32581 + Interview Questions in Mathematics Page 186 InterviewSolution

9251.	A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready. [CBSE 2008C]
Answer» A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready. [CBSE 2008C]

Discussion

9252.	Evaluate each of the followingsin 30°-sin 90°+2 cos 0°tan 30° tan 60°
Answer» Evaluate each of the following $\frac{\sin 30 ° - \sin 90 ° + 2 \cos 0 °}{\tan 30 ° \tan 60 °}$

Discussion

9253.	The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". (i) Write down the co-ordinates of A". (ii) Write down a single transformation that maps A onto A".
Answer» The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". (i) Write down the co-ordinates of A". (ii) Write down a single transformation that maps A onto A".

9253.

The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". (i) Write down the co-ordinates of A". (ii) Write down a single transformation that maps A onto A".

Answer»

The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

Discussion

9254.	The given figure shows a circle with centre O and BCD is tangent to it at C. Then, ∠ACD+∠BAC= __________
Answer» The given figure shows a circle with centre O and BCD is tangent to it at C. Then, $∠ A C D + ∠ B A C =$ __________

9254.

The given figure shows a circle with centre O and BCD is tangent to it at C. Then, ∠ACD+∠BAC= __________

Answer»

The given figure shows a circle with centre O and BCD is tangent to it at C. Then, $∠ A C D + ∠ B A C =$ __________

Discussion

9255.	Shri. Batliwala sold shares of Rs 30,350 and purchased shares of Rs 69,650 in a day. He paid brokerage at the rate of 0.1% on sale and purchase. 18% GST was charged on brokerage. Find his total expenditure on brokerage and tax.
Answer» Shri. Batliwala sold shares of Rs 30,350 and purchased shares of Rs 69,650 in a day. He paid brokerage at the rate of 0.1% on sale and purchase. 18% GST was charged on brokerage. Find his total expenditure on brokerage and tax.

Discussion

9256.	tanθ(1−cotθ)+cotθ(1−tanθ)=(1+secθcosecθ)
Answer» $\frac{t a n θ}{(1 - c o t θ)} + \frac{c o t θ}{(1 - t a n θ)} = (1 + s e c θ c o s e c θ)$

Discussion

9257.	Choose the correct answer of the following question:A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm [CBSE 2011]
Answer» Choose the correct answer of the following question: A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm [CBSE 2011]

Discussion

9258.	An observer on the top of a monument AB, 500m above sea level, observers the angles of depression of two boats C and D to 45o and 30o respectively. Find the distance between the boats if they are on the same side of the monument.
Answer» An observer on the top of a monument AB, 500m above sea level, observers the angles of depression of two boats C and D to 45^o and 30^o respectively. Find the distance between the boats if they are on the same side of the monument.

9258.

An observer on the top of a monument AB, 500m above sea level, observers the angles of depression of two boats C and D to 45o and 30o respectively. Find the distance between the boats if they are on the same side of the monument.

Answer»

An observer on the top of a monument AB, 500m above sea level, observers the angles of depression of two boats C and D to 45^o and 30^o respectively. Find the distance between the boats if they are on the same side of the monument.

Discussion

9259.	If [1 2 3] A = [4 5], the order of matrix A is
Answer» If [1 2 3] A = [4 5], the order of matrix A is

Discussion

9260.	BE and CF, the altitudes of △ABC are equal. Prove that △ABC is an equilateral triangle.
Answer» BE and CF, the altitudes of $△$ ABC are equal. Prove that $△$ ABC is an equilateral triangle.

Discussion

9261.	Aditya has 5 exams in an academic year. His marks increase by 2% based on his previous test marks. If Aditya scores 70 in his 1st exam, what is his score in the last academic exam?
Answer» Aditya has $5$ exams in an academic year. His marks increase by $2 %$ based on his previous test marks. If Aditya scores $70$ in his $1$ st exam, what is his score in the last academic exam?

