32581 + Interview Questions in Mathematics

1.

The following distribution gives the daily income of 50 workers of a factory: Daily income in (Rs): 100−120 120−140 140−160 160−180 180−200 Number of workers: 12 14 8 6 10 Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

Answer» The following distribution gives the daily income of 50 workers of a factory:

Daily income in (Rs):	100−120	120−140	140−160	160−180	180−200
Number of workers:	12	14	8	6	10

Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

Discussion

2.	Question 2 (ii) Find the surface area of a sphere of diameter: (ii) 21 cm [Assume π=227]
Answer» Question 2 (ii) Find the surface area of a sphere of diameter: (ii) 21 cm $[A s s u m e π = \frac{22}{7}]$

2.

Question 2 (ii) Find the surface area of a sphere of diameter: (ii) 21 cm [Assume π=227]

Answer»

Question 2 (ii)
Find the surface area of a sphere of diameter:

(ii) 21 cm

$[A s s u m e π = \frac{22}{7}]$

Discussion

3.	In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B. If OB = 1 cm and AB = 3 cm, then ∠OCB = _____
Answer» In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B. If OB = 1 cm and AB = 3 cm, then $∠ O C B$ = _____

3.

In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B. If OB = 1 cm and AB = 3 cm, then ∠OCB = _____

Answer»

In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B.

If OB = 1 cm and AB = 3 cm, then $∠ O C B$ = _____

Discussion

4.	The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?
Answer» The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?

Discussion

5.	A boiler was purchased from abroad for ₹ 10,000. Shipping and forwarding charges ₹ 2,000, Import duty ₹ 7,000 and expenses of installation amounted to ₹ 1,000.Calculate the Depreciation for the first three years (separately for each year) 10% p.a. on Diminishing Balance Method.
Answer» A boiler was purchased from abroad for ₹ 10,000. Shipping and forwarding charges ₹ 2,000, Import duty ₹ 7,000 and expenses of installation amounted to ₹ 1,000. Calculate the Depreciation for the first three years (separately for each year) 10% p.a. on Diminishing Balance Method.

Discussion

6.	Write the nth term of an A.P. the sum of whose n terms is Sn.
Answer» Write the nth term of an A.P. the sum of whose n terms is S_n.

Discussion

7.	Question 5You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for Δ ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).
Answer» Question 5 You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for $Δ$ ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).

Discussion

8.	Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
Answer» Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).

Discussion

9.	If A =[abba] and A2 =[xyyx] , then
Answer» If A = $[\begin{matrix} a & b b & a \end{matrix}]$ and $A^{2}$ = $[\begin{matrix} x & y y & x \end{matrix}]$ , then

Discussion

10.	The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?
Answer» The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

Discussion

11.	If the cumulative frequency for the class interval (50-60) is 92, then find x Class Interval0−1010−2020−3030−4040−5050−60Frequency 12 20 x 18 10 6
Answer» If the cumulative frequency for the class interval (50-60) is 92, then find x $\begin{matrix} Class Interval & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Frequency & 12 & 20 & x & 18 & 10 & 6 \end{matrix}$

11.

If the cumulative frequency for the class interval (50-60) is 92, then find x Class Interval0−1010−2020−3030−4040−5050−60Frequency 12 20 x 18 10 6

Answer»

If the cumulative frequency for the class interval (50-60) is 92, then find x

$\begin{matrix} Class Interval & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Frequency & 12 & 20 & x & 18 & 10 & 6 \end{matrix}$

Discussion

12.	35. If the points A(4,3) & B(x,5) are on the circle with centre O(2,3). Find the value of 'x'.
Answer» 35. If the points A(4,3) & B(x,5) are on the circle with centre O(2,3). Find the value of 'x'.

Discussion

13.	A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. The volume of the tent is and the area of the cloth used for making it is .
Answer» A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. The volume of the tent is and the area of the cloth used for making it is .

Discussion

14.	Question 2 (v)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.−14,14
Answer» Question 2 (v) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. $\frac{- 1}{4}, \frac{1}{4}$

14.

