32581 + Interview Questions in Mathematics Page 94 InterviewSolution

4651.	what is the another method to find zeroes of polynomial??
Answer» what is the another method to find zeroes of polynomial??

Discussion

4652.	Prove that the following equations have a unique solution and solve the equations. (When k≠0 k≠-2) kx+y+z=1x+ky+z=kx+y+kz=k²
Answer» Prove that the following equations have a unique solution and solve the equations. (When k≠0 k≠-2) kx+y+z=1 x+ky+z=k x+y+kz=k²

Discussion

4653.	A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of 60∘ to the ground. What should be the length of the slide (in m)?
Answer» A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide (in m)?

Discussion

4654.	Corresponding sides of two triangles are congruent. What is this condition known as?
Answer» Corresponding sides of two triangles are congruent. What is this condition known as?

Discussion

4655.	The position vectors of points A, B and C are λi^+ 3j^, 12i^+μj^ and 11i^-3j^ respectively. If C divides the line segment joining A and B in the ratio 3:1, find the values of λ and μ
Answer» The position vectors of points $A, B$ and $C$ are $λ \hat{i} +$ 3 $\hat{j}$ , 12 $\hat{i} + μ$ $\hat{j}$ and 11 $\hat{i} -$ 3 $\hat{j}$ respectively. If C divides the line segment joining A and B in the ratio 3:1, find the values of $λ$ and $μ$

Discussion

4656.	If m + m' + 2 mm' cosx= 1, n +n'+2nn' cosx=1 and mn + m' n' + ( mn'+ m'n) cosx = 0,prove that (a). m + n =cosecx (b).m'+n'=cosecx
Answer» If m + m' + 2 mm' cosx= 1, n +n'+2nn' cosx=1 and mn + m' n' + ( mn'+ m'n) cosx = 0,prove that (a). m + n =cosecx (b).m'+n'=cosecx

Discussion

4657.	show that y=x+c\sqrt2 touches the circle x^2+y^2=c^2 and find its point of contact
Answer» show that y=x+c\sqrt2 touches the circle x^2+y^2=c^2 and find its point of contact

Discussion

4658.	Volume enclosed between a cylindrical vessel consisting of 2 concentric cylinders is 90π m3. If outer radius is 5m and height of the cylinder is 10m. Find the thickness of the cylindrical vessel.
Answer» Volume enclosed between a cylindrical vessel consisting of 2 concentric cylinders is 90 $π$ $m^{3}$ . If outer radius is 5m and height of the cylinder is 10m. Find the thickness of the cylindrical vessel.

Discussion

4659.	In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.
Answer» In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.

4659.

In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.

Answer»

In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.

Discussion

4660.	Find the zeroes of the polynomial \sqrt3x2-8x+4\sqrt3
Answer» Find the zeroes of the polynomial \sqrt3x2-8x+4\sqrt3

Discussion

4661.	Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is 30∘, find the length of the second pole.
Answer» Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is $30^{\circ}$ , find the length of the second pole.

Discussion

4662.	A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below. Find the median marks obtained by the students of the class.
Answer» A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below. Find the median marks obtained by the students of the class.

Discussion

4663.	A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]
Answer» A heap of wheat is in the form of a cone whose diameter is $10.5 m$ and height is $3 m$ . Find its volume. The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required. $[A s s u m e π = \frac{22}{7}]$

Discussion

4664.	Question 2 (ii)On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.9x + 3y + 12 = 018x + 6y + 24 = 0
Answer» Question 2 (ii) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 9x + 3y + 12 = 0 18x + 6y + 24 = 0

Discussion

4665.	Question 5In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Answer» Question 5 In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Discussion

4666.	Give an example of a statement P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.
Answer» Give an example of a statement P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.

Discussion

4667.	If alpha and beta are the zeros of quadratic polynomial f (x)= ax^2+bx+c, then evaluate
Answer» If alpha and beta are the zeros of quadratic polynomial f (x)= ax^2+bx+c, then evaluate

Discussion

4668.	The manufacturing and expiry date written on a product are 21/06/21 and 25/06/21 respectively. If Ravi bought the product on 23/06/21, in how many days he should consume it?
Answer» The manufacturing and expiry date written on a product are 21/06/21 and 25/06/21 respectively. If Ravi bought the product on 23/06/21, in how many days he should consume it?

Discussion

4669.

