32581 + Interview Questions in Mathematics Page 89 InterviewSolution

4401.	Lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and water rises by 40 cm. find the number of lead spheres dropped in the water.
Answer» Lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and water rises by 40 cm. find the number of lead spheres dropped in the water.

Discussion

4402.

The following tables gives the distribution of total household expenditure (in rupees) of manual workers in a city. Expenditure (in rupees) (xi) Frequency (fi) Expenditure (in rupees) (xi) Frequency (fi) 100-150 150-200 200-250 250-300 24 40 33 28 300-350 350-400 400-450 450-500 30 22 16 7 Find the average expenditure (in rupees) per household

Answer» The following tables gives the distribution of total household expenditure (in rupees) of manual workers in a city.

Expenditure (in rupees) (x_i)	Frequency (f_i)	Expenditure (in rupees) (x_i)	Frequency (f_i)
100-150 150-200 200-250 250-300	24 40 33 28	300-350 350-400 400-450 450-500	30 22 16 7

Find the average expenditure (in rupees) per household

Discussion

4403.	the largest number by which the expression x^3+6x^2+11x+6 is divisible for all the possible integral values of x is
Answer» the largest number by which the expression x^3+6x^2+11x+6 is divisible for all the possible integral values of x is

Discussion

4404.	What is the difference between sector and segment!
Answer» What is the difference between sector and segment!

Discussion

4405.	Question 25(ii) A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 heads?
Answer» Question 25(ii) A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 heads?

Discussion

4406.	A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1, 2 or 3)
Answer» A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1, 2 or 3)

Discussion

4407.	The set of values of k for which the equation x4+(k−1)x3+x2+(k−1)x+1=0 has only 2 real roots which are negative is
Answer» The set of values of $k$ for which the equation $x^{4} + (k - 1) x^{3} + x^{2} + (k - 1) x + 1 = 0$ has only $2$ real roots which are negative is

Discussion

4408.	If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area. [CBSE 2014]
Answer» If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area. [CBSE 2014]

Discussion

4409.	Find the difference between compound interest and simple interest on ₹45000 at 12% per annum for 5 years.
Answer» Find the difference between compound interest and simple interest on ₹45000 at 12% per annum for 5 years.

Discussion

4410.	The minimum number of D-flip flops needed to design a mod-260 counter is ________9
Answer» The minimum number of D-flip flops needed to design a mod-260 counter is ________ 9

Discussion

4411.	27. The probability that an archer hits the target when it is windy is equal to 1/5, when it is not windy his probability of hitting the target is 2/5. On any shot the probability of gust of wind is 2/5. the probability that there is gust of wind on the occasion when he hits the target is equal to ?
Answer» 27. The probability that an archer hits the target when it is windy is equal to 1/5, when it is not windy his probability of hitting the target is 2/5. On any shot the probability of gust of wind is 2/5. the probability that there is gust of wind on the occasion when he hits the target is equal to ?

Discussion

4412.	Question 1 If the polynomials az3+4z2+3z–4 and z3–4z+a leave the same remainder when divided by z – 3, find the value of a.
Answer» Question 1 If the polynomials $a z^{3} + 4 z^{2} + 3 z - 4$ and $z^{3} - 4 z + a$ leave the same remainder when divided by z – 3, find the value of a.

Discussion

4413.	If the number 91876y2 is completely divisible by 8, then the smallest whole number in place of y will be ___.
Answer» If the number $91876 y 2$ is completely divisible by $8$ , then the smallest whole number in place of $y$ will be ___.

Discussion

4414.	A triangle ABC with sides BC =7cm, ∠B=45∘,∠A=105∘ is given. The image of constructing a similar triangle of ΔABC whose sides are 34 times the corresponding sides of the ΔABC is given below. Then A′C′AC is equal to :
Answer» A triangle ABC with sides BC =7cm, $∠ B = 45^{\circ}, ∠ A = 105^{\circ}$ is given. The image of constructing a similar triangle of $Δ A B C$ whose sides are $\frac{3}{4}$ times the corresponding sides of the $Δ A B C$ is given below. Then $\frac{A^{'} C^{'}}{A C}$ is equal to :

Discussion

4415.	What is the base-radius and slant height of the cone made by rolling up a sector of radius 10 centimetres and central angle 60°?
Answer» What is the base-radius and slant height of the cone made by rolling up a sector of radius 10 centimetres and central angle 60°?

