32581 + Interview Questions in Mathematics Page 116 InterviewSolution

5751.	If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN2 + CM2) =(a) 4 AC2(b) 5 AC2(c) 54AC2(d) 6 AC2
Answer» If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN² + CM²) = (a) 4 AC² (b) 5 AC² (c) $\frac{5}{4} {AC}^{2}$ (d) 6 AC²

Discussion

5752.	How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm?
Answer» How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm $\times$ 11 cm $\times$ 12 cm?

Discussion

5753.	If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
Answer» If α and β are the zeros of the quadratic polynomial f(t) = t² − 4t + 3, find the value of α⁴β³ + α³β⁴.

Discussion

5754.	Question 1Find the mean of the distribution.Class1−33−55−77−10Frequency9222717
Answer» Question 1 Find the mean of the distribution. $\begin{matrix} Class & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 10 Frequency & 9 & 22 & 27 & 17 \end{matrix}$

Discussion

5755.	Which of the following are harmonic progressions.(a) (b) (c) (d)
Answer» Which of the following are harmonic progressions. (a) (b) (c) (d)

5755.

Which of the following are harmonic progressions.(a) (b) (c) (d)

Answer»

Which of the following are harmonic progressions.

(a)

(b)

(c)

(d)

Discussion

5756.	Two arithmetic progression have the same common difference. The difference between their 100th terms is 100, What is the difference between their 1000th terms?
Answer» Two arithmetic progression have the same common difference. The difference between their 100th terms is 100, What is the difference between their 1000th terms?

Discussion

5757.	30. An aeroplane is flying at a height of 300m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60 degrees and 45 degrees respectively.The height of the lower plane above the ground is
Answer» 30. An aeroplane is flying at a height of 300m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60 degrees and 45 degrees respectively.The height of the lower plane above the ground is

Discussion

5758.	18. A two digit number becomes five - sixth of itself when its didits are reversed . The two digit differ by 1 . The number is
Answer» 18. A two digit number becomes five - sixth of itself when its didits are reversed . The two digit differ by 1 . The number is

Discussion

5759.	ABCD is a cyclic quadrilateral such that ∠A=(4y+20)∘,∠B=(3y−5)∘,∠C=(4x)∘and∠D=(7x+5)∘. Find the four angles.
Answer» ABCD is a cyclic quadrilateral such that $∠ A = (4 y + 20)^{\circ}, ∠ B = (3 y - 5)^{\circ}, ∠ C = (4 x)^{\circ} a n d ∠ D = (7 x + 5)^{\circ}$ . Find the four angles.

Discussion

5760.	The LCM of the smallest prime number and the smallest composite number is _________.
Answer» The LCM of the smallest prime number and the smallest composite number is _________.

Discussion

5761.

Record the following transactions in the Journal of Ashoka Furniture Traders, Ludhiana (Punjab): 2019 ₹ Jan. 1 Started business with cash 50,000 Jan. 2 Opened a Current Account by personal cheque 3,50,000 Jan. 10 Purchased machinery against cheque 1,00,000 Jan. 15 Paid wages for installation of machinery 2,000 Jan. 20 Purchased timber from Singh & Co., Ludhiana (Punjab) of the list price of ₹ 20,000 at 10% trade discount Jan. 25 Out of the above, timber used for furnishing the office 5,000 Jan. 31 Sold timber to Rakesh of the list price of ₹ 10,000 and allowed him 10% trade discount Feb. 10 Issued to Singh & Co. a cheque in full settlement 20,000 Feb. 15 Received from Rakesh in full and final settlement 10,000 Feb. 20 Paid Wages 15,000 Feb. 28 Issued a cheque for ₹ 5,000 in favour of the landlord for rent of February CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Answer» Record the following transactions in the Journal of Ashoka Furniture Traders, Ludhiana (Punjab):

2019		₹
Jan. 1	Started business with cash	50,000
Jan. 2	Opened a Current Account by personal cheque	3,50,000
Jan. 10	Purchased machinery against cheque	1,00,000
Jan. 15	Paid wages for installation of machinery	2,000
Jan. 20	Purchased timber from Singh & Co., Ludhiana (Punjab) of the list price of ₹ 20,000 at 10% trade discount
Jan. 25	Out of the above, timber used for furnishing the office	5,000
Jan. 31	Sold timber to Rakesh of the list price of ₹ 10,000 and allowed him 10% trade discount
Feb. 10	Issued to Singh & Co. a cheque in full settlement	20,000
Feb. 15	Received from Rakesh in full and final settlement	10,000
Feb. 20	Paid Wages	15,000
Feb. 28	Issued a cheque for ₹ 5,000 in favour of the landlord for rent of February

CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Discussion

5762.	In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)
Answer» In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)

Discussion

5763.	The following are the ages of 300 patients getting medical treatment in a hospital on a particular dayAge(in year)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form:More than type cumulative frequency distribution.
Answer» The following are the ages of 300 patients getting medical treatment in a hospital on a particular day $\begin{matrix} A g e (i n y e a r) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 N u m b e r o f p a t i e n t s & 60 & 42 & 55 & 70 & 53 & 20 \end{matrix}$ Form: More than type cumulative frequency distribution.