Journalise the following in the books of Som Nath & Sons : 2018 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 along with 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 :

2018
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 along with 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

4670.	For each of the following , find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorization.(i) -83, 43 (ii) 218, 516 (iii) -23, -9 (iv) -325, -12Question
Answer» For each of the following , find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorization. (i) $- \frac{8}{3}, \frac{4}{3}$ (ii) $\frac{21}{8}, \frac{5}{16}$ (iii) $- 2 \sqrt{3}, - 9$ (iv) $\frac{- 3}{2 \sqrt{5}}, - \frac{1}{2}$ Question

Discussion

4671.	Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = x3 – 8, g(x) = x – 2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when p(x) = x³ – 8, g(x) = x – 2

Discussion

4672.	Evaluate the following :(i) sin 49°cos 41°2+cos 41°sin 49°2(ii) cos 48° − sin 42°(iii) cot 40°tan 50°-12 cos 35°sin 55°(iv) sin 27°cos 63°2-cos 63°sin 27°2(v) tan 35°cot 55°+cot 78°tan 12°-1(vi) sec 70°cosec 20°+sin 59°cos 31°(vii) cosec 31° − sec 59°(viii) (sin 72° + cos 18°) (sin 72° − cos 18°)(ix) sin 35° sin 55° − cos 35° cos 55°(x) tan 48° tan 23° tan 42° tan 67°(xi) sec50° sin 40° + cos40° cosec 50°
Answer» Evaluate the following : (i) ${(\frac{\sin 49 °}{\cos 41 °})}^{2} + {(\frac{\cos 41 °}{\sin 49 °})}^{2}$ (ii) cos 48° − sin 42° (iii) $\frac{\cot 40 °}{\tan 50 °} - \frac{1}{2} (\frac{\cos 35 °}{\sin 55 °})$ (iv) ${(\frac{\sin 27 °}{\cos 63 °})}^{2} - {(\frac{\cos 63 °}{\sin 27 °})}^{2}$ (v) $\frac{\tan 35 °}{\cot 55 °} + \frac{\cot 78 °}{\tan 12 °} - 1$ (vi) $\frac{\sec 70 °}{cosec 20 °} + \frac{\sin 59 °}{\cos 31 °}$ (vii) cosec 31° − sec 59° (viii) (sin 72° + cos 18°) (sin 72° − cos 18°) (ix) sin 35° sin 55° − cos 35° cos 55° (x) tan 48° tan 23° tan 42° tan 67° (xi) sec50° sin 40° + cos40° cosec 50°

Discussion

4673.	A can do a piece of work in x days and B can do the same work in x+16 days. If both working together can do it in 15 days, find the value of x.
Answer» A can do a piece of work in $x$ days and B can do the same work in $x + 16$ days. If both working together can do it in 15 days, find the value of $x$ .

Discussion

4674.	The arithmetic mean of 25 and 11 is ________
Answer» The arithmetic mean of 25 and 11 is ________

Discussion

4675.	In ΔABC, AB = AC and BD ⊥ AC prove that BD2 + CD2 = 2AC.CD.
Answer» In ΔABC, AB = AC and BD ⊥ AC prove that BD² + CD² = 2AC.CD.

Discussion

4676.	a vertically straight tree 15m high is broken by the wind in such a way that its top just touches the ground and makes an angle of 60 degree with the ground at what height from the ground did the tree brea
Answer» a vertically straight tree 15m high is broken by the wind in such a way that its top just touches the ground and makes an angle of 60 degree with the ground at what height from the ground did the tree brea

Discussion

4677.	the value of k for which the lines x+y=6 and 2x-5y=1 are perpendicular to each other is
Answer» the value of k for which the lines x+y=6 and 2x-5y=1 are perpendicular to each other is

Discussion

4678.	The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.
Answer» The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.

Discussion

4679.	The decimal expansion of 141120 will terminate after how many places?
Answer» The decimal expansion of $\frac{141}{120}$ will terminate after how many places?

Discussion

4680.	Question 1 (iii) Solve the following pair of linear equations by the substitution method. 3x - y = 3 ; 9x - 3y = 9
Answer» Question 1 (iii) Solve the following pair of linear equations by the substitution method. 3x - y = 3 ; 9x - 3y = 9

Discussion

4681.	Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and find their lengths.
Answer» Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and find their lengths.

