32581 + Interview Questions in Mathematics Page 49 InterviewSolution

2401.	From the top of a 16 m high building the angle of elevation of the top of a tower is 45^° and the angle of depression of its foot is 30^°, then height of the tower is (in m)
Answer» From the top of a 16 m high building the angle of elevation of the top of a tower is 45^° and the angle of depression of its foot is 30^°, then height of the tower is (in m)

Discussion

2402.	If a year of 22nd century is randomly selected, find out the probability of the year having 53 sundays.
Answer» If a year of 22nd century is randomly selected, find out the probability of the year having 53 sundays.

Discussion

2403.	52. For real numbers X and Y ,we write xRy = x-y+square root 2 is an irrational number then the relation is
Answer» 52. For real numbers X and Y ,we write xRy = x-y+square root 2 is an irrational number then the relation is

Discussion

2404.	The range of probability of any event of a random experiment is ___________.
Answer» The range of probability of any event of a random experiment is ___________.

Discussion

2405.	If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms
Answer» If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms

Discussion

2406.	The value of a for which the lines x=1, y=2 and a2x+2y−20=0 are concurrent is:
Answer» The value of a for which the lines $x = 1$ , $y = 2$ and $a^{2} x + 2 y - 20 = 0$ are concurrent is:

Discussion

2407.	Pranalee was practising for a 100 m running race. She ran 100 m distance 20 times. The time required, in seconds, for each attempt was as follows.18, 17, 17, 16, 15, 16, 15, 14, 16, 15, 15, 17, 15, 16, 15, 17, 16, 15, 14, 15.Find the mean of the times taken for running.
Answer» Pranalee was practising for a 100 m running race. She ran 100 m distance 20 times. The time required, in seconds, for each attempt was as follows. 18, 17, 17, 16, 15, 16, 15, 14, 16, 15, 15, 17, 15, 16, 15, 17, 16, 15, 14, 15. Find the mean of the times taken for running.

Discussion

2408.	Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. Find the equation representing the situation.
Answer» Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. Find the equation representing the situation.

Discussion

2409.	If a, b and c are the zeroes of a cubic polynomial px3 + qx2 + rx + s and 0 > a > b > c, then which of the following is true?Options:p > 0, q > 0, r > 0, s > 0p < 0, q < 0, r < 0, s > 0p > 0, q > 0, r > 0, s < 0p > 0, q < 0, r < 0, s > 0
Answer» If a, b and c are the zeroes of a cubic polynomial px3 + qx2 + rx + s and 0 > a > b > c, then which of the following is true? Options: p > 0, q > 0, r > 0, s > 0 p < 0, q < 0, r < 0, s > 0 p > 0, q > 0, r > 0, s < 0 p > 0, q < 0, r < 0, s > 0

Discussion

2410.	draw the graph of 2x+y-6=0 and 2x-y=-2 also,find the area of the triangle formed by the above lines and x axis
Answer» draw the graph of 2x+y-6=0 and 2x-y=-2 also,find the area of the triangle formed by the above lines and x axis

Discussion

2411.	The digits of a two digit number differ by three. If the digits are interchange and the resulting number is added to the original number, we get 143. What can be the number.
Answer» The digits of a two digit number differ by three. If the digits are interchange and the resulting number is added to the original number, we get 143. What can be the number.

Discussion

2412.	What is a lemma?
Answer» What is a lemma?

Discussion

2413.	Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.
Answer» Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.

Discussion

2414.

Prepare Purchases and Sales Book from the following transactions of Rahul, Bengaluru: 2019 Jan. 1 Bought from M/s. Uma Datt, Mumbai: 1,000 Registers ₹ 80 each 50 Reams Paper ₹ 250 per ream Less: Trade Discount 25% Plus: IGST 5% Jan. 2 Sold to Shri Dayal, Bengaluru: 250 Registers ₹ 85 each 5 Reams paper ₹ 300 per ream Charged CGST and SGST 2.5% each Jan. 8 Bought from BILT, Delhi: 100 Reams Ruled Paper ₹ 600 per ream Less: Trade Discount 15% Plus IGST 5% Jan. 12 Sold to Gupta Bros., Delhi: 250 Registers ₹ 85 each 50 Reams Ruled Paper 700 per ream Less: Trade Discount 5%, charged IGST 5% Jan. 18 Sold to Ram Saran Das: 20 copies Double Entry Book Keeping ₹ 85 each Jan. 25 Bought from Hari Ram, Delhi: 1,000 pens ₹ 10 each Less: Trade Discount 15% Plus IGST 5% Jan. 31 Sold to Rishi Kumar, Bengaluru: 300 Registers ₹ 90 each 50 Reams Ruled Paper ₹ 700 per ream 20 Reams Paper ₹ 300 per ream Less: Trade Discount 10%, charged CGST and SGST 2.5% each