Discussion

4416.	If A (−1, 3) , B(1, −1) and C (5, 1) are the vertices of a triangle ABC, what is the length of the median through vertex A?
Answer» If A (−1, 3) , B(1, −1) and C (5, 1) are the vertices of a triangle ABC, what is the length of the median through vertex A?

Discussion

4417.	John invests ₹7,200 in MojoRojo Inc, paying 10% per annum when its ₹20 shares can be bought for ₹16. His annual income, and percentage return on his investment are respectively ____.
Answer» John invests ₹7,200 in MojoRojo Inc, paying 10% per annum when its ₹20 shares can be bought for ₹16. His annual income, and percentage return on his investment are respectively ____.

Discussion

4418.	58. Triangles ABC and DBC are on same base with A and D on opposite sides of LINE BC such that area(Δ ABC) = area(Δ DBC). Show that BC bisects AD.
Answer» 58. Triangles ABC and DBC are on same base with A and D on opposite sides of LINE BC such that area(Δ ABC) = area(Δ DBC). Show that BC bisects AD.

Discussion

4419.	In the given figure, the point O is situated within the triangle PQR in such a way the ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then length of QR is ___ .
Answer» In the given figure, the point O is situated within the triangle PQR in such a way the $∠ P O Q = 90^{\circ}$ , OP = 6 cm , OQ = 8 cm , If PR = 24 cm & $∠ Q P R = 90^{\circ}$ , then length of QR is ___ .

4419.

In the given figure, the point O is situated within the triangle PQR in such a way the ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then length of QR is ___ .

Answer»

In the given figure, the point O is situated within the triangle PQR in such a way the $∠ P O Q = 90^{\circ}$ , OP = 6 cm , OQ = 8 cm , If PR = 24 cm & $∠ Q P R = 90^{\circ}$ , then length of QR is ___ .

Discussion

4420.	Find the coordinate of those point on the Line x+1/2=y+2/3=z-3/6 which is at distance of 3 units from the points (1,-2,3)
Answer» Find the coordinate of those point on the Line x+1/2=y+2/3=z-3/6 which is at distance of 3 units from the points (1,-2,3)

Discussion

4421.	Question 2(i) (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.
Answer» Question 2(i) (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

Discussion

4422.	A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
Answer» A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

Discussion

4423.	If cos3θ=√32, 0°<3θ<90°, the value of θ (in degrees) is10
Answer» If $cos 3 θ = \frac{\sqrt{3}}{2}$ , $0 ° < 3 θ < 90 °$ , the value of $θ$ (in degrees) is 10

Discussion

4424.	Match the unknown angle x in each case if O is the centre of each circle.
Answer» Match the unknown angle $x$ in each case if O is the centre of each circle.

Discussion

4425.	Write the value of tan 10° tan 15° tan 75° tan 80°?
Answer» Write the value of tan 10° tan 15° tan 75° tan 80°?

Discussion

4426.	show that \overrightarrow a\cdot(\overrightarrow b×\overrightarrow c) is equal to the magnitude of the volume of parallelpiped formed on the three vector \overrightarrow a,\overrightarrow b and \overrightarrow c.
Answer» show that \overrightarrow a\cdot(\overrightarrow b×\overrightarrow c) is equal to the magnitude of the volume of parallelpiped formed on the three vector \overrightarrow a,\overrightarrow b and \overrightarrow c.

Discussion

4427.	Question 4 If tan A = cot B, prove that A+B=90∘.
Answer» Question 4 If tan A = cot B, prove that $A + B = 90^{\circ}$ .

