32581 + Interview Questions in Mathematics

1.	The following are the heights in centimetres of the students in class X. 162, 155, 166, 173, 170, 161, 166, 151, 167, 176, 178, 175, 163, 165, 170, 152, 172, 166, 176, 159, 157, 158, 148, 174, 152, 162, 171, 178, 157, 145, 148. The given data has been grouped into class intervals in the given frequency distribution table. Fill in the table with the missing frequencies. Class intervalFrequency(fi)145−1503150−1553155−160p=−−−−160−165q=−−−−165−170r=−−−−170−175s=−−−−175−1805
Answer» The following are the heights in centimetres of the students in class X. 162, 155, 166, 173, 170, 161, 166, 151, 167, 176, 178, 175, 163, 165, 170, 152, 172, 166, 176, 159, 157, 158, 148, 174, 152, 162, 171, 178, 157, 145, 148. The given data has been grouped into class intervals in the given frequency distribution table. Fill in the table with the missing frequencies. $\begin{matrix} Class interval & Frequency (f_{i}) 145 - 150 & 3 150 - 155 & 3 155 - 160 & p = - - - - 160 - 165 & q = - - - - 165 - 170 & r = - - - - 170 - 175 & s = - - - - 175 - 180 & 5 \end{matrix}$

Discussion

2.	Each of the letters in the word VALIANT is on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be a vowel? [1 MARK]
Answer» Each of the letters in the word VALIANT is on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be a vowel? [1 MARK]

Discussion

3.	If y is the mean proportional between x and z ; show that xy + yz is the mean proportional between x2+y2 and y2+z2.
Answer» If y is the mean proportional between x and z ; show that xy + yz is the mean proportional between $x^{2} + y^{2}$ and $y^{2} + z^{2}$ .

Discussion

4.	1. Let be a set with exactly 5 elements and y be a set with exactly 7 elements. If A Is the number of one - one functions from x to y and B is the number of onto functions from y to X, then find the value of B-A/5!
Answer» 1. Let be a set with exactly 5 elements and y be a set with exactly 7 elements. If A Is the number of one - one functions from x to y and B is the number of onto functions from y to X, then find the value of B-A/5!

Discussion

5.

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of a plants in 20 houses in a locality. Find the mean number of plants per house. Number of plants: 0-2 2-4 4-6 6-8 8-10 10-12 12-14 Number of houses: 1 2 1 5 6 2 3 Which method did you use for finding the mean, and why?

Answer» A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of a plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants:	0-2	2-4	4-6	6-8	8-10	10-12	12-14
Number of houses:	1	2	1	5	6	2	3

Which method did you use for finding the mean, and why?

Discussion

6.	A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.
Answer» A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ} t o 60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

Discussion

7.	Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.
Answer» Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.

Discussion

8.	If tan−1x+cos−1y√1+y2=sin−13√10 where x,y∈N, then x+y can be
Answer» If ${tan}^{- 1} x + {cos}^{- 1} \frac{y}{\sqrt{1 + y^{2}}} = {sin}^{- 1} \frac{3}{\sqrt{10}}$ where $x, y \in N,$ then $x + y$ can be

Discussion

9.	Mark the correct alternative in each of the following:A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not an ace is(a) 113 (b) 913 (c) 413 (d) 1213 [CBSE 2014]
Answer» Mark the correct alternative in each of the following: A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not an ace is (a) $\frac{1}{13}$ (b) $\frac{9}{13}$ (c) $\frac{4}{13}$ (d) $\frac{12}{13}$ [CBSE 2014]

Discussion

10.	Anushree has to pay 4% sales tax in addition to the price of a certain article. Find the price of her article ,if she pays Rs2.60 in all.
Answer» Anushree has to pay 4% sales tax in addition to the price of a certain article. Find the price of her article ,if she pays Rs2.60 in all.

Discussion

11.	The radii of the ends of a frustum of a cone are r1 and r2. If l is the slant height of the frustum, then the slant height of the cone of which the frustum is apart, is ________.
Answer» The radii of the ends of a frustum of a cone are r₁ and r₂. If l is the slant height of the frustum, then the slant height of the cone of which the frustum is apart, is ________.

