32581 + Interview Questions in Mathematics Page 120 InterviewSolution

5951.	Determine whether x=-1 is a root of the equation x2−3x+2=0 or not.
Answer» Determine whether x=-1 is a root of the equation $x^{2} - 3 x + 2 = 0$ or not.

Discussion

5952.	40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.
Answer» 40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.

Discussion

5953.	Find k for which the system 2x + 3y − 5 = 0 and 4x + ky − 10 = 0 has an infinite number of solutions.
Answer» Find k for which the system 2x + 3y − 5 = 0 and 4x + ky − 10 = 0 has an infinite number of solutions.

Discussion

5954.	AB is a diameter of a circle and AC is the chord such that ∠ BAC = 30∘. If the tangent at C intersects AB extended at D, then BC = BD.
Answer» AB is a diameter of a circle and AC is the chord such that $∠$ BAC = $30^{\circ}$ . If the tangent at C intersects AB extended at D, then BC = BD.

Discussion

5955.	A man on a top of a tower observes a truck at an angle of depression α where tanα = 1/√5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tanβ = √5. If the truck is moving at a uniform speed, then how much more time ti will take to reach the base of the cover.
Answer» A man on a top of a tower observes a truck at an angle of depression α where tanα = ¹/_√5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tanβ = √5. If the truck is moving at a uniform speed, then how much more time ti will take to reach the base of the cover.

Discussion

5956.	The distance between two stations A and B is 540 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than the other by 5km/ hr. If the distance between these two trains after 3 hrs of their start is 165 km, what is the speed of each train?
Answer» The distance between two stations A and B is 540 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than the other by 5km/ hr. If the distance between these two trains after 3 hrs of their start is 165 km, what is the speed of each train?

Discussion

5957.	The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is___
Answer» The probability of getting a bad egg in a lot of $400$ is $0.035$ . The number of bad eggs in the lot is___

Discussion

5958.	If △ABC is an isosceles right-triangle right angled at C such that AC = 5 cm. Then, AB =(a) 2.5cm(b) 52 cm(c) 10 cm(d) 5 cm
Answer» If △ABC is an isosceles right-triangle right angled at C such that AC = 5 cm. Then, AB = (a) 2.5cm (b) $5 \sqrt{2}$ cm (c) 10 cm (d) 5 cm

Discussion

5959.	Question 1 (ii) Express 156 as the product of its prime factors.
Answer» Question 1 (ii) Express 156 as the product of its prime factors.

Discussion

5960.	Find the annual income derived from 125, Rs 120 shares paying 5% dividend.
Answer» Find the annual income derived from 125, Rs 120 shares paying 5% dividend.

Discussion

5961.	Find the sum and product of the roots of 2x2 – 3x + 5 = 0
Answer» Find the sum and product of the roots of $2 x^{2}$ – 3x + 5 = 0

Discussion

5962.	A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square.
Answer» A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square.

Discussion

5963.	Find the roots of the equation 5x2−6x−2=0 by the method of completing the square.[3 MARKS]
Answer» Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square. [3 MARKS]

Discussion

5964.	Two poles of height 6 m and 11 m stand vertically on the ground such that the distance between them is 12 m, find the distance between their tops.
Answer» Two poles of height 6 m and 11 m stand vertically on the ground such that the distance between them is 12 m, find the distance between their tops.

Discussion

5965.	A company declares dividends of 15% on Rs 100 shares which is quoted at Rs 140. If the company has Rs 12,600 Find: i) What is the dividend? ii) What is the rate of interest on the investment?
Answer» A company declares dividends of 15% on Rs 100 shares which is quoted at Rs 140. If the company has Rs 12,600 Find: i) What is the dividend? ii) What is the rate of interest on the investment?

5965.

A company declares dividends of 15% on Rs 100 shares which is quoted at Rs 140. If the company has Rs 12,600 Find: i) What is the dividend? ii) What is the rate of interest on the investment?

Answer»

A company declares dividends of 15% on Rs 100 shares which is quoted at Rs 140. If the company has Rs 12,600 Find:

i) What is the dividend?

ii) What is the rate of interest on the investment?

Discussion

5966.	Evaluate the following(i) sin60° cos30° + sin30° cos 60°(ii) 2tan245° + cos230° − sin260°(iii) (iv) (v)
Answer» Evaluate the following (i) sin60° cos30° + sin30° cos 60° (ii) 2tan²45° + cos²30° − sin²60° (iii) (iv) (v)

5966.