Discussion

4428.	A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7)
Answer» A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7)

Discussion

4429.	The sides BA and DC of the parallelogram ABCD are produced as shown in figure. Then
Answer» The sides BA and DC of the parallelogram ABCD are produced as shown in figure. Then

Discussion

4430.	If P(E) denotes the probability of an event E then [CBSE 2013C](a) P(E) < 0(b) P(E) > 1(c) 0 ≤ P(E) ≤ 1(d) −1 ≤ P(E) ≤ 1
Answer» If P(E) denotes the probability of an event E then [CBSE 2013C] (a) P(E) < 0 (b) P(E) > 1 (c) 0 ≤ P(E) ≤ 1 (d) −1 ≤ P(E) ≤ 1

Discussion

4431.	If the sum of two non-zero numbers is 4, then the minimum value of the sum of their reciprocals is _______________.
Answer» If the sum of two non-zero numbers is 4, then the minimum value of the sum of their reciprocals is _______________.

Discussion

4432.	Question 11The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Answer» Question 11 The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

Discussion

4433.	Find the LCM of 32, 64 and 128.
Answer» Find the LCM of 32, 64 and 128.

Discussion

4434.	An architect draws a scaled down plan of a building. On the map, the dimensions of a room is written as 5 cm × 4 cm. According to the scale that he uses, 2 cm = 100 km. What are the actual dimensions of the room?
Answer» An architect draws a scaled down plan of a building. On the map, the dimensions of a room is written as 5 cm × 4 cm. According to the scale that he uses, 2 cm = 100 km. What are the actual dimensions of the room?

Discussion

4435.

The mean of the following distribution is 54, find the missing frequency x CI 0-20 20-40 40-60 60-80 80-100 F 16 14 24 26 x

Answer» The mean of the following distribution is 54, find the missing frequency x

CI	0-20	20-40	40-60	60-80	80-100
F	16	14	24	26	x

Discussion

4436.	Consider a sequence of 100 zeroes. It is decided to modify the sequence by following steps. In step 1,to every position in the sequence we add 2 in step 3,to every position in the sequence we add 2.in step 3, to every position which is multiple of 3, we add 2 this is continued up to 100th step after the 100th step what will be the value in 64 th position
Answer» Consider a sequence of 100 zeroes. It is decided to modify the sequence by following steps. In step 1,to every position in the sequence we add 2 in step 3,to every position in the sequence we add 2.in step 3, to every position which is multiple of 3, we add 2 this is continued up to 100th step after the 100th step what will be the value in 64 th position

Discussion

4437.	ABCD is a rectangle. Points M and N are on BD such that AM ⊥ BD and CN ⊥ BD. Prove that BM2 + BN2 = DM2 + DN2.
Answer» ABCD is a rectangle. Points M and N are on BD such that AM ⊥ BD and CN ⊥ BD. Prove that BM² + BN²= DM²+ DN².

Discussion

4438.

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure. Expenditure (in Rs) Number of families 1000 − 1500 24 1500 − 2000 40 2000 − 2500 33 2500 − 3000 28 3000 − 3500 30 3500 − 4000 22 4000 − 4500 16 4500 − 5000 7

Answer»

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs)	Number of families
1000 − 1500	24
1500 − 2000	40
2000 − 2500	33
2500 − 3000	28
3000 − 3500	30
3500 − 4000	22
4000 − 4500	16
4500 − 5000	7

Discussion

4439.	Rahim tosses two different coins simultaneously. Find the probability of getting at least one tail.
Answer» Rahim tosses two different coins simultaneously. Find the probability of getting at least one tail.

Discussion

4440.	If the first term and common ratio of a G.P. are 5 and -5 respectively, then the ___ term is 3125.
Answer» If the first term and common ratio of a G.P. are 5 and -5 respectively, then the ___ term is 3125.

Discussion

4441.