Discussion

12.	The area of a triangle whose vertices are A(2,7), B(3,-1) and C(-5,6) is
Answer» The area of a triangle whose vertices are A(2,7), B(3,-1) and C(-5,6) is

Discussion

13.	Question 2 (iii)Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
Answer» Question 2 (iii) Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

Discussion

14.	If a circle is drawn with centre 'C' (0,5) and radius 13 units, then the point (0,0) lies
Answer» If a circle is drawn with centre 'C' (0,5) and radius 13 units, then the point (0,0) lies

Discussion

15.	Factorize:16x2+4y2+9z2−16xy−12yz+24xz
Answer» Factorize: $16 x^{2} + 4 y^{2} + 9 z^{2} - 16 x y - 12 y z + 24 x z$

15.

Factorize:16x2+4y2+9z2−16xy−12yz+24xz

Answer»

Factorize:

$16 x^{2} + 4 y^{2} + 9 z^{2} - 16 x y - 12 y z + 24 x z$

Discussion

16.	Construct a regular hexagon in a circle of radius 3 cm.
Answer» Construct a regular hexagon in a circle of radius 3 cm.

Discussion

17.	Question 2 (ii)Find the value of 'k', for which the following points are collinear.(ii) (8, 1), (k, -4), (2, -5)
Answer» Question 2 (ii) Find the value of 'k', for which the following points are collinear. (ii) (8, 1), (k, -4), (2, -5)

Discussion

18.	Find the area of the triangle whose sides are 8cm 6cm and 7cm by Heron's Formula
Answer» Find the area of the triangle whose sides are 8cm 6cm and 7cm by Heron's Formula

Discussion

19.	Question 9A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. Find the height of the cone. (A) 12 cm(B) 14 cm(C) 15 cm(D) 18 cm
Answer» Question 9 A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. Find the height of the cone. (A) 12 cm (B) 14 cm (C) 15 cm (D) 18 cm

Discussion

20.	a) A positive number is divided into two parts, such that the sum of the squares of the two parts is 208. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number. b) Solve the following quadratic equation and give the answer correct to two significant figures: 4x2−7x+2=0 [6 MARKS]
Answer» a) A positive number is divided into two parts, such that the sum of the squares of the two parts is 208. The square of the larger part is 8 times the smaller part. Taking $x$ as the smaller part of the two parts, find the number. b) Solve the following quadratic equation and give the answer correct to two significant figures: $4 x^{2} - 7 x + 2 = 0$ [6 MARKS]

Discussion

21.	Give one example of a situation in which the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Answer» Give one example of a situation in which the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Discussion

22.	A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows: The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also, he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the 2nd digit, given that ‘b’ is the second digit?
Answer» A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows: The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also, he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the $2^{n d}$ digit, given that ‘b’ is the second digit?

Discussion

23.	Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (a) r2 sq. units (b) 12 r2 sq. units (c) 2 r2 sq. units (d) 2 r2 sq. units
Answer» Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (a) r²sq. units (b) $\frac{1}{2}$ r²sq. units (c) 2 r²sq. units (d) $\sqrt{2}$ r²sq. units

Discussion

24.	One out of every three consecutive integer is always divisible by 7.How
Answer» One out of every three consecutive integer is always divisible by 7.How

Discussion

25.	If the variance of the following frequency distribution :Class10−2020−3030−40Frequency2x2is 50, then x is equal to
Answer» If the variance of the following frequency distribution : $\begin{matrix} Class & 10 - 20 & 20 - 30 & 30 - 40 Frequency & 2 & x & 2 \end{matrix}$ is $50$ , then $x$ is equal to

Discussion

26.	Solve for x and y: 23x−29y=98,29x−23y=110.
Answer» Solve for x and y: $23 x - 29 y = 98, 29 x - 23 y = 110.$

26.

Solve for x and y: 23x−29y=98,29x−23y=110.

Answer»

Solve for x and y:

$23 x - 29 y = 98, 29 x - 23 y = 110.$

Discussion

27.	If –4 is a zero of the polynomial x2 – x – (2k + 2), then k = _________.
Answer» If –4 is a zero of the polynomial x² – x – (2k + 2), then k = _________.