Evaluate the following(i) sin60° cos30° + sin30° cos 60°(ii) 2tan245° + cos230° − sin260°(iii) (iv) (v)

Answer»

Evaluate the following

(i) sin60° cos30° + sin30° cos 60°

(ii) 2tan²45° + cos²30° − sin²60°

(iii)

(iv)

(v)

Discussion

5967.	In a ΔABC,right angled at B, AB=24 cm, BC=7 cm. Determine (i) sin A, cos A (ii) sin C, cos C
Answer» In a $Δ A B C$ ,right angled at B, AB=24 cm, BC=7 cm. Determine (i) sin A, cos A (ii) sin C, cos C

5967.

In a ΔABC,right angled at B, AB=24 cm, BC=7 cm. Determine (i) sin A, cos A (ii) sin C, cos C

Answer»

In a $Δ A B C$ ,right angled at B, AB=24 cm, BC=7 cm. Determine

(i) sin A, cos A

(ii) sin C, cos C

Discussion

5968.	If the triangles ABC and ADE are similar, then ABAD=.
Answer» If the triangles ABC and ADE are similar, then $\frac{A B}{A D}$ =.

5968.

If the triangles ABC and ADE are similar, then ABAD=.

Answer»

If the triangles ABC and ADE are similar, then $\frac{A B}{A D}$ =.

Discussion

5969.	Indians , Egyptians , Europeans and Australians are residing in a village of area 200 km2. If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?
Answer» Indians , Egyptians , Europeans and Australians are residing in a village of area 200 $k m^{2}$ . If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?

Discussion

5970.	Question 1 (iv)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.x - 3y - 7 = 0 ; 3x - 3y - 15= 0
Answer» Question 1 (iv) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. x - 3y - 7 = 0 ; 3x - 3y - 15= 0

Discussion

5971.	Solve for θ if 4cos2θ + 2sinθ – 4 = 0, where 0 ≤ θ ≤ 90.
Answer» Solve for $θ$ if $4 c o s^{2} θ$ + 2 $s i n θ$ – 4 = 0, where 0 $\leq$ $θ$ $\leq$ 90.

Discussion

5972.	Area fo a sector of central angle 200∘ of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
Answer» Area fo a sector of central angle $200^{\circ}$ of a circle is $770 c m^{2}$ . Find the length of the corresponding arc of this sector.

Discussion

5973.	Question 2Determine graphically, the vertices of the triangle formed by the linesy = x, 3y = x and x + y = 8.
Answer» Question 2 Determine graphically, the vertices of the triangle formed by the lines y = x, 3y = x and x + y = 8.

Discussion

5974.	The correct ratio representing the sides of the triangle is
Answer» The correct ratio representing the sides of the triangle is

Discussion

5975.	47. \|x+1\|/\|x-1\|>1
Answer» 47. \|x+1\|/\|x-1\|>1

Discussion

5976.	In a circle of radius 3 cm, construct a chord of length 4 cm. Measure the distance between the centre and the chord.
Answer» In a circle of radius 3 cm, construct a chord of length 4 cm. Measure the distance between the centre and the chord.

Discussion

5977.	Find the values of m and n in polynomial 2x³+MX²+nx-14 such that x-1and x+2 are it's factors
Answer» Find the values of m and n in polynomial 2x³+MX²+nx-14 such that x-1and x+2 are it's factors

Discussion

5978.	Hello sir, I have a doubt. I'm now in 8 grade and I changed my sd card from 7 grade to 8th . And from the profile , I changed it to 8th grade. My doubt is that , will I get 365 days of subscription
Answer» Hello sir, I have a doubt. I'm now in 8 grade and I changed my sd card from 7 grade to 8th . And from the profile , I changed it to 8th grade. My doubt is that , will I get 365 days of subscription

5978.

Hello sir, I have a doubt. I'm now in 8 grade and I changed my sd card from 7 grade to 8th . And from the profile , I changed it to 8th grade. My doubt is that , will I get 365 days of subscription

Answer»

Hello sir,

I have a doubt. I'm now in 8 grade and I changed my sd card from 7 grade to 8th . And from the profile , I changed it to 8th grade. My doubt is that , will I get 365 days of subscription

Discussion

5979.	Solve the following equations: 2x−4y+9z=28 7x+3y−5z=3 9x+10y−11z=4
Answer» Solve the following equations: $2 x - 4 y + 9 z = 28$ $7 x + 3 y - 5 z = 3$ $9 x + 10 y - 11 z = 4$

Discussion

5980.	If [548−3]−3X=[−475−9]. Find X?
Answer» If $[\begin{matrix} 5 & 4 8 & - 3 \end{matrix}] - 3 X = [\begin{matrix} - 4 & 7 5 & - 9 \end{matrix}]$ . Find X?