Discussion

5764.	17. The length of a room is 50 per cent more than its breadth. The cost of carpeting the room at the rate of 38.50 Sq m is 924 and the cost of painting the walls at the rate of 5.50 per Sq m is 1,320. Find the dimensions of the room.
Answer» 17. The length of a room is 50 per cent more than its breadth. The cost of carpeting the room at the rate of 38.50 Sq m is 924 and the cost of painting the walls at the rate of 5.50 per Sq m is 1,320. Find the dimensions of the room.

Discussion

5765.	Find the value of sinθ+cosθ ,when θ=45∘
Answer» Find the value of $s i n θ + c o s θ,when θ = 45^{\circ}$

Discussion

5766.	The nth term of the sequence 5×(1+6),10×(2+6),15×(3+6)___ is
Answer» The $n^{t h}$ term of the sequence $5 \times (1 + 6), 10 \times (2 + 6), 15 \times (3 + 6)$ ___ is

Discussion

5767.	On selling a tea at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹7. If he sells the tea set at 5% gain and thelemon set at 10% gain, he gains ₹13. Find the actual price of each of the tea set and the lemon set.
Answer» On selling a tea at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains ₹13. Find the actual price of each of the tea set and the lemon set.

Discussion

5768.	Using prime factorisation, find the HCF and LCM of : (i) 36, 84 (ii) 23, 31 (iii) 96, 404 (iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664 In each case, verify that: HCF× LCM = product of given numbers.
Answer» Using prime factorisation, find the HCF and LCM of : (i) 36, 84 (ii) 23, 31 (iii) 96, 404 (iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664 In each case, verify that: HCF $\times$ LCM = product of given numbers.

5768.

Using prime factorisation, find the HCF and LCM of : (i) 36, 84 (ii) 23, 31 (iii) 96, 404 (iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664 In each case, verify that: HCF× LCM = product of given numbers.

Answer»

Using prime factorisation, find the HCF and LCM of :

(i) 36, 84 (ii) 23, 31 (iii) 96, 404

(iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664

In each case, verify that:

HCF $\times$ LCM = product of given numbers.

Discussion

5769.	A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre. (Use π=3.14)
Answer» A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre. (Use $π = 3.14$ )

Discussion

5770.	Define Major Segment of a Circle.
Answer» Define Major Segment of a Circle.

Discussion

5771.	Thephotograph of a house occupies an area of 1.75 cm2ona 35 mm slide. The slide is projected on to a screen, and the area ofthe house on the screen is 1.55 m2.What is the linear magnification of the projector-screen arrangement?
Answer» The photograph of a house occupies an area of 1.75 cm²on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m². What is the linear magnification of the projector-screen arrangement?

Discussion

5772.	f(x)f(y)=f(xy)+2(1/x+1/y+1)Find f(x)
Answer» f(x)f(y)=f(xy)+2(1/x+1/y+1) Find f(x)

Discussion

5773.	If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is(a) 2r(b) 3r(c) r(d) 4r
Answer» If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is (a) 2r (b) 3r (c) r (d) 4r

Discussion

5774.	The screw gauge has two types of scale. Explain.
Answer» The screw gauge has two types of scale. Explain.

Discussion

5775.	If Abhilash was younger by 2 years than what he really is, then the square of his age (in years) would have been 68 more than 8 times his actual age. What is his age now?
Answer» If Abhilash was younger by 2 years than what he really is, then the square of his age (in years) would have been 68 more than 8 times his actual age. What is his age now?

Discussion

5776.	The vertices of ΔABC are (-2,1), (5,4) and (2,-3) respectively. The area of the triangle is
Answer» The vertices of ΔABC are (-2,1), (5,4) and (2,-3) respectively. The area of the triangle is

Discussion

5777.	If point P lies on the line y=−1, find the following a) Its Y-coordinate b) Its X-coordinate
Answer» If point $P$ lies on the line $y = - 1$ , find the following a) Its Y-coordinate b) Its X-coordinate

Discussion

5778.	Ross purchase an article for ₹ 7000 and sells it to the customer for ₹ 8200. If VAT is 6%, find the VAT paid by Ross.
Answer» Ross purchase an article for ₹ 7000 and sells it to the customer for ₹ 8200. If VAT is $6 %$ , find the VAT paid by Ross.