Discussion

28.	In the given figure, ABCD and EFCD are two parallelograms and G is the mid-point of CD. Then, prove that ar (∆DPC)=ar(EFCD).
Answer» In the given figure, ABCD and EFCD are two parallelograms and G is the mid-point of CD. Then, prove that ar (∆DPC)=ar(EFCD).

Discussion

29.	'Chetana Store' paid total GST of Rs 1,00,500 at the time of purchase and collected GST Rs 1,22,500 at the time of sale during 1st of July 2017 to 31st July 2017. Find the GST payable by Chetana Stores.
Answer» 'Chetana Store' paid total GST of Rs 1,00,500 at the time of purchase and collected GST Rs 1,22,500 at the time of sale during 1^stof July 2017 to 31^st July 2017. Find the GST payable by Chetana Stores.

Discussion

30.	Two chords AB and CD of a circle whose centre is O,meet at the point P and angle AOC=50 , angle BOD = 40,then the value of Angle BPD is ??
Answer» Two chords AB and CD of a circle whose centre is O,meet at the point P and angle AOC=50 , angle BOD = 40,then the value of Angle BPD is ??

Discussion

31.	Match the following based on the construction of similar triangles, if scale factor (mn) isI. >1a) The similar triangle is smaller than the original triangle.II. <1b) The two triangles are congruent triangles.III. =1c) The similar triangle is larger than the original triangle.
Answer» Match the following based on the construction of similar triangles, if scale factor $(\frac{m}{n})$ is $\begin{matrix} I . > 1 & a) T h e s i m i l a r t r i a n g l e i s s m a l l e r t h a n t h e o r i g i n a l t r i a n g l e . I I . < 1 & b) T h e t w o t r i a n g l e s a r e c o n g r u e n t t r i a n g l e s . I I I . = 1 & c) T h e s i m i l a r t r i a n g l e i s l a r g e r t h a n t h e o r i g i n a l t r i a n g l e . \end{matrix}$

Discussion

32.	Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.
Answer» Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Discussion

33.	Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio
Answer» Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio

33.

Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio

Answer»

Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio

Discussion

34.	A man sold 600 (Rs 25) shares paying 6½% dividend at Rs 22 and invested the sale proceeds in Rs 10 shares, paying 9% at Rs 12. What was his annual income at 9%?
Answer» A man sold 600 (Rs 25) shares paying 6½% dividend at Rs 22 and invested the sale proceeds in Rs 10 shares, paying 9% at Rs 12. What was his annual income at 9%?

Discussion

35.	If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is(a) 2(b) 3(c) 1(d) 4
Answer» If the sum of n terms of an A.P. be 3n² + n and its common difference is 6, then its first term is (a) 2 (b) 3 (c) 1 (d) 4

Discussion

36.	Let Sn be the sum of the first n terms of an arithmetic progression. If S3n=3S2n, then the value of S4nS2n is
Answer» Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3 n} = 3 S_{2 n},$ then the value of $\frac{S_{4 n}}{S_{2 n}}$ is

Discussion

37.	If −4 is a root of the quadratic equation x2+2x+4p=0, find the value of k for which the quadratic equation x2+px1+3k+73+2k=0 has equal roots. [CBSE 2015]
Answer» If −4 is a root of the quadratic equation $x^{2} + 2 x + 4 p = 0$ , find the value of k for which the quadratic equation $x^{2} + p x (1 + 3 k) + 7 (3 + 2 k) = 0$ has equal roots. [CBSE 2015]

Discussion

38.	20. A boat is being towed away from a cliff 150m high.From the top of the cliff the angle of depression of the boat changes from 60^° to 40^° in 2min.Find the speed of the boat
Answer» 20. A boat is being towed away from a cliff 150m high.From the top of the cliff the angle of depression of the boat changes from 60^° to 40^° in 2min.Find the speed of the boat

Discussion

39.	There are 121 articles in a bag. Out of which 11 are defective articles. If you just pick one article at random, (i)what is the probability of picking the non-defective article? (ii) If the article drawn the first time is non-defective and is not replaced, then find the probability of getting the defective article in the next draw.
Answer» There are 121 articles in a bag. Out of which 11 are defective articles. If you just pick one article at random, (i)what is the probability of picking the non-defective article? (ii) If the article drawn the first time is non-defective and is not replaced, then find the probability of getting the defective article in the next draw.

