rs. 257 whereas 4 bags and 3 pens together cost Rs.324.Find the total cost of 1 bag and 10 pens.

From the following frequency distribution,prepare the 'more than' ogive. ScoreNumber of candidates400−4502450−50035500−55040550−60032600−65024650−70027700−75018750−80034Total212

If tanA+cotA =2 then find the value of tan2A+cot2A

Question 1 (i) Which of the drawings from (a) to (d) shows: 2×15 a) b) c) d)

Question 30 Encircle the odd one of the following: (a) (−1)×(−1) (b) (−1)×(−1)×(−1) (c) (−1)×(−1)×(−1)×(−1) (d) (−1)×(−1)×(−1)×(−1)×(−1)×(−1)

Which of the following is/are correct for an AP whose common difference is d.

Question 6 If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60∘ , then OP = a √3.

Question 2(i) Represent the following situations in the form of quadratic equations. (i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Question 7 In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ=30∘. A chord RS is drawn parallel to the tangent PQ. Find the ∠ RQS.

Question 86 State whether the statement is True or False. (−1)×(−2)×(−3)=1×2×3

Find the sum to n terms od A.P. whose kth term is 5k + 1.

Question 1(iii) Check whether the following are quadratic equations: (iii)(x−2)(x+1)=(x−1)(x+3)

The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the larger one is

The figure shows a circle with centre O and radius 4cm. ∠ BOD = 72∘. A point is selected at random inside the circle. Find the probability that point lies inside the sector.

If α, β are the zeros of the polynomial f(x)=2x2+5x+k satisfying the relation α2+β2+αβ=214, then find the value of k for this condition to be true. [3 MARKS]

Aarush used to solve 4 questions in 16 minutes. After much practice, he is now able to solve 6 questions in 18 minutes. What is the percentage decrease in the time he has achieved to solve each question? [3 MARKS]

Triangle ABC is similar to triangle DEF and their areas are respectively 64 cm2 and 121 cm2. If EF= 15.4 cm, then BC=

If y = 12 (3x+7) is rewritten in the form ax+by+c=0, what are the values of a, b and c?

Find the number nearest to 24001 and between 24001 and 25000 divisible by 16,24,40

In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of ∠BAC−∠OBC.

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2. Find the cost of ploughing the field in Rupees. (Take π=227). [3 MARKS]

Select the wrong number in the series: 6, 26, 62, 123, 214, 341

Is 200 any term of the sequence 3, 7, 11, 15,...?

Are all three at the same point on the road?

Students who took all three subjects i.e. Physics, Chemistry and Maths Read the statements and choose the letters of the region which correctly represent the statement in Venn diagram.

In ΔABC, E is a point on AB, G and D are two points on BC such that EG is parallel to AD and ED is parallel to AC. Find the value of BC if BG = 4cm, GD = 6cm, and BE = 8cm.

Question 8 Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

If the distances of P(x,y) from A(5, 1) and B (-1, 5)are equal, then prove that 3x = 2y.

504 cones each of diameter 3.5 cm and height 3 cm are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.[π=227]

Question 5 Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.

A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as divident, find : (i) the number of shares he has in the company. (ii) the dividend percent per share.

Find the probability of getting the difference of two numbers obtained as a prime number, if a pair of dice are thrown simultaneously.

Question 1 Which of the following expressions are polynomials? Justify your answer. I. 8 II. √3x2−2x III. 1−√5x IV. 15x−2+5x+7 V. (x−2)(x−4)x VI. 1x+1 VII. 17a3−2√3a2+4a−7 VIII. 12x

Posted of concurrence of median is called.....&amp; notation is.......

In the following figure A, B, C are the midpoints of the sides of △PQR. If A, B and Q has the coordinates (3,3), (4,2) and (2,1) respectively, then the coordinates of P,C and R are

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

In the △PQR, find ∠PCQ where C is the circumcenter of △PQR.

Posted of concurrence of median is called.....& notation is.......