Question 2 (v)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.−14,14

Answer»

Question 2 (v)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$\frac{- 1}{4}, \frac{1}{4}$

Discussion

15.	The angle of elevation of the top Q of a vertical tower PQ, from a point X on the ground is 60∘. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45∘. Find the height of the tower PQ and the distance PX. (Use √3=1.73)
Answer» The angle of elevation of the top Q of a vertical tower PQ, from a point X on the ground is $60^{\circ}$ . From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is $45^{\circ}$ . Find the height of the tower PQ and the distance PX. (Use $\sqrt{3} = 1.73$ )

Discussion

16.	In the given figure, DE \|\| BD. Determine AC and AE.
Answer» In the given figure, DE \|\| BD. Determine AC and AE.

Discussion

17.	While learning I came across a question which was as follows: Find the sum of the first 40 positive integers divisible by 6. My doubt is that should I find the sum of the 1st 40 multiples of 6 or the multiples of 6 from starting from 1 to 40 (i.e, 6,12,18,24,30,36).
Answer» While learning I came across a question which was as follows: Find the sum of the first 40 positive integers divisible by 6. My doubt is that should I find the sum of the 1st 40 multiples of 6 or the multiples of 6 from starting from 1 to 40 (i.e, 6,12,18,24,30,36).

17.

While learning I came across a question which was as follows: Find the sum of the first 40 positive integers divisible by 6. My doubt is that should I find the sum of the 1st 40 multiples of 6 or the multiples of 6 from starting from 1 to 40 (i.e, 6,12,18,24,30,36).

Answer»

While learning I came across a question which was as follows:

Find the sum of the first 40 positive integers divisible by 6.

My doubt is that should I find the sum of the 1st 40 multiples of 6 or the multiples of 6 from starting from 1 to 40 (i.e, 6,12,18,24,30,36).

Discussion

18.	Which term of the arithmetic progression 8,14,20,26,... will be 72 more than its 41st term?
Answer» Which term of the arithmetic progression 8,14,20,26,... will be 72 more than its 41st term?

Discussion

19.	When f(x)= x³- 6x²+ 2x- 4 is divided by y(x)= 3x- 1, then the remainder is
Answer» When f(x)= x³- 6x²+ 2x- 4 is divided by y(x) = 3x- 1, then the remainder is

Discussion

20.	The number of hours for which students of a particular class watched television during holidays is shown in the given graph.We draw the histogram for above frequency table:Answer the following:(i) For how many hours did the maximum number of students watch T.V?(ii) How many students watched TV for less than 4 hours?(iii) How many students spend more than 5 hours in watching TV?
Answer» The number of hours for which students of a particular class watched television during holidays is shown in the given graph. We draw the histogram for above frequency table: Answer the following: (i) For how many hours did the maximum number of students watch T.V? (ii) How many students watched TV for less than 4 hours? (iii) How many students spend more than 5 hours in watching TV?

Discussion

21.	Derive the formula for the volume of the frustum of a cone.
Answer» Derive the formula for the volume of the frustum of a cone.

Discussion

22.	Line l touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.(1) What is d(O, P) = ? Why ?(2) If d(O, Q) = 8 cm, where does the point Q lie ?(3) If d(OQ) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?
Answer» Line l touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following. (1) What is d(O, P) = ? Why ? (2) If d(O, Q) = 8 cm, where does the point Q lie ? (3) If d(OQ) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?

Discussion

23.

An incomplete distribution is given below : Variable: 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 12 30 − 65 − 25 18 You are given that the median value is 46 and the total number of items is 230.(i) Using the median formula fill up missing frequencies.(ii) Calculate the AM of the completed distribution.

Answer» An incomplete distribution is given below :

Variable:	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	12	30	−	65	−	25	18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

Discussion

24.	If the nth terms of two A.P.s: 9,7,5.... and 24, 21, 18, ... are the same, then the value of n is _________.
Answer» If the n^th terms of two A.P.s: 9,7,5.... and 24, 21, 18, ... are the same, then the value of n is _________.

Discussion

25.	when at t=0, particle is at the extreme position,we use the equation x=acoswt when at t=0 particle is at mean position we use the equation y=asinwtDo we need to follow any sign convention for using these two formulas
Answer» when at t=0, particle is at the extreme position,we use the equation x=acoswt when at t=0 particle is at mean position we use the equation y=asinwt Do we need to follow any sign convention for using these two formulas

Discussion

26.	Question 7Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Answer» Question 7 Find the sum of first 22 terms of an AP in which d = 7 and $22^{n d}$ term is 149.