Discussion

5779.	Question 1 (iii) Without actually performing the long division, state whether 64455 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Question 1 (iii) Without actually performing the long division, state whether $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

5780.	Question 82(v)Given below is a frequency distribution table. Read it and answer the questions that follow.Class intervalFrequency10−20520−301030−40440−501550−6012Which interval has the lowest frequency ?
Answer» Question 82(v) Given below is a frequency distribution table. Read it and answer the questions that follow. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 10 - 20 & 5 20 - 30 & 10 30 - 40 & 4 40 - 50 & 15 50 - 60 & 12 \end{matrix}$ Which interval has the lowest frequency ?

5780.

Question 82(v)Given below is a frequency distribution table. Read it and answer the questions that follow.Class intervalFrequency10−20520−301030−40440−501550−6012Which interval has the lowest frequency ?

Answer»

Question 82(v)

Given below is a frequency distribution table. Read it and answer the questions that follow.

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 10 - 20 & 5 20 - 30 & 10 30 - 40 & 4 40 - 50 & 15 50 - 60 & 12 \end{matrix}$

Which interval has the lowest frequency ?

Discussion

5781.	A particle describes a horizontal circle of radius r on the smooth surface of an inverted cone asshown. The height of plane of circle above vertex is h. The speed of particle should be -\sqrt{rg} -\sqrt{2rg} -\sqrt{gh} -\sqrt{2gh}
Answer» A particle describes a horizontal circle of radius r on the smooth surface of an inverted cone asshown. The height of plane of circle above vertex is h. The speed of particle should be -\sqrt{rg} -\sqrt{2rg} -\sqrt{gh} -\sqrt{2gh}

Discussion

5782.	The LCM of (x−1)3(x+8) and (x−1)(x+8)2 is:
Answer» $The LCM of (x - 1)^{3} (x + 8) and (x - 1) (x + 8)^{2} is :$

Discussion

5783.	In a rhombus ABCD, if ∠CDO = 48°, then find ∠OAB.
Answer» In a rhombus ABCD, if ∠CDO = 48°, then find ∠OAB.

Discussion

5784.	Water in a canal 1.5 m wide and 6 m deep is flowing with a speed of 10km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?
Answer» Water in a canal 1.5 m wide and 6 m deep is flowing with a speed of 10km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?

Discussion

5785.	What is the probability that a number selected at random from the numbers 3, 4, 5, ....9 is a multiple of 4?
Answer» What is the probability that a number selected at random from the numbers 3, 4, 5, ....9 is a multiple of 4?

Discussion

5786.	Find the angle subtended at the centre of a circle of radius 'a' by an arc of length (aπ/4) cm.
Answer» Find the angle subtended at the centre of a circle of radius 'a' by an arc of length (aπ/4) cm.

Discussion

5787.	Find the capacity (in litres) of a conical vessel with radius 7 cm, slant height 25 cm.[Assume π=227]
Answer» Find the capacity (in $l i t r e s$ ) of a conical vessel with radius $7 c m$ , slant height $25 c m$ . $[A s s u m e π = \frac{22}{7}]$

Discussion

5788.	Question 3 (iii)For the following A.Ps, write the first term and the common difference.(iii) 13,53,93,133……
Answer» Question 3 (iii) For the following A.Ps, write the first term and the common difference. (iii) $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3} \dots \dots$

Discussion

5789.	ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB=3.6 cm,AC=2.4 cm and AD=2.1 cm, then AE = ______.
Answer» $A B C$ is a triangle and $D E$ is drawn parallel to $B C$ cutting the other sides at $D$ and $E$ . If $A B = 3.6 c m, A C = 2.4 c m$ and $A D = 2.1 c m$ , then $A E$ = ______.

Discussion

5790.	Question 2In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41,39,48,52, 46, 62,54, 40, 96,52,98, 40,42,52, 60Find the mean,median and mode of this data.
Answer» Question 2 In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41,39,48,52, 46, 62,54, 40, 96,52,98, 40,42,52, 60 Find the mean,median and mode of this data.

Discussion

5791.	The LCM of two numbers is 1200. Which of the following cannot be their HCF?(a) 600(b) 500(c) 400(d) 200
Answer» The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600 (b) 500 (c) 400 (d) 200

Discussion

5792.	The value of tan 1° tan 2° tan 3° _________ tan 89° is _________.
Answer» The value of tan 1° tan 2° tan 3° _________ tan 89° is _________.

Discussion

5793.	Question 6 Draw a triangle ABC with side BC=7 cm,∠B=45∘,∠A=105∘. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.
Answer» Question 6 Draw a triangle ABC with side $B C = 7 c m, ∠ B = 45^{\circ}, ∠ A = 105^{\circ}$ . Then, construct a triangle whose sides are 4/3 times the corresponding sides of $Δ A B C$ .