5980.

If [548−3]−3X=[−475−9]. Find X?

Answer»

If $[\begin{matrix} 5 & 4 8 & - 3 \end{matrix}] - 3 X = [\begin{matrix} - 4 & 7 5 & - 9 \end{matrix}]$ .

Find X?

Discussion

5981.	A circular swimming pool has protection bars installed along the circumference of 220 metres. Find the radius of the swimming pool.
Answer» A circular swimming pool has protection bars installed along the circumference of 220 metres. Find the radius of the swimming pool.

Discussion

5982.	Calculate the average daily income of the following data about men working in a company Daily income <100. < 200 <300. <400. <500 No. Of men. 12. 28. 34. 41. 50
Answer» Calculate the average daily income of the following data about men working in a company Daily income <100. < 200 <300. <400. <500 No. Of men. 12. 28. 34. 41. 50

5982.

Calculate the average daily income of the following data about men working in a company Daily income <100. < 200 <300. <400. <500 No. Of men. 12. 28. 34. 41. 50

Answer»

Calculate the average daily income of the following data about men working in a company

Daily income <100. < 200 <300. <400. <500

No. Of men. 12. 28. 34. 41. 50

Discussion

5983.	Prove the following identities:(i) (1 + cot⁡ θ - cosec θ)(1 + tan⁡ θ + sec⁡ θ) = 2(ii) tan^2⁡ θ + cot^2⁡ θ + 2 = sec^2⁡ θ cosec^2 θ(iii) √(sec^2⁡ θ + cosec^2 θ) = tan⁡ θ + cot⁡θ
Answer» Prove the following identities: (i) (1 + cot⁡ θ - cosec θ)(1 + tan⁡ θ + sec⁡ θ) = 2 (ii) tan^2⁡ θ + cot^2⁡ θ + 2 = sec^2⁡ θ cosec^2 θ (iii) √(sec^2⁡ θ + cosec^2 θ) = tan⁡ θ + cot⁡θ

Discussion

5984.	If tan 2A=cot(A−12∘), where 2A is an acute angle, find the value of A.
Answer» If $t a n 2 A = c o t (A - 12^{\circ}),$ where 2A is an acute angle, find the value of A.

Discussion

5985.	If one root of polynomial equation ax2 + bx + c = 0 be reciprocal of other, then
Answer» If one root of polynomial equation ax² + bx + c = 0 be reciprocal of other, then

Discussion

5986.	Question 4 (v)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(v) 3,3+√2,3+2√2,3+3√2
Answer» Question 4 (v) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (v) $3, 3 + \sqrt{2}, 3 + 2 \sqrt{2}, 3 + 3 \sqrt{2}$

Discussion

5987.	Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Answer» Write the set of value of 'a' for which the equation x² + ax − 1 = 0 has real roots.

Discussion

5988.	Find the3rd term in the sequence of whole number set 0, 1, 2, 3, 4, 5, .....
Answer» Find the $3^{r d}$ term in the sequence of whole number set 0, 1, 2, 3, 4, 5, .....

Discussion

5989.	Two number differ by 4 and their product is 192. Find the numbers.
Answer» Two number differ by 4 and their product is 192. Find the numbers.

Discussion

5990.	In two concentric circles of radii 6 cm and 10 cm with centre ‘O’. OP is the radius of the smaller circle, OP ⊥ AB which cuts the outer circle at A and B. Find the length of AB.
Answer» In two concentric circles of radii 6 cm and 10 cm with centre ‘O’. OP is the radius of the smaller circle, OP ⊥ AB which cuts the outer circle at A and B. Find the length of AB.

Discussion

5991.	The image below shows the two triangular rocks. If the ratio of the sides of △ABC to △XYZ is A:1 , find A.10
Answer» The image below shows the two triangular rocks. If the ratio of the sides of △ABC to △XYZ is A:1 , find A. 10

Discussion

5992.	(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.
Answer» ( $x^{2} + 4 x + 3$ ) can be visualised by the rectangle below. Identify the region depicting the constant term.

Discussion

5993.	If △ABC and △PQR are two similar triangles shown in the figure. AM and PN are the medians on △ABC and △PQR respectively. The ratio of areas of △ABC and △PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.
Answer» If $△$ ABC and $△$ PQR are two similar triangles shown in the figure. AM and PN are the medians on $△$ ABC and $△$ PQR respectively. The ratio of areas of $△$ ABC and $△$ PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

5993.