Discussion

27.	The points (other than origin) for which abscissa is equal to the ordinate will lie in(a) I quadrant only(b) I and II quadrants(c) I and III quadrants(d) II and IV quadrants
Answer» The points (other than origin) for which abscissa is equal to the ordinate will lie in (a) I quadrant only (b) I and II quadrants (c) I and III quadrants (d) II and IV quadrants

Discussion

28.	For the following set of numbers find the difference between the mean and the median 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15
Answer» For the following set of numbers find the difference between the mean and the median 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15

Discussion

29.	The unit vector along the vector a= 5i^+4j^+√8k^ is
Answer» The unit vector along the vector a= 5i^+4j^+√8k^ is

Discussion

30.	What is the decimal form of 311?0.272727
Answer» What is the decimal form of $\frac{3}{11}$ ? 0.272727

Discussion

31.	If x=2+√3,xy=1, then find x2−x+y2−y.
Answer» If $x = 2 + \sqrt{3}, x y = 1,$ then find $\frac{x}{2 - x} + \frac{y}{2 - y}$ .

Discussion

32.	If ΔABC is right angled at B, what is the value of sin(A+C)
Answer» If $Δ A B C$ is right angled at B, what is the value of $s i n (A + C)$

Discussion

33.	A boat can go 20 km upstream and 30 km downstream in 3 hrs. It can go 20 downstream and 10km upstream in 1 hrs 40 min . Find the speed of the boat in still water and speed of the stream.
Answer» A boat can go 20 km upstream and 30 km downstream in 3 hrs. It can go 20 downstream and 10km upstream in 1 hrs 40 min . Find the speed of the boat in still water and speed of the stream.

Discussion

34.	What is the locus of the center of a cycle wheel?
Answer» What is the locus of the center of a cycle wheel?

Discussion

35.	Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
Answer» Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Discussion

36.	The length of the diagonal of rectangular playground is 125 m, and the length of one side is 75 m. Find the length of other side.
Answer» The length of the diagonal of rectangular playground is 125 m, and the length of one side is 75 m. Find the length of other side.

Discussion

37.	If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is2 h sec αtan β-tan α
Answer» If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is $\frac{2 h s e c α}{\tan β - \tan α}$

Discussion

38.	John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John and x marbles.
Answer» John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John and x marbles.

Discussion

39.	If the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b,a+2b for some real numbers a and b then find the value of a and b
Answer» If the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b,a+2b for some real numbers a and b then find the value of a and b

Discussion

40.	Consider the following AP sequence: 134, 104, 74,… The 6thterm is
Answer» Consider the following AP sequence: 134, 104, 74,… The $6^{t h}$ term is

Discussion

41.

Consider the following frequency distribution: Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 3 9 15 30 18 5 The modal class is (a) 10-20 (b)20-30 (c)30-40 (d) 50-60

Answer»

Consider the following frequency distribution:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	3	9	15	30	18	5

The modal class is

(a) 10-20 (b)20-30 (c)30-40 (d) 50-60

Discussion

42.	If axn+bx(n−1)−1+c=0 is a quadratic equation, then n = ___
Answer» If $a x^{n} + b x^{(n - 1)} - 1 + c = 0$ is a quadratic equation, then n = ___

Discussion

43.	A man wants to buy 62 shares available at Rs 132(par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5 %. What will be his annual income?
Answer» A man wants to buy 62 shares available at Rs 132(par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5 %. What will be his annual income?

43.

A man wants to buy 62 shares available at Rs 132(par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5 %. What will be his annual income?

Answer»

A man wants to buy 62 shares available at Rs 132(par value of Rs 100)

(i) How much should he invest?

(ii) If the dividend is 7.5 %. What will be his annual income?