Discussion

9262.	Find the solution of \|x²+3x+2\| +\|x²+4x+3\|=\|x+1\|
Answer» Find the solution of \|x²+3x+2\| +\|x²+4x+3\|=\|x+1\|

Discussion

9263.	Draw a line segment of length 8 cm and divide it internally in the ratio 4:5.
Answer» Draw a line segment of length 8 cm and divide it internally in the ratio 4:5.

Discussion

9264.	In the given figure, LMN is tangent to the circle with centre O. If ∠ PMN = 60∘, find ∠ MOP.
Answer» In the given figure, LMN is tangent to the circle with centre O. If $∠$ PMN = $60^{\circ}$ , find $∠$ MOP.

9264.

In the given figure, LMN is tangent to the circle with centre O. If ∠ PMN = 60∘, find ∠ MOP.

Answer»

In the given figure, LMN is tangent to the circle with centre O. If $∠$ PMN = $60^{\circ}$ , find $∠$ MOP.

Discussion

9265.	Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.(i) 3, 6, 12, 24, ...(ii) 0, −4, −8, −12, ...(iii) 12,14,16,18, ...(iv) 12, 2, −8, −18, ...(v) 3, 3, 3, 3, ...(vi) p, p + 90, p + 180 p + 270, ... where p = (999)999(vii) 1.0, 1.7, 2.4, 3.1, ...(viii) −225, −425, −625, −825, ...(ix) 10, 10 + 25, 10 + 26, 10 + 27,...(x) a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...(xi) 12, 32, 52, 72, ...(xii) 12, 52, 72, 73, ...
Answer» Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference. (i) 3, 6, 12, 24, ... (ii) 0, −4, −8, −12, ... (iii) $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, . . .$ (iv) 12, 2, −8, −18, ... (v) 3, 3, 3, 3, ... (vi) p, p + 90, p + 180 p + 270, ... where p = (999)⁹⁹⁹ (vii) 1.0, 1.7, 2.4, 3.1, ... (viii) −225, −425, −625, −825, ... (ix) 10, 10 + 2⁵, 10 + 2⁶, 10 + 2⁷,... (x) a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ... (xi) 1², 3², 5², 7², ... (xii) 1², 5², 7², 73, ...

Discussion

9266.	The radius and height of a cone are in the ratio of 4:3. The area of the base is 154 sq.cm. Find the area of curved surface
Answer» The radius and height of a cone are in the ratio of 4:3. The area of the base is 154 sq.cm. Find the area of curved surface

Discussion

9267.	If two positive ingeters a and b are expressible in the form a = pq2 and b = p3q; p, q being prime number, then LCM (a, b) is(a) pq(b) p3q3(c) p3q2(d) p2q2
Answer» If two positive ingeters a and b are expressible in the form a = pq² and b = p³q; p, q being prime number, then LCM (a, b) is (a) pq (b) p³q³ (c) p³q² (d) p²q²

Discussion

9268.	In a right triangle, with respect to an acute angle θ, the opposite side is twice the adjacent side. The value of cosec θ is
Answer» In a right triangle, with respect to an acute angle $θ$ , the opposite side is twice the adjacent side. The value of cosec $θ$ is

Discussion

9269.	Find whether the points (b, b), (−b, −b) and (2b, 2b) are the vertices of an equilateral triangle.
Answer» Find whether the points (b, b), (−b, −b) and (2b, 2b) are the vertices of an equilateral triangle.

Discussion

9270.	If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.
Answer» If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.

Discussion

9271.	The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(¯¯¯¯A)+P(¯¯¯¯B) is (a) 1.2 (b) 1.1(c) 1.0 (d) 0.9
Answer» The probability that at least one of the two events $A$ and $B$ occurs is $0.6$ . If $A$ and $B$ occur simultaneously with probability $0.3$ , then $P (¯ ¯¯ ¯ A) + P (¯ ¯¯ ¯ B)$ is $(a) 1.2 (b) 1.1 (c) 1.0 (d) 0.9$

Discussion

9272.	If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is(a) 183 sq. units(b) 1832 sq. units(c) 366 sq. units(d) 1834 sq. units
Answer» If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is (a) 183 sq. units (b) $\frac{183}{2}$ sq. units (c) 366 sq. units (d) $\frac{183}{4}$ sq. units

Discussion

9273.	A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.
Answer» A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.