Discussion

40.

The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure (in Rs) 100 − 150 150 − 200 200 − 250 250 − 300 300 − 350 Number of households 4 5 12 2 2 Find the mean daily expenditure on food by a suitable method.

Answer»

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure (in Rs)	100 − 150	150 − 200	200 − 250	250 − 300	300 − 350
Number of households	4	5	12	2	2

Find the mean daily expenditure on food by a suitable method.

Discussion

41.	find the locus of poles of the normal chord of the ellipse x^2/a^2+y^2/b^2=1
Answer» find the locus of poles of the normal chord of the ellipse x^2/a^2+y^2/b^2=1

Discussion

42.	If x6+y6+6x2y2=16, then dydx=
Answer» If $x^{6} + y^{6} + 6 x^{2} y^{2} = 16,$ then $\frac{d y}{d x} =$

Discussion

43.	If 0<cos−1x<1 and 1+cos−1x+(cos−1x)2+……∞=2, then x is equal to
Answer» If $0 < {cos}^{- 1} x < 1$ and $1 + {cos}^{- 1} x + ({cos}^{- 1} x)^{2} + \dots \dots \infty = 2,$ then $x$ is equal to

Discussion

44.	Question 6 If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer» Question 6 If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Discussion

45.	A circle is kept inside an isosceles right angled triangle as shown in the figure, where G is the centre of the circle. If the area of ADGE is xcm2, find the area of BFGD.
Answer» A circle is kept inside an isosceles right angled triangle as shown in the figure, where G is the centre of the circle. If the area of ADGE is $x c m^{2}$ , find the area of BFGD.

45.

A circle is kept inside an isosceles right angled triangle as shown in the figure, where G is the centre of the circle. If the area of ADGE is xcm2, find the area of BFGD.

Answer»

A circle is kept inside an isosceles right angled triangle as shown in the figure, where G is the centre of the circle. If the area of ADGE is $x c m^{2}$ , find the area of BFGD.

Discussion

46.	Consider the above figure where O is the center of the circle, AB = CD and ∠AOB=30∘. Find ∠AED and ∠COD.
Answer» Consider the above figure where O is the center of the circle, AB = CD and $∠ A O B = 30^{\circ} .$ Find $∠ A E D$ and $∠ C O D$ .

Discussion

47.	Question 2 Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.
Answer» Question 2 Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Discussion

48.	123.Find the inverse of matrix A= 1 3 -2 -3 0 -5 2 5 0
Answer» 123.Find the inverse of matrix A= 1 3 -2 -3 0 -5 2 5 0

Discussion

49.	Question 1A cylindrical pencil sharpened at one edge is the combination of(A) a cone and a cylinder(B) frustum of a cone and a cylinder(C) a hemisphere and a cylinder(D) two cylinders.
Answer» Question 1 A cylindrical pencil sharpened at one edge is the combination of (A) a cone and a cylinder (B) frustum of a cone and a cylinder (C) a hemisphere and a cylinder (D) two cylinders.

Discussion

50.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Each of the letters in the word VALIANT is on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be a vowel? [1 MARK]

If y is the mean proportional between x and z ; show that xy + yz is the mean proportional between x2+y2 and y2+z2.

1. Let be a set with exactly 5 elements and y be a set with exactly 7 elements. If A Is the number of one - one functions from x to y and B is the number of onto functions from y to X, then find the value of B-A/5!

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.

Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.

If tan−1x+cos−1y√1+y2=sin−13√10 where x,y∈N, then x+y can be

Mark the correct alternative in each of the following:A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not an ace is(a) 113 (b) 913 (c) 413 (d) 1213 [CBSE 2014]

Anushree has to pay 4% sales tax in addition to the price of a certain article. Find the price of her article ,if she pays Rs2.60 in all.

The radii of the ends of a frustum of a cone are r1 and r2. If l is the slant height of the frustum, then the slant height of the cone of which the frustum is apart, is ________.