Discussion

44.	10. At selection , the probability of selection of A is 2/5 and that of B is 3/7 . The probability that both of them would not be selected is (if A and B are independent)
Answer» 10. At selection , the probability of selection of A is 2/5 and that of B is 3/7 . The probability that both of them would not be selected is (if A and B are independent)

Discussion

45.	Determine whether the points are collinear.(1) A(1, –3), B(2, –5), C(–4, 7)(2) L(–2, 3), M(1, –3), N(5, 4)(3) R(0, 3), D(2, 1), S(3, –1)(4) P(–2, 3), Q(1, 2), R(4, 1)
Answer» Determine whether the points are collinear. (1) A(1, –3), B(2, –5), C(–4, 7) (2) L(–2, 3), M(1, –3), N(5, 4) (3) R(0, 3), D(2, 1), S(3, –1) (4) P(–2, 3), Q(1, 2), R(4, 1)

Discussion

46.	Check whether the following is a quadratic equation or not (2x-1)(x-3)=(X+5)(x-1)
Answer» Check whether the following is a quadratic equation or not (2x-1)(x-3)=(X+5)(x-1)

Discussion

47.	If one zero of the quadratic polynomial (k−1)x2+kx+1 is -4 then the value of k is (a) −54 (b) 54 (c) −43 (d) 43
Answer» If one zero of the quadratic polynomial $(k - 1) x^{2} + k x + 1$ is -4 then the value of k is (a) $\frac{- 5}{4}$ (b) $\frac{5}{4}$ (c) $\frac{- 4}{3}$ (d) $\frac{4}{3}$

47.

If one zero of the quadratic polynomial (k−1)x2+kx+1 is -4 then the value of k is (a) −54 (b) 54 (c) −43 (d) 43

Answer»

If one zero of the quadratic polynomial $(k - 1) x^{2} + k x + 1$ is -4 then the value of k is

(a) $\frac{- 5}{4}$ (b) $\frac{5}{4}$ (c) $\frac{- 4}{3}$ (d) $\frac{4}{3}$

Discussion

48.	There are six girls and four boys in a class. If one candidate is to be selected to take part in a competition, then which of the following is the probability of selecting a girl candidate?
Answer» There are six girls and four boys in a class. If one candidate is to be selected to take part in a competition, then which of the following is the probability of selecting a girl candidate?

Discussion

49.

Journalise the following in the books of Som Nath & Sons: 2019 May 1 Purchased a Machinery for ₹ 1,00,000 and the payment was made by issuing a cheque from Proprietor's saving bank account. 4 Received an order from Chakravarti for goods of ₹ 4,00,000 alongwith a cheque of 10% of the order as advance. 8 Paid cash ₹ 8,000 to Dushyant and discount allowed by him ₹ 800. 10 Goods stolen by an employee (Sale Price ₹ 20,000; Cost ₹ 15,000). 15 Purchased stationery worth ₹ 8,000 for office use and ₹ 2,000 for personal use. 20 Manoj pays us ₹ 5,400 after deducting 10% for prompt payment. 28 Sold goods to Kuber costing ₹ 2,00,000 at 25% above cost less trade discount of 10% and cash discount of 5%. Kuber did not avail the cash discount.

Answer» Journalise the following in the books of Som Nath & Sons:

2019
May 1	Purchased a Machinery for ₹ 1,00,000 and the payment was made by issuing a cheque from Proprietor's saving bank account.
4	Received an order from Chakravarti for goods of ₹ 4,00,000 alongwith a cheque of 10% of the order as advance.
8	Paid cash ₹ 8,000 to Dushyant and discount allowed by him ₹ 800.
10	Goods stolen by an employee (Sale Price ₹ 20,000; Cost ₹ 15,000).
15	Purchased stationery worth ₹ 8,000 for office use and ₹ 2,000 for personal use.
20	Manoj pays us ₹ 5,400 after deducting 10% for prompt payment.
28	Sold goods to Kuber costing ₹ 2,00,000 at 25% above cost less trade discount of 10% and cash discount of 5%. Kuber did not avail the cash discount.

Discussion

50.	2 tan 30°1-tan2 30° is equal to(a) cos 60°(b) sin 60°(c) tan 60°(d) sin 30°
Answer» $\frac{2 \tan 30 °}{1 - \tan^{2} 30 °}$ is equal to (a) cos 60° (b) sin 60° (c) tan 60° (d) sin 30°

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The following distribution gives the daily income of 50 workers of a factory: Daily income in (Rs): 100−120 120−140 140−160 160−180 180−200 Number of workers: 12 14 8 6 10 Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

Question 2 (ii) Find the surface area of a sphere of diameter: (ii) 21 cm [Assume π=227]

In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B. If OB = 1 cm and AB = 3 cm, then ∠OCB = _____

The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?