Discussion

9274.	Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
Answer» Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

Discussion

9275.	For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where 0≤r b.
Answer» For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where $0 \leq r$ $b$ .

Discussion

9276.	A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes foods for 20 days, he has to pay Rs 1000 as hostel charges whereas a students B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.
Answer» A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes foods for 20 days, he has to pay Rs 1000 as hostel charges whereas a students B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Discussion

9277.	Find the length of side AC.
Answer» Find the length of side AC.

Discussion

9278.	In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?
Answer» In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of $25 c m$ from O as shown in the figure. The radius of the circle with centre O is $7 c m$ . The diameter of the circle with centre O’ is $10 c m .$ What is the length of the tangent PC?

Discussion

9279.	The probability of a bomb hitting a bridge is 0.5 and 2 direct hits are needed to destroyit.The least number of bombs required so that the prob of bridge being destroyed isgreater than 0.9 is?why can't we do 0.9>((n-1)!/(n-2)!)*(1/2)^n
Answer» The probability of a bomb hitting a bridge is 0.5 and 2 direct hits are needed to destroy it.The least number of bombs required so that the prob of bridge being destroyed is greater than 0.9 is? why can't we do 0.9>((n-1)!/(n-2)!)*(1/2)^n

Discussion

9280.	Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.figure
Answer» Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder. figure

Discussion

9281.	Sum to infinite terms of the GP 25,352,253,354..is ___.
Answer» Sum to infinite terms of the GP $\frac{2}{5}, \frac{3}{5^{2}}, \frac{2}{5^{3}}, \frac{3}{5^{4}} . .$ is ___.

Discussion

9282.	Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?
Answer» Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

9282.

Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

Answer»

Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

Discussion

9283.	The curved surface area of a hemisphere is 308 m2. Then,the volume of the hemisphere is the total surface area of the hemisphere .
Answer» The curved surface area of a hemisphere is $308 m^{2}$ . Then, the volume of the hemisphere is the total surface area of the hemisphere .

Discussion

9284.	If the numerical value of the area of a circle is equal to the numerical value of its circumference , find its radius.
Answer» If the numerical value of the area of a circle is equal to the numerical value of its circumference , find its radius.

Discussion

9285.	X and Y are partners sharing profits in the ratio of 2 : 1. On 31st March, 2019, their Balance Sheet showed General Reserve of ₹ 60,000. It was decided that in future they will share profits and losses in the ratio of 3 : 2. Pass necessary Journal entry in each of the following alternative cases:(i) When General Reserve is not to be shown in the new Balance Sheet.(ii) When General Reserve is to be shown in the new Balance Sheet.
Answer» X and Y are partners sharing profits in the ratio of 2 : 1. On 31st March, 2019, their Balance Sheet showed General Reserve of ₹ 60,000. It was decided that in future they will share profits and losses in the ratio of 3 : 2. Pass necessary Journal entry in each of the following alternative cases: (i) When General Reserve is not to be shown in the new Balance Sheet. (ii) When General Reserve is to be shown in the new Balance Sheet.

Discussion

9286.	The surface area of a sphere is 154 cm2. The volume of the sphere is (a) 17923 cm3 (b) 35913 cm3 (c) 143713 cm3 (d) none of these
Answer» The surface area of a sphere is 154 $c m^{2} .$ The volume of the sphere is (a) $179 \frac{2}{3} c m^{3}$ (b) $359 \frac{1}{3} c m^{3}$ (c) $1437 \frac{1}{3} c m^{3}$ (d) none of these

9286.