Discussion

4682.	The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth term is (2m–1):(2n–1). [4 MARKS]
Answer» The ratio of the sums of m and n terms of an A.P. is $m^{2}$ : $n^{2}$ . Show that the ratio of the $m^{t h}$ and $n^{t h}$ term is $(2 m - 1) : (2 n - 1)$ . [4 MARKS]

Discussion

4683.	A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. Find the maximum volume available to place machinery in the factory in m3. (Take π=227)5805
Answer» A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 $m^{3}$ . Find the maximum volume available to place machinery in the factory in $m^{3}$ . (Take $π = \frac{22}{7}$ ) 5805

Discussion

4684.	Slope of the line passing through the points (1,5) and (x,6) is 12. Then the value of x is
Answer» Slope of the line passing through the points $(1, 5)$ and $(x, 6)$ is $\frac{1}{2}$ . Then the value of $x$ is

Discussion

4685.	If TP and TQ are two tangents to a circle with center O such that ∠POQ=110∘, then, ∠PTQ is equal to:
Answer» If TP and TQ are two tangents to a circle with center O such that $∠ P O Q = 110^{\circ}$ , then, $∠$ PTQ is equal to:

4685.

If TP and TQ are two tangents to a circle with center O such that ∠POQ=110∘, then, ∠PTQ is equal to:

Answer»

If TP and TQ are two tangents to a circle with center O such that $∠ P O Q = 110^{\circ}$ , then, $∠$ PTQ is equal to:

Discussion

4686.	Which of the following represents factors of the cubic polynomial, 2x3+x2−2x−1?[1 Mark]
Answer» Which of the following represents factors of the cubic polynomial, $2 x^{3} + x^{2} - 2 x - 1 ?$ [1 Mark]

Discussion

4687.	21. (0, 0), (3,3) and (0,2\sqrt3) are the three verticesof a triangle. The distance between the orthocentreand the circumcentre of the triangle is equal to(in units) (1) 2\sqrt3 (2) \sqrt3 (3)\sqrt6 (4) 0
Answer» 21. (0, 0), (3,3) and (0,2\sqrt3) are the three verticesof a triangle. The distance between the orthocentreand the circumcentre of the triangle is equal to(in units) (1) 2\sqrt3 (2) \sqrt3 (3)\sqrt6 (4) 0

Discussion

4688.	Sima has more than ₹100, but less than ₹110. If the money that she has is a palindrome number, how much money does she have?101
Answer» Sima has more than ₹100, but less than ₹110. If the money that she has is a palindrome number, how much money does she have? 101

Discussion

4689.	Prove that the volume of the largestcone that can be inscribed in a sphere of radius Ris ofthe volume of the sphere.
Answer» Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is of the volume of the sphere.

Discussion

4690.	The graph of a polynomial y = f(x), shown in Fig. 2.18. Find the number of real zeros of f(x).
Answer» The graph of a polynomial y = f(x), shown in Fig. 2.18. Find the number of real zeros of f(x).

Discussion

4691.	A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.
Answer» A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.

4691.

A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.

Answer»

A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.

Discussion

4692.	Evaluate each of the following(cos 0° + sin 45° + sin 30°) (sin 90° − cos 45° + cos 60°)
Answer» Evaluate each of the following (cos 0° + sin 45° + sin 30°) (sin 90° − cos 45° + cos 60°)

Discussion

4693.	Question 83 Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.
Answer» Question 83 Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.

4693.

Question 83 Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.

Answer»

Question 83

Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.

Discussion

4694.	Find the G. M. between 32 and 272
Answer» Find the G. M. between $\frac{3}{2}$ and $\frac{27}{2}$

Discussion

4695.	Construct two tangents to a circle of radius 4 cm from a point 5 cm. away from the centre.
Answer» Construct two tangents to a circle of radius 4 cm from a point 5 cm. away from the centre.

Discussion

4696.	If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
Answer» If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Discussion

4697.	Question 83 (xviii)Multiply the following :(34x−43y),(23x+32y)
Answer» Question 83 (xviii) Multiply the following : $(\frac{3}{4} x - \frac{4}{3} y), (\frac{2}{3} x + \frac{3}{2} y)$

4697.

Question 83 (xviii)Multiply the following :(34x−43y),(23x+32y)

Answer»

Question 83 (xviii)

Multiply the following :

$(\frac{3}{4} x - \frac{4}{3} y), (\frac{2}{3} x + \frac{3}{2} y)$

Discussion

4698.	Solve the following system of equations graphically and find the vertices and area of thetriangle formed by these lines and the x-axis: x-y+3=02x+3y-4=0
Answer» Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: $x - y + 3 = 0 2 x + 3 y - 4 = 0$

Discussion

4699.	What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?(a) 30(b) 14(c) 15(d) 16
Answer» What should be subtracted to the polynomial x² − 16x + 30, so that 15 is the zero of the resulting polynomial? (a) 30 (b) 14 (c) 15 (d) 16

Discussion

4700.	If alpha and beta are zeroes of the quadratic polynomial 2x²+5x+2, then find the value of alpha⁴+beta⁴.
Answer» If alpha and beta are zeroes of the quadratic polynomial 2x²+5x+2, then find the value of alpha⁴+beta⁴.