A boiler was purchased from abroad for ₹ 10,000. Shipping and forwarding charges ₹ 2,000, Import duty ₹ 7,000 and expenses of installation amounted to ₹ 1,000.Calculate the Depreciation for the first three years (separately for each year) 10% p.a. on Diminishing Balance Method.

Write the nth term of an A.P. the sum of whose n terms is Sn.

Question 5You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for Δ ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).

Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).

If A =[abba] and A2 =[xyyx] , then

The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

If the cumulative frequency for the class interval (50-60) is 92, then find x Class Interval0−1010−2020−3030−4040−5050−60Frequency 12 20 x 18 10 6

35. If the points A(4,3) & B(x,5) are on the circle with centre O(2,3). Find the value of 'x'.

A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. The volume of the tent is and the area of the cloth used for making it is .

Question 2 (v)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.−14,14

The angle of elevation of the top Q of a vertical tower PQ, from a point X on the ground is 60∘. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45∘. Find the height of the tower PQ and the distance PX. (Use √3=1.73)

In the given figure, DE || BD. Determine AC and AE.

While learning I came across a question which was as follows: Find the sum of the first 40 positive integers divisible by 6. My doubt is that should I find the sum of the 1st 40 multiples of 6 or the multiples of 6 from starting from 1 to 40 (i.e, 6,12,18,24,30,36).

Which term of the arithmetic progression 8,14,20,26,... will be 72 more than its 41st term?

When f(x)= x³- 6x²+ 2x- 4 is divided by y(x)= 3x- 1, then the remainder is

Derive the formula for the volume of the frustum of a cone.

If the nth terms of two A.P.s: 9,7,5.... and 24, 21, 18, ... are the same, then the value of n is _________.

when at t=0, particle is at the extreme position,we use the equation x=acoswt when at t=0 particle is at mean position we use the equation y=asinwtDo we need to follow any sign convention for using these two formulas

Question 7Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

The points (other than origin) for which abscissa is equal to the ordinate will lie in(a) I quadrant only(b) I and II quadrants(c) I and III quadrants(d) II and IV quadrants

For the following set of numbers find the difference between the mean and the median 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15

The unit vector along the vector a= 5i^+4j^+√8k^ is

What is the decimal form of 311?0.272727

If x=2+√3,xy=1, then find x2−x+y2−y.

If ΔABC is right angled at B, what is the value of sin(A+C)

A boat can go 20 km upstream and 30 km downstream in 3 hrs. It can go 20 downstream and 10km upstream in 1 hrs 40 min . Find the speed of the boat in still water and speed of the stream.

What is the locus of the center of a cycle wheel?

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

The length of the diagonal of rectangular playground is 125 m, and the length of one side is 75 m. Find the length of other side.

If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is2 h sec αtan β-tan α

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John and x marbles.

If the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b,a+2b for some real numbers a and b then find the value of a and b

Consider the following AP sequence: 134, 104, 74,… The 6thterm is

Consider the following frequency distribution: Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 3 9 15 30 18 5 The modal class is (a) 10-20 (b)20-30 (c)30-40 (d) 50-60

If axn+bx(n−1)−1+c=0 is a quadratic equation, then n = ___

A man wants to buy 62 shares available at Rs 132(par value of Rs 100) (i) How much should he invest? (ii) If the dividend is 7.5 %. What will be his annual income?

10. At selection , the probability of selection of A is 2/5 and that of B is 3/7 . The probability that both of them would not be selected is (if A and B are independent)

Determine whether the points are collinear.(1) A(1, –3), B(2, –5), C(–4, 7)(2) L(–2, 3), M(1, –3), N(5, 4)(3) R(0, 3), D(2, 1), S(3, –1)(4) P(–2, 3), Q(1, 2), R(4, 1)

Check whether the following is a quadratic equation or not (2x-1)(x-3)=(X+5)(x-1)

If one zero of the quadratic polynomial (k−1)x2+kx+1 is -4 then the value of k is (a) −54 (b) 54 (c) −43 (d) 43

There are six girls and four boys in a class. If one candidate is to be selected to take part in a competition, then which of the following is the probability of selecting a girl candidate?

2 tan 30°1-tan2 30° is equal to(a) cos 60°(b) sin 60°(c) tan 60°(d) sin 30°