The surface area of a sphere is 154 cm2. The volume of the sphere is (a) 17923 cm3 (b) 35913 cm3 (c) 143713 cm3 (d) none of these

Answer»

The surface area of a sphere is 154 $c m^{2} .$ The volume of the sphere is

(a) $179 \frac{2}{3} c m^{3}$ (b) $359 \frac{1}{3} c m^{3}$ (c) $1437 \frac{1}{3} c m^{3}$ (d) none of these

Discussion

9287.	Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Answer» Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Discussion

9288.	If sec θ + tan θ = x, find the value of sec θ.
Answer» If sec $θ$ + tan $θ$ = x, find the value of sec $θ$ .

Discussion

9289.	△ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. △ DEF is similar to △ABC. If EF= 4 cm, then find the perimeter of △DEF.
Answer» $△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ ABC. If EF= 4 cm, then find the perimeter of $△$ DEF.

Discussion

9290.	Two pillars of height 8 m and 14 m are 8m apart, find the distance between their top.
Answer» Two pillars of height 8 m and 14 m are 8m apart, find the distance between their top.

Discussion

9291.	Question 6 (ii) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (ii) (- 3, 5), (3, 1), (0, 3), (- 1, - 4)
Answer» Question 6 (ii) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (ii) (- 3, 5), (3, 1), (0, 3), (- 1, - 4)

Discussion

9292.	The hypotenuse of a right-angled triangle is 30 cm. and one of the sides is 18 cm. Find the third side and the sine, consine and the tangent of the angle opposite to the third side.
Answer» The hypotenuse of a right-angled triangle is 30 cm. and one of the sides is 18 cm. Find the third side and the sine, consine and the tangent of the angle opposite to the third side.

Discussion

9293.	The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data.Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054
Answer» The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data. $\begin{matrix} Monthly consumption (in units) & Numbers of customers 65 - 85 & 4 85 - 105 & 5 105 - 125 & 13 125 - 145 & 20 145 - 165 & 14 165 - 185 & 8 185 - 205 & 4 \end{matrix}$

9293.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data.Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054

Answer»

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.

Find the median of the data.

$\begin{matrix} Monthly consumption (in units) & Numbers of customers 65 - 85 & 4 85 - 105 & 5 105 - 125 & 13 125 - 145 & 20 145 - 165 & 14 165 - 185 & 8 185 - 205 & 4 \end{matrix}$

Discussion

9294.	AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.
Answer» AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

Discussion

9295.	The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.
Answer» The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.

Discussion

9296.	A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656 cm3. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2 . (Takeπ=227). [CBSE 2015]
Answer» A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is $166 \frac{5}{6}$ cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm² . (Take $π = \frac{22}{7}$ ). [CBSE 2015]

Discussion

9297.	Which of the following can be the nth term of an AP?
Answer» Which of the following can be the $n^{t h}$ term of an AP?

Discussion

9298.	Find the length of AD.Given: ∠ABC = 60∘, ∠DBC = 45∘ and BC = 40 cm
Answer» Find the length of AD. Given: ∠ABC = $60^{\circ}$ , ∠DBC = $45^{\circ}$ and BC = 40 cm

Discussion

9299.	In the given figure, AB = BE = 7 cm such that ABE is a quadrant of a circle, BC = 9 cm, BD = 15 cm, CF ⊥ AD such that CF = 8 cm. If the given figure is rotated about the side AD, then the surface area of the resulting solid is
Answer» In the given figure, AB = BE = 7 cm such that ABE is a quadrant of a circle, BC = 9 cm, BD = 15 cm, CF ⊥ AD such that CF = 8 cm. If the given figure is rotated about the side AD, then the surface area of the resulting solid is

Discussion

9300.	The point (4,5) lies on the graph of the equation 5y = ax + 9. Find the value of a.
Answer» The point (4,5) lies on the graph of the equation 5y = ax + 9. Find the value of a.

Discussion

Explore topic-wise InterviewSolutions in .

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready. [CBSE 2008C]

Evaluate each of the followingsin 30°-sin 90°+2 cos 0°tan 30° tan 60°

The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". (i) Write down the co-ordinates of A". (ii) Write down a single transformation that maps A onto A".