If △ABC and △PQR are two similar triangles shown in the figure. AM and PN are the medians on △ABC and △PQR respectively. The ratio of areas of △ABC and △PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

Answer»

If $△$ ABC and $△$ PQR are two similar triangles shown in the figure. AM and PN are the medians on $△$ ABC and $△$ PQR respectively. The ratio of areas of $△$ ABC and $△$ PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

Discussion

5994.	AB is a line segment & M is its mid- point. Semi- circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C (0, r) is drawn so that it touches all the three semicircles. The length of AB is 'x' times r. Find x. ___
Answer» AB is a line segment & M is its mid- point. Semi- circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C (0, r) is drawn so that it touches all the three semicircles. The length of AB is 'x' times r. Find x. ___

Discussion

5995.	Question 17A line intersects the Y-axis and X-axis at the points P and Q, respectively. If (2, -5) is the mid point of PQ, then the coordinates of P and Q are, respectively.(A) (0, – 5) and (2, 0)(B) (0, 10) and (– 4, 0)(C) (0, 4) and (– 10, 0)(D) (0, – 10) and (4, 0)
Answer» Question 17 A line intersects the Y-axis and X-axis at the points P and Q, respectively. If (2, -5) is the mid point of PQ, then the coordinates of P and Q are, respectively. (A) (0, – 5) and (2, 0) (B) (0, 10) and (– 4, 0) (C) (0, 4) and (– 10, 0) (D) (0, – 10) and (4, 0)

Discussion

5996.	In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find the value of angle BAC.
Answer» In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find the value of angle BAC.

Discussion

5997.	Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2 0.1x - 0.1y = 0.1
Answer» Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2 0.1x - 0.1y = 0.1

5997.

Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2 0.1x - 0.1y = 0.1

Answer»

Find the solution to the following system of linear equations:

0.2x + 0.3y = 1.2
0.1x - 0.1y = 0.1

Discussion

5998.	The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___
Answer» The table below shows the sale of shirts of various sizes in a week. $\begin{matrix} Shirt size & 38 & 39 & 40 & 41 & 42 Number sold & 60 & 73 & 89 & 90 & 23 \end{matrix}$ The size which is demanded the most is ___

5998.

The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___

Answer»

The table below shows the sale of shirts of various sizes in a week.

$\begin{matrix} Shirt size & 38 & 39 & 40 & 41 & 42 Number sold & 60 & 73 & 89 & 90 & 23 \end{matrix}$
The size which is demanded the most is ___

Discussion

5999.	For the given trading chain prepare the tax invoice I, II, III, GST at the rate of 12% was chanrged for the article supplied.(1) Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government.(2) At the end what amount is paid by the consumer ?(3) Write which of the invoices issued are B2B and B2C ?
Answer» For the given trading chain prepare the tax invoice I, II, III, GST at the rate of 12% was chanrged for the article supplied. (1) Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government. (2) At the end what amount is paid by the consumer ? (3) Write which of the invoices issued are B2B and B2C ?

Discussion

6000.	Express each of the following in terms of trigonometric ratios of angles between 0° and 45°.(i) sin 72° + cosec 72°(ii) cosec 66° + tan 66°(iii) tan 68° + sec 68°(iv) cot 59° + cosec 59°(v) cos 51° + cot 49° – sec 47°(vi) sin 67° + cos 75°
Answer» Express each of the following in terms of trigonometric ratios of angles between 0° and 45°. (i) sin 72° + cosec 72° (ii) cosec 66° + tan 66° (iii) tan 68° + sec 68° (iv) cot 59° + cosec 59° (v) cos 51° + cot 49° – sec 47° (vi) sin 67° + cos 75°

Discussion

Explore topic-wise InterviewSolutions in .

Determine whether x=-1 is a root of the equation x2−3x+2=0 or not.

40 people take 10 days to dig a well. Using the theory of variation , how many extra people will be required to dig the well in 8 days.

Find k for which the system 2x + 3y − 5 = 0 and 4x + ky − 10 = 0 has an infinite number of solutions.

AB is a diameter of a circle and AC is the chord such that ∠ BAC = 30∘. If the tangent at C intersects AB extended at D, then BC = BD.

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is___

If △ABC is an isosceles right-triangle right angled at C such that AC = 5 cm. Then, AB =(a) 2.5cm(b) 52 cm(c) 10 cm(d) 5 cm

Question 1 (ii) Express 156 as the product of its prime factors.

Find the annual income derived from 125, Rs 120 shares paying 5% dividend.

Find the sum and product of the roots of 2x2 – 3x + 5 = 0

A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square.