Discussion

Explore topic-wise InterviewSolutions in .

what is the another method to find zeroes of polynomial??

Prove that the following equations have a unique solution and solve the equations. (When k≠0 k≠-2) kx+y+z=1x+ky+z=kx+y+kz=k²

A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of 60∘ to the ground. What should be the length of the slide (in m)?

Corresponding sides of two triangles are congruent. What is this condition known as?

The position vectors of points A, B and C are λi^+ 3j^, 12i^+μj^ and 11i^-3j^ respectively. If C divides the line segment joining A and B in the ratio 3:1, find the values of λ and μ

If m + m' + 2 mm' cosx= 1, n +n'+2nn' cosx=1 and mn + m' n' + ( mn'+ m'n) cosx = 0,prove that (a). m + n =cosecx (b).m'+n'=cosecx

show that y=x+c\sqrt2 touches the circle x^2+y^2=c^2 and find its point of contact

Volume enclosed between a cylindrical vessel consisting of 2 concentric cylinders is 90π m3. If outer radius is 5m and height of the cylinder is 10m. Find the thickness of the cylindrical vessel.

In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.

Find the zeroes of the polynomial \sqrt3x2-8x+4\sqrt3

Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is 30∘, find the length of the second pole.

A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below. Find the median marks obtained by the students of the class.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.[Assume π=227]

Question 2 (ii)On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.9x + 3y + 12 = 018x + 6y + 24 = 0

Question 5In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Give an example of a statement P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.

If alpha and beta are the zeros of quadratic polynomial f (x)= ax^2+bx+c, then evaluate

The manufacturing and expiry date written on a product are 21/06/21 and 25/06/21 respectively. If Ravi bought the product on 23/06/21, in how many days he should consume it?

For each of the following , find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorization.(i) -83, 43 (ii) 218, 516 (iii) -23, -9 (iv) -325, -12Question

Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = x3 – 8, g(x) = x – 2

A can do a piece of work in x days and B can do the same work in x+16 days. If both working together can do it in 15 days, find the value of x.

The arithmetic mean of 25 and 11 is ________

In ΔABC, AB = AC and BD ⊥ AC prove that BD2 + CD2 = 2AC.CD.

a vertically straight tree 15m high is broken by the wind in such a way that its top just touches the ground and makes an angle of 60 degree with the ground at what height from the ground did the tree brea

the value of k for which the lines x+y=6 and 2x-5y=1 are perpendicular to each other is

The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.

The decimal expansion of 141120 will terminate after how many places?

Question 1 (iii) Solve the following pair of linear equations by the substitution method. 3x - y = 3 ; 9x - 3y = 9

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and find their lengths.

The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth term is (2m–1):(2n–1). [4 MARKS]

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. Find the maximum volume available to place machinery in the factory in m3. (Take π=227)5805

Slope of the line passing through the points (1,5) and (x,6) is 12. Then the value of x is

If TP and TQ are two tangents to a circle with center O such that ∠POQ=110∘, then, ∠PTQ is equal to:

Which of the following represents factors of the cubic polynomial, 2x3+x2−2x−1?[1 Mark]

21. (0, 0), (3,3) and (0,2\sqrt3) are the three verticesof a triangle. The distance between the orthocentreand the circumcentre of the triangle is equal to(in units) (1) 2\sqrt3 (2) \sqrt3 (3)\sqrt6 (4) 0

Sima has more than ₹100, but less than ₹110. If the money that she has is a palindrome number, how much money does she have?101

Prove that the volume of the largestcone that can be inscribed in a sphere of radius Ris ofthe volume of the sphere.

The graph of a polynomial y = f(x), shown in Fig. 2.18. Find the number of real zeros of f(x).

A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.

Evaluate each of the following(cos 0° + sin 45° + sin 30°) (sin 90° − cos 45° + cos 60°)

Question 83 Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.

Find the G. M. between 32 and 272

Construct two tangents to a circle of radius 4 cm from a point 5 cm. away from the centre.

If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Question 83 (xviii)Multiply the following :(34x−43y),(23x+32y)

Solve the following system of equations graphically and find the vertices and area of thetriangle formed by these lines and the x-axis: x-y+3=02x+3y-4=0

What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?(a) 30(b) 14(c) 15(d) 16

If alpha and beta are zeroes of the quadratic polynomial 2x²+5x+2, then find the value of alpha⁴+beta⁴.