Prepare the Purchase Book and Sales Book from the following transactions: 2018 Jan. 1 Bought from M/s. Uma Datt, Mumbai, on credit: 1,000 Ragisters ₹ 80 each 50 Reams Paper ₹ 250 per ream Less: Trade Discount 25% Add: 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 Trade Discount 10%, charged CGST and SGST 2.5% each

Answer» Prepare the Purchase Book and Sales Book from the following transactions:

2018
Jan. 1	Bought from M/s. Uma Datt, Mumbai, on credit:
	1,000 Ragisters ₹ 80 each
	50 Reams Paper ₹ 250 per ream
	Less: Trade Discount 25%
	Add: 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
	Trade Discount 10%, charged CGST and SGST 2.5% each

Discussion

4442.	Each card bears one letter from the word ‘mathematics’ The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.
Answer» Each card bears one letter from the word ‘mathematics’ The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.

Discussion

4443.	Figure shows a sector of a circle, centre O, containing an angle θ ∘. Prove that:(i) Perimeter of the shaded region is r(tanθ+secθ+πθ180−1)(ii) Area of the shaded region is r22(tanθ−πθ180)
Answer» Figure shows a sector of a circle, centre O, containing an angle $θ^{\circ}$ . Prove that: (i) Perimeter of the shaded region is $r (t a n θ + s e c θ + \frac{π θ}{180} - 1)$ (ii) Area of the shaded region is $\frac{r^{2}}{2} (t a n θ - \frac{π θ}{180})$

4443.

Figure shows a sector of a circle, centre O, containing an angle θ ∘. Prove that:(i) Perimeter of the shaded region is r(tanθ+secθ+πθ180−1)(ii) Area of the shaded region is r22(tanθ−πθ180)

Answer»

Figure shows a sector of a circle, centre O, containing an angle $θ^{\circ}$ . Prove that:

(i) Perimeter of the shaded region is $r (t a n θ + s e c θ + \frac{π θ}{180} - 1)$

(ii) Area of the shaded region is $\frac{r^{2}}{2} (t a n θ - \frac{π θ}{180})$

Discussion

4444.	The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.
Answer» The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.

Discussion

4445.	A conical block is melted to form 60 spherical balls. If the radius and the height of the conical block are 8 cm and 30 cm respectively, then what is the radius of a spherical ball?
Answer» A conical block is melted to form 60 spherical balls. If the radius and the height of the conical block are 8 cm and 30 cm respectively, then what is the radius of a spherical ball?

Discussion

4446.	Find the solution for the pair of linear equations:2x+4y=124x+2y=18
Answer» Find the solution for the pair of linear equations: $2 x + 4 y = 12$ $4 x + 2 y = 18$

Discussion

4447.

The product of the number got by adding the square root of a number to itself, and the number got by subtracting its square root from itself (See the section Sum and difference, of the lesson Algebra, in the Class 8 text book)

Answer»

The product of the number got by adding the square root of a number to itself, and the number got by subtracting its square root from itself (See the section Sum and difference, of the lesson Algebra, in the Class 8 text book)

Discussion

4448.	20. A window of a house is h m above the ground. From the widow, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively. Prove that the height of the house is h(1+tan alpha.tan beta) metres.
Answer» 20. A window of a house is h m above the ground. From the widow, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively. Prove that the height of the house is h(1+tan alpha.tan beta) metres.

Discussion

4449.	Find the value of 10 + 20 + 30 + 40 + 50 + 60.210
Answer» Find the value of 10 + 20 + 30 + 40 + 50 + 60. 210

Discussion

4450.	A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Answer» A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Discussion

Explore topic-wise InterviewSolutions in .

Lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and water rises by 40 cm. find the number of lead spheres dropped in the water.

the largest number by which the expression x^3+6x^2+11x+6 is divisible for all the possible integral values of x is

What is the difference between sector and segment!

Question 25(ii) A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 heads?

A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1, 2 or 3)

The set of values of k for which the equation x4+(k−1)x3+x2+(k−1)x+1=0 has only 2 real roots which are negative is

If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area. [CBSE 2014]

Find the difference between compound interest and simple interest on ₹45000 at 12% per annum for 5 years.

The minimum number of D-flip flops needed to design a mod-260 counter is ________9

Question 1 If the polynomials az3+4z2+3z–4 and z3–4z+a leave the same remainder when divided by z – 3, find the value of a.