Find the roots of the equation 5x2−6x−2=0 by the method of completing the square.[3 MARKS]

Two poles of height 6 m and 11 m stand vertically on the ground such that the distance between them is 12 m, find the distance between their tops.

A company declares dividends of 15% on Rs 100 shares which is quoted at Rs 140. If the company has Rs 12,600 Find: i) What is the dividend? ii) What is the rate of interest on the investment?

Evaluate the following(i) sin60° cos30° + sin30° cos 60°(ii) 2tan245° + cos230° − sin260°(iii) (iv) (v)

In a ΔABC,right angled at B, AB=24 cm, BC=7 cm. Determine (i) sin A, cos A (ii) sin C, cos C

If the triangles ABC and ADE are similar, then ABAD=.

Indians , Egyptians , Europeans and Australians are residing in a village of area 200 km2. If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?

Question 1 (iv)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.x - 3y - 7 = 0 ; 3x - 3y - 15= 0

Solve for θ if 4cos2θ + 2sinθ – 4 = 0, where 0 ≤ θ ≤ 90.

Area fo a sector of central angle 200∘ of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

Question 2Determine graphically, the vertices of the triangle formed by the linesy = x, 3y = x and x + y = 8.

The correct ratio representing the sides of the triangle is

47. |x+1|/|x-1|>1

In a circle of radius 3 cm, construct a chord of length 4 cm. Measure the distance between the centre and the chord.

Find the values of m and n in polynomial 2x³+MX²+nx-14 such that x-1and x+2 are it's factors

Hello sir, I have a doubt. I'm now in 8 grade and I changed my sd card from 7 grade to 8th . And from the profile , I changed it to 8th grade. My doubt is that , will I get 365 days of subscription

Solve the following equations: 2x−4y+9z=28 7x+3y−5z=3 9x+10y−11z=4

If [548−3]−3X=[−475−9]. Find X?

A circular swimming pool has protection bars installed along the circumference of 220 metres. Find the radius of the swimming pool.

Calculate the average daily income of the following data about men working in a company Daily income &lt;100. &lt; 200 &lt;300. &lt;400. &lt;500 No. Of men. 12. 28. 34. 41. 50

Prove the following identities:(i) (1 + cot⁡ θ - cosec θ)(1 + tan⁡ θ + sec⁡ θ) = 2(ii) tan^2⁡ θ + cot^2⁡ θ + 2 = sec^2⁡ θ cosec^2 θ(iii) √(sec^2⁡ θ + cosec^2 θ) = tan⁡ θ + cot⁡θ

If tan 2A=cot(A−12∘), where 2A is an acute angle, find the value of A.

If one root of polynomial equation ax2 + bx + c = 0 be reciprocal of other, then

Question 4 (v)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(v) 3,3+√2,3+2√2,3+3√2

Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.

Find the3rd term in the sequence of whole number set 0, 1, 2, 3, 4, 5, .....

Two number differ by 4 and their product is 192. Find the numbers.

In two concentric circles of radii 6 cm and 10 cm with centre ‘O’. OP is the radius of the smaller circle, OP ⊥ AB which cuts the outer circle at A and B. Find the length of AB.

The image below shows the two triangular rocks. If the ratio of the sides of △ABC to △XYZ is A:1 , find A.10

(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.

If △ABC and △PQR are two similar triangles shown in the figure. AM and PN are the medians on △ABC and △PQR respectively. The ratio of areas of △ABC and △PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

AB is a line segment &amp; M is its mid- point. Semi- circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C (0, r) is drawn so that it touches all the three semicircles. The length of AB is 'x' times r. Find x. ___

Question 17A line intersects the Y-axis and X-axis at the points P and Q, respectively. If (2, -5) is the mid point of PQ, then the coordinates of P and Q are, respectively.(A) (0, – 5) and (2, 0)(B) (0, 10) and (– 4, 0)(C) (0, 4) and (– 10, 0)(D) (0, – 10) and (4, 0)

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find the value of angle BAC.

Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2 0.1x - 0.1y = 0.1

The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___

Express each of the following in terms of trigonometric ratios of angles between 0° and 45°.(i) sin 72° + cosec 72°(ii) cosec 66° + tan 66°(iii) tan 68° + sec 68°(iv) cot 59° + cosec 59°(v) cos 51° + cot 49° – sec 47°(vi) sin 67° + cos 75°

Calculate the average daily income of the following data about men working in a company Daily income <100. < 200 <300. <400. <500 No. Of men. 12. 28. 34. 41. 50

AB is a line segment & M is its mid- point. Semi- circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C (0, r) is drawn so that it touches all the three semicircles. The length of AB is 'x' times r. Find x. ___