Answer» Prepare Purchases and Sales Book from the following transactions of Rahul, Bengaluru:

2019
Jan. 1	Bought from M/s. Uma Datt, Mumbai:
	1,000 Registers ₹ 80 each
	50 Reams Paper ₹ 250 per ream
	Less: Trade Discount 25%
	Plus: IGST 5%
Jan. 2	Sold to Shri Dayal, Bengaluru:
	250 Registers ₹ 85 each
	5 Reams paper ₹ 300 per ream
	Charged CGST and SGST 2.5% each
Jan. 8	Bought from BILT, Delhi:
	100 Reams Ruled Paper ₹ 600 per ream
	Less: Trade Discount 15%
	Plus IGST 5%
Jan. 12	Sold to Gupta Bros., Delhi:
	250 Registers ₹ 85 each
	50 Reams Ruled Paper 700 per ream
	Less: Trade Discount 5%, charged IGST 5%
Jan. 18	Sold to Ram Saran Das:
	20 copies Double Entry Book Keeping ₹ 85 each
Jan. 25	Bought from Hari Ram, Delhi:
	1,000 pens ₹ 10 each
	Less: Trade Discount 15%
	Plus IGST 5%
Jan. 31	Sold to Rishi Kumar, Bengaluru:
	300 Registers ₹ 90 each
	50 Reams Ruled Paper ₹ 700 per ream
	20 Reams Paper ₹ 300 per ream
	Less: Trade Discount 10%, charged CGST and SGST 2.5% each

Discussion

2415.

The table below shows the daily expenditure on food of 25 household 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 household 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

2416.	Which of the following equations are quadratic?
Answer» Which of the following equations are quadratic?

Discussion

2417.	There are four children A,B,C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 10 chocolates. Which of these children has close to the average number of chocolates?
Answer» There are four children A,B,C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 10 chocolates. Which of these children has close to the average number of chocolates?

Discussion

2418.	To construct a triangle similar to a given ΔABC with its sides 74 of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then, locate points B1,B2,B3,…… on BX at equal distances and next step is to join the points
Answer» To construct a triangle similar to a given $Δ A B C$ with its sides $\frac{7}{4}$ of the corresponding sides of $Δ A B C$ , first draw a ray BX such that $∠ C B X$ is an acute angle and X lies on the opposite side of A with respect to BC. Then, locate points $B_{1}, B_{2}, B_{3}, \dots \dots$ on BX at equal distances and next step is to join the points

Discussion

2419.	A Ramraj pencil box of dimensions 30cm × 5cm × 5cm consists of 10 sharpened cylindrical pencils placed in a vertical fashion each of length 20cm and diameter 1.4cm and having a conical surmount whose slant height is 2.5m. There are 2 rows of 5 pencils each. Find available volume in the box. Can a sharpener and an eraser in shape of a cube each of side 5cm be placed on top of the pencils such that sharpener is placed on top of the eraser.
Answer» A Ramraj pencil box of dimensions 30cm × 5cm × 5cm consists of 10 sharpened cylindrical pencils placed in a vertical fashion each of length 20cm and diameter 1.4cm and having a conical surmount whose slant height is 2.5m. There are 2 rows of 5 pencils each. Find available volume in the box. Can a sharpener and an eraser in shape of a cube each of side 5cm be placed on top of the pencils such that sharpener is placed on top of the eraser.

Discussion

2420.	Grace took a loan of ₹5000. She paid ₹445 every month for a year to repay it. How much interest did she pay?
Answer» Grace took a loan of $₹ 5000$ . She paid $₹ 445$ every month for a year to repay it. How much interest did she pay?

Discussion

2421.

The following table 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 Find the mean, mode and median of the above data.

Answer» The following table 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

Find the mean, mode and median of the above data.

Discussion

2422.	A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number? [CBSE 2014](a) 23(b) 16(c) 13(d) 1130
Answer» A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number? [CBSE 2014] (a) $\frac{2}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{3}$ (d) $\frac{11}{30}$

Discussion

2423.	The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in cm2).
Answer» The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c m^{2}$ ).

Discussion

2424.	Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Answer» Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Discussion

2425.	5. Prove that 1/1+2+1/2+3+1/3+4+1/4+5+1/5+6+1/6+7+1/7+8+1/8+9
Answer» 5. Prove that 1/1+2+1/2+3+1/3+4+1/4+5+1/5+6+1/6+7+1/7+8+1/8+9

Discussion

2426.	In Fig. 7.242, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = _______ and AB = __________.
Answer» In Fig. 7.242, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = _______ and AB = __________.