The given figure shows a circle with centre O and BCD is tangent to it at C. Then, ∠ACD+∠BAC= __________

Shri. Batliwala sold shares of Rs 30,350 and purchased shares of Rs 69,650 in a day. He paid brokerage at the rate of 0.1% on sale and purchase. 18% GST was charged on brokerage. Find his total expenditure on brokerage and tax.

tanθ(1−cotθ)+cotθ(1−tanθ)=(1+secθcosecθ)

Choose the correct answer of the following question:A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm [CBSE 2011]

An observer on the top of a monument AB, 500m above sea level, observers the angles of depression of two boats C and D to 45o and 30o respectively. Find the distance between the boats if they are on the same side of the monument.

If [1 2 3] A = [4 5], the order of matrix A is

BE and CF, the altitudes of △ABC are equal. Prove that △ABC is an equilateral triangle.

Aditya has 5 exams in an academic year. His marks increase by 2% based on his previous test marks. If Aditya scores 70 in his 1st exam, what is his score in the last academic exam?

Find the solution of |x²+3x+2| +|x²+4x+3|=|x+1|

Draw a line segment of length 8 cm and divide it internally in the ratio 4:5.

In the given figure, LMN is tangent to the circle with centre O. If ∠ PMN = 60∘, find ∠ MOP.

The radius and height of a cone are in the ratio of 4:3. The area of the base is 154 sq.cm. Find the area of curved surface

If two positive ingeters a and b are expressible in the form a = pq2 and b = p3q; p, q being prime number, then LCM (a, b) is(a) pq(b) p3q3(c) p3q2(d) p2q2

In a right triangle, with respect to an acute angle θ, the opposite side is twice the adjacent side. The value of cosec θ is

Find whether the points (b, b), (−b, −b) and (2b, 2b) are the vertices of an equilateral triangle.

If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.

The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(¯¯¯¯A)+P(¯¯¯¯B) is (a) 1.2 (b) 1.1(c) 1.0 (d) 0.9

If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is(a) 183 sq. units(b) 1832 sq. units(c) 366 sq. units(d) 1834 sq. units

A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.

Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where 0≤r b.

Find the length of side AC.

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?

The probability of a bomb hitting a bridge is 0.5 and 2 direct hits are needed to destroyit.The least number of bombs required so that the prob of bridge being destroyed isgreater than 0.9 is?why can't we do 0.9>((n-1)!/(n-2)!)*(1/2)^n

Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.figure

Sum to infinite terms of the GP 25,352,253,354..is ___.

Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

The curved surface area of a hemisphere is 308 m2. Then,the volume of the hemisphere is the total surface area of the hemisphere .

If the numerical value of the area of a circle is equal to the numerical value of its circumference , find its radius.

The surface area of a sphere is 154 cm2. The volume of the sphere is (a) 17923 cm3 (b) 35913 cm3 (c) 143713 cm3 (d) none of these

Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

If sec θ + tan θ = x, find the value of sec θ.

△ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. △ DEF is similar to △ABC. If EF= 4 cm, then find the perimeter of △DEF.

Two pillars of height 8 m and 14 m are 8m apart, find the distance between their top.

Question 6 (ii) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (ii) (- 3, 5), (3, 1), (0, 3), (- 1, - 4)

The hypotenuse of a right-angled triangle is 30 cm. and one of the sides is 18 cm. Find the third side and the sine, consine and the tangent of the angle opposite to the third side.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data.Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054

AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.

Which of the following can be the nth term of an AP?

Find the length of AD.Given: ∠ABC = 60∘, ∠DBC = 45∘ and BC = 40 cm

In the given figure, AB = BE = 7 cm such that ABE is a quadrant of a circle, BC = 9 cm, BD = 15 cm, CF ⊥ AD such that CF = 8 cm. If the given figure is rotated about the side AD, then the surface area of the resulting solid is

The point (4,5) lies on the graph of the equation 5y = ax + 9. Find the value of a.