The area of a triangle whose vertices are A(2,7), B(3,-1) and C(-5,6) is

Question 2 (iii)Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

If a circle is drawn with centre 'C' (0,5) and radius 13 units, then the point (0,0) lies

Factorize:16x2+4y2+9z2−16xy−12yz+24xz

Construct a regular hexagon in a circle of radius 3 cm.

Question 2 (ii)Find the value of 'k', for which the following points are collinear.(ii) (8, 1), (k, -4), (2, -5)

Find the area of the triangle whose sides are 8cm 6cm and 7cm by Heron's Formula

Question 9A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. Find the height of the cone. (A) 12 cm(B) 14 cm(C) 15 cm(D) 18 cm

Give one example of a situation in which the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (a)​ r2 sq. units (b) 12 r2 sq. units (c) 2 r2 sq. units (d) 2 r2 sq. units

One out of every three consecutive integer is always divisible by 7.How

If the variance of the following frequency distribution :Class10−2020−3030−40Frequency2x2is 50, then x is equal to

Solve for x and y: 23x−29y=98,29x−23y=110.

If –4 is a zero of the polynomial x2 – x – (2k + 2), then k = _________.

In the given figure, ABCD and EFCD are two parallelograms and G is the mid-point of CD. Then, prove that ar (∆DPC)=ar(EFCD).

'Chetana Store' paid total GST of Rs 1,00,500 at the time of purchase and collected GST Rs 1,22,500 at the time of sale during 1st of July 2017 to 31st July 2017. Find the GST payable by Chetana Stores.

Two chords AB and CD of a circle whose centre is O,meet at the point P and angle AOC=50 , angle BOD = 40,then the value of Angle BPD is ??

Match the following based on the construction of similar triangles, if scale factor (mn) isI. &gt;1a) The similar triangle is smaller than the original triangle.II. &lt;1b) The two triangles are congruent triangles.III. =1c) The similar triangle is larger than the original triangle.

Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio

A man sold 600 (Rs 25) shares paying 6½% dividend at Rs 22 and invested the sale proceeds in Rs 10 shares, paying 9% at Rs 12. What was his annual income at 9%?

If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is(a) 2(b) 3(c) 1(d) 4

Let Sn be the sum of the first n terms of an arithmetic progression. If S3n=3S2n, then the value of S4nS2n is

If −4 is a root of the quadratic equation x2+2x+4p=0, find the value of k for which the quadratic equation x2+px1+3k+73+2k=0 has equal roots. [CBSE 2015]

20. A boat is being towed away from a cliff 150m high.From the top of the cliff the angle of depression of the boat changes from 60^° to 40^° in 2min.Find the speed of the boat

The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure (in Rs) 100 − 150 150 − 200 200 − 250 250 − 300 300 − 350 Number of households 4 5 12 2 2 Find the mean daily expenditure on food by a suitable method.

find the locus of poles of the normal chord of the ellipse x^2/a^2+y^2/b^2=1

If x6+y6+6x2y2=16, then dydx=

If 0&lt;cos−1x&lt;1 and 1+cos−1x+(cos−1x)2+……∞=2, then x is equal to

Question 6 If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

A circle is kept inside an isosceles right angled triangle as shown in the figure, where G is the centre of the circle. If the area of ADGE is xcm2, find the area of BFGD.

Consider the above figure where O is the center of the circle, AB = CD and ∠AOB=30∘. Find ∠AED and ∠COD.

Question 2 Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

123.Find the inverse of matrix A= 1 3 -2 -3 0 -5 2 5 0

Question 1A cylindrical pencil sharpened at one edge is the combination of(A) a cone and a cylinder(B) frustum of a cone and a cylinder(C) a hemisphere and a cylinder(D) two cylinders.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (a) r2 sq. units (b) 12 r2 sq. units (c) 2 r2 sq. units (d) 2 r2 sq. units

Match the following based on the construction of similar triangles, if scale factor (mn) isI. >1a) The similar triangle is smaller than the original triangle.II. <1b) The two triangles are congruent triangles.III. =1c) The similar triangle is larger than the original triangle.

If 0<cos−1x<1 and 1+cos−1x+(cos−1x)2+……∞=2, then x is equal to