Discussion

2427.	Find the curved surface area of a cone whose radius is 14cm and slant height is 10 cm
Answer» Find the curved surface area of a cone whose radius is 14cm and slant height is 10 cm

Discussion

2428.	A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use π =22/7.
Answer» A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use $π = 22 / 7$ .

Discussion

2429.	If P(n) : "2 × 42n + 1 + 33n + 1 is divisible by λ for all n ∈ N" is true, then the value of λ is _____________.
Answer» If P(n) : "2 × 4^{2n + 1} + 3^{3n + 1} is divisible by λ for all n ∈ N" is true, then the value of λ is _____________.

Discussion

2430.	If the x-intercept and y-intercept of a straight line are 32 and 43 respectively, then find the equation of the straight line.
Answer» If the x-intercept and y-intercept of a straight line are $\frac{3}{2}$ and $\frac{4}{3}$ respectively, then find the equation of the straight line.

Discussion

2431.	Find the simple interest on ₹3000, at a simple interest rate of 10% per annum for eight months.
Answer» Find the simple interest on ₹3000, at a simple interest rate of 10% per annum for eight months.

Discussion

2432.	In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find ∠PTR.
Answer» $In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If ∠ P O R = 78^{\circ}, then find ∠ P T R .$

Discussion

2433.	Prove that n^2 - n is divisible by 2 for every positive integer 'n'.
Answer» Prove that n^2 - n is divisible by 2 for every positive integer 'n'.

Discussion

2434.	Find the next term of the arithmetic sequence:3, 7, 11, 15, 19 …
Answer» Find the next term of the arithmetic sequence: 3, 7, 11, 15, 19 …

2434.

Find the next term of the arithmetic sequence:3, 7, 11, 15, 19 …

Answer»

Find the next term of the arithmetic sequence:

3, 7, 11, 15, 19 …

Discussion

2435.	The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.
Answer» The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.

Discussion

2436.	Find k, if PQ \|\| RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k).
Answer» Find k, if PQ \|\| RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k).

Discussion

2437.	A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?
Answer» A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

Discussion

2438.	Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and(i) deg p(x) = deg q(x)(ii) deg q(x) = deg r(x)(iii) deg r(x) = 0
Answer» Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0

2438.

Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and(i) deg p(x) = deg q(x)(ii) deg q(x) = deg r(x)(iii) deg r(x) = 0

Answer»

Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

(i) deg p(x) = deg q(x)

(ii) deg q(x) = deg r(x)

(iii) deg r(x) = 0

Discussion

2439.	Find teh number which should be added to x2+x+3 so that the resulting polynomial is completely divisible by (x+3).
Answer» Find teh number which should be added to $x^{2} + x + 3$ so that the resulting polynomial is completely divisible by (x+3).

Discussion

2440.	If two circles are such that one is not contained in the other and are not intersecting then the number of common tangents are
Answer» If two circles are such that one is not contained in the other and are not intersecting then the number of common tangents are

Discussion

2441.	In which ratio is the line segment joining points (-3,-4) and (1,-2) divided by y - axis
Answer» In which ratio is the line segment joining points (-3,-4) and (1,-2) divided by y - axis

Discussion

2442.	Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following tableSumFrequency214330442555672775870953104611281215If the dice are thrown once more, then what is the probability of getting a sum(i) 3?(ii) More than 10?(iii) Less than or equal to 5?(iv) Between 8 and 12?
Answer» Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table $\begin{matrix} Sum & Frequency 2 & 14 3 & 30 4 & 42 5 & 55 6 & 72 7 & 75 8 & 70 9 & 53 10 & 46 11 & 28 12 & 15 \end{matrix}$ If the dice are thrown once more, then what is the probability of getting a sum (i) 3? (ii) More than 10? (iii) Less than or equal to 5? (iv) Between 8 and 12?

Discussion

2443.	What is the ratio ACBC for the following construction method?
Answer» What is the ratio $\frac{A C}{B C}$ for the following construction method?

Discussion

2444.	in which of thre following cases change in volume is more:1)rise in temperature from 0 to 5^° c (2) rise in temperature from 100 to 105^°
Answer» in which of thre following cases change in volume is more:1)rise in temperature from 0 to 5^° c (2) rise in temperature from 100 to 105^°

Discussion

2445.	A line that intersects a circle at only one point is called as ___.
Answer» A line that intersects a circle at only one point is called as ___.

Discussion

2446.	If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.
Answer» If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.

2446.

If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.

Answer»

If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.