If the number 91876y2 is completely divisible by 8, then the smallest whole number in place of y will be ___.

A triangle ABC with sides BC =7cm, ∠B=45∘,∠A=105∘ is given. The image of constructing a similar triangle of ΔABC whose sides are 34 times the corresponding sides of the ΔABC is given below. Then A′C′AC is equal to :

What is the base-radius and slant height of the cone made by rolling up a sector of radius 10 centimetres and central angle 60°?

If A (−1, 3) , B(1, −1) and C (5, 1) are the vertices of a triangle ABC, what is the length of the median through vertex A?

John invests ₹7,200 in MojoRojo Inc, paying 10% per annum when its ₹20 shares can be bought for ₹16. His annual income, and percentage return on his investment are respectively ____.

58. Triangles ABC and DBC are on same base with A and D on opposite sides of LINE BC such that area(Δ ABC) = area(Δ DBC). Show that BC bisects AD.

In the given figure, the point O is situated within the triangle PQR in such a way the ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm &amp; ∠QPR=90∘, then length of QR is ___ .

Find the coordinate of those point on the Line x+1/2=y+2/3=z-3/6 which is at distance of 3 units from the points (1,-2,3)

Question 2(i) (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

If cos3θ=√32, 0°&lt;3θ&lt;90°, the value of θ (in degrees) is10

Match the unknown angle x in each case if O is the centre of each circle.

Write the value of tan 10° tan 15° tan 75° tan 80°?

show that \overrightarrow a\cdot(\overrightarrow b×\overrightarrow c) is equal to the magnitude of the volume of parallelpiped formed on the three vector \overrightarrow a,\overrightarrow b and \overrightarrow c.

Question 4 If tan A = cot B, prove that A+B=90∘.

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7)

The sides BA and DC of the parallelogram ABCD are produced as shown in figure. Then

If P(E) denotes the probability of an event E then [CBSE 2013C](a) P(E) < 0(b) P(E) > 1(c) 0 ≤ P(E) ≤ 1(d) −1 ≤ P(E) ≤ 1

If the sum of two non-zero numbers is 4, then the minimum value of the sum of their reciprocals is _______________.

Question 11The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

Find the LCM of 32, 64 and 128.

An architect draws a scaled down plan of a building. On the map, the dimensions of a room is written as 5 cm × 4 cm. According to the scale that he uses, 2 cm = 100 km. What are the actual dimensions of the room?

The mean of the following distribution is 54, find the missing frequency x CI 0-20 20-40 40-60 60-80 80-100 F 16 14 24 26 x

ABCD is a rectangle. Points M and N are on BD such that AM ⊥ BD and CN ⊥ BD. Prove that BM2 + BN2 = DM2 + DN2.

Rahim tosses two different coins simultaneously. Find the probability of getting at least one tail.

If the first term and common ratio of a G.P. are 5 and -5 respectively, then the ___ term is 3125.

Each card bears one letter from the word ‘mathematics’ The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.

Figure shows a sector of a circle, centre O, containing an angle θ ∘. Prove that:(i) Perimeter of the shaded region is r(tanθ+secθ+πθ180−1)(ii) Area of the shaded region is r22(tanθ−πθ180)

The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.

A conical block is melted to form 60 spherical balls. If the radius and the height of the conical block are 8 cm and 30 cm respectively, then what is the radius of a spherical ball?

Find the solution for the pair of linear equations:2x+4y=124x+2y=18

The product of the number got by adding the square root of a number to itself, and the number got by subtracting its square root from itself (See the section Sum and difference, of the lesson Algebra, in the Class 8 text book)

20. A window of a house is h m above the ground. From the widow, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively. Prove that the height of the house is h(1+tan alpha.tan beta) metres.

Find the value of 10 + 20 + 30 + 40 + 50 + 60.210

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

In the given figure, the point O is situated within the triangle PQR in such a way the ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then length of QR is ___ .

If cos3θ=√32, 0°<3θ<90°, the value of θ (in degrees) is10