Discussion

2447.	19. A tree stands vertically on a hill side makes an angle of 15 degree with the horizontal. From a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60 degree. Find the height of the tree.
Answer» 19. A tree stands vertically on a hill side makes an angle of 15 degree with the horizontal. From a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60 degree. Find the height of the tree.

Discussion

2448.	In △ABC, ∠B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then AD.DC=
Answer» In $△$ ABC, $∠ B$ is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then $A D . D C =$

Discussion

2449.	Find the value of x if ΔABC∼ΔPQR.
Answer» $Find the value of x if Δ A B C \sim Δ P Q R .$

Discussion

2450.	What number should be added to 3x3 + 2x2 - 7x so that when the resulting polynomial is divided by x - 2, the remainder is 2?
Answer» What number should be added to 3 $x^{3}$ + 2 $x^{2}$ - 7x so that when the resulting polynomial is divided by x - 2, the remainder is 2?

Discussion

Explore topic-wise InterviewSolutions in .

From the top of a 16 m high building the angle of elevation of the top of a tower is 45^° and the angle of depression of its foot is 30^°, then height of the tower is (in m)

If a year of 22nd century is randomly selected, find out the probability of the year having 53 sundays.

52. For real numbers X and Y ,we write xRy = x-y+square root 2 is an irrational number then the relation is

The range of probability of any event of a random experiment is ___________.

If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms

The value of a for which the lines x=1, y=2 and a2x+2y−20=0 are concurrent is:

Pranalee was practising for a 100 m running race. She ran 100 m distance 20 times. The time required, in seconds, for each attempt was as follows.18, 17, 17, 16, 15, 16, 15, 14, 16, 15, 15, 17, 15, 16, 15, 17, 16, 15, 14, 15.Find the mean of the times taken for running.

Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. Find the equation representing the situation.

If a, b and c are the zeroes of a cubic polynomial px3 + qx2 + rx + s and 0 > a > b > c, then which of the following is true?Options:p > 0, q > 0, r > 0, s > 0p < 0, q < 0, r < 0, s > 0p > 0, q > 0, r > 0, s < 0p > 0, q < 0, r < 0, s > 0

draw the graph of 2x+y-6=0 and 2x-y=-2 also,find the area of the triangle formed by the above lines and x axis

The digits of a two digit number differ by three. If the digits are interchange and the resulting number is added to the original number, we get 143. What can be the number.

What is a lemma?

Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

The table below shows the daily expenditure on food of 25 household 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.

Which of the following equations are quadratic?

There are four children A,B,C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 10 chocolates. Which of these children has close to the average number of chocolates?

Grace took a loan of ₹5000. She paid ₹445 every month for a year to repay it. How much interest did she pay?

The following table 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 Find the mean, mode and median of the above data.

A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number? [CBSE 2014](a) 23(b) 16(c) 13(d) 1130

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in cm2).

Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

5. Prove that 1/1+2+1/2+3+1/3+4+1/4+5+1/5+6+1/6+7+1/7+8+1/8+9

In Fig. 7.242, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = _______ and AB = __________.

Find the curved surface area of a cone whose radius is 14cm and slant height is 10 cm

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use π =22/7.

If P(n) : "2 × 42n + 1 + 33n + 1 is divisible by λ for all n ∈ N" is true, then the value of λ is _____________.

If the x-intercept and y-intercept of a straight line are 32 and 43 respectively, then find the equation of the straight line.

Find the simple interest on ₹3000, at a simple interest rate of 10% per annum for eight months.

In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find ∠PTR.

Prove that n^2 - n is divisible by 2 for every positive integer 'n'.

Find the next term of the arithmetic sequence:3, 7, 11, 15, 19 …

The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.

Find k, if PQ || RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k).

A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and(i) deg p(x) = deg q(x)(ii) deg q(x) = deg r(x)(iii) deg r(x) = 0

Find teh number which should be added to x2+x+3 so that the resulting polynomial is completely divisible by (x+3).

If two circles are such that one is not contained in the other and are not intersecting then the number of common tangents are

In which ratio is the line segment joining points (-3,-4) and (1,-2) divided by y - axis

What is the ratio ACBC for the following construction method?

in which of thre following cases change in volume is more:1)rise in temperature from 0 to 5^° c (2) rise in temperature from 100 to 105^°

A line that intersects a circle at only one point is called as ___.

If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.

19. A tree stands vertically on a hill side makes an angle of 15 degree with the horizontal. From a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60 degree. Find the height of the tree.

In △ABC, ∠B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then AD.DC=

Find the value of x if ΔABC∼ΔPQR.

What number should be added to 3x3 + 2x2 - 7x so that when the resulting polynomial is divided by x - 2, the remainder is 2?

In Fig. 7.242, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = _ and AB = ____.