Discussion

5794.	A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the approximate volume of the toy.
Answer» A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the approximate volume of the toy.

Discussion

5795.	Vijay had some bananas , and he divided them into two lots A and B . He sold first lot at the rate of ₹2 for 3 bananas and the second lot at the rate of ₹1 per banana and got a total of ₹400 . If he had sold the first lot at the rate of ₹1 per banana and the second lot at the rate of ₹4 per five bananas, his total collection would have been ₹460 . Find the total number of bananas he had .
Answer» Vijay had some bananas , and he divided them into two lots A and B . He sold first lot at the rate of ₹2 for 3 bananas and the second lot at the rate of ₹1 per banana and got a total of ₹400 . If he had sold the first lot at the rate of ₹1 per banana and the second lot at the rate of ₹4 per five bananas, his total collection would have been ₹460 . Find the total number of bananas he had .

Discussion

5796.	Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor is blue?
Answer» Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor is blue?

Discussion

5797.	Which of the following numbers is irrational?(a) 49(b) 12508(c) 8(d) 246
Answer» Which of the following numbers is irrational? (a) $\sqrt{\frac{4}{9}}$ (b) $\frac{\sqrt{1250}}{\sqrt{8}}$ (c) $\sqrt{8}$ (d) $\frac{\sqrt{24}}{\sqrt{6}}$

Discussion

5798.	What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
Answer» What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

Discussion

5799.	Rukshar painted the outside of the cabinet of measure 1m×2m×1.5m. How much surface area did she cover if she painted all except the bottom of the cabinet?
Answer» Rukshar painted the outside of the cabinet of measure $1 m \times 2 m \times 1.5 m .$ How much surface area did she cover if she painted all except the bottom of the cabinet?

Discussion

5800.	A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show thatab=cos α-cos βsin β-sin α
Answer» A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that $\frac{a}{b} = \frac{\cos α - \cos β}{\sin β - \sin α}$

Discussion

Explore topic-wise InterviewSolutions in .

If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN2 + CM2) =(a) 4 AC2(b) 5 AC2(c) 54AC2(d) 6 AC2

How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm?

If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.

Question 1Find the mean of the distribution.Class1−33−55−77−10Frequency9222717

Which of the following are harmonic progressions.(a) (b) (c) (d)

Two arithmetic progression have the same common difference. The difference between their 100th terms is 100, What is the difference between their 1000th terms?

30. An aeroplane is flying at a height of 300m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60 degrees and 45 degrees respectively.The height of the lower plane above the ground is

18. A two digit number becomes five - sixth of itself when its didits are reversed . The two digit differ by 1 . The number is

ABCD is a cyclic quadrilateral such that ∠A=(4y+20)∘,∠B=(3y−5)∘,∠C=(4x)∘and∠D=(7x+5)∘. Find the four angles.

The LCM of the smallest prime number and the smallest composite number is _________.

In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB &gt; BC)

The following are the ages of 300 patients getting medical treatment in a hospital on a particular dayAge(in year)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form:More than type cumulative frequency distribution.

17. The length of a room is 50 per cent more than its breadth. The cost of carpeting the room at the rate of 38.50 Sq m is 924 and the cost of painting the walls at the rate of 5.50 per Sq m is 1,320. Find the dimensions of the room.

Find the value of sinθ+cosθ ,when θ=45∘

The nth term of the sequence 5×(1+6),10×(2+6),15×(3+6)___ is

On selling a tea at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹7. If he sells the tea set at 5% gain and thelemon set at 10% gain, he gains ₹13. Find the actual price of each of the tea set and the lemon set.

Using prime factorisation, find the HCF and LCM of : (i) 36, 84 (ii) 23, 31 (iii) 96, 404 (iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664 In each case, verify that: HCF× LCM = product of given numbers.

A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre. (Use π=3.14)

Define Major Segment of a Circle.

Thephotograph of a house occupies an area of 1.75 cm2ona 35 mm slide. The slide is projected on to a screen, and the area ofthe house on the screen is 1.55 m2.What is the linear magnification of the projector-screen arrangement?

f(x)f(y)=f(xy)+2(1/x+1/y+1)Find f(x)

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is(a) 2r(b) 3r(c) r(d) 4r

The screw gauge has two types of scale. Explain.

If Abhilash was younger by 2 years than what he really is, then the square of his age (in years) would have been 68 more than 8 times his actual age. What is his age now?

The vertices of ΔABC are (-2,1), (5,4) and (2,-3) respectively. The area of the triangle is

If point P lies on the line y=−1, find the following a) Its Y-coordinate b) Its X-coordinate

Ross purchase an article for ₹ 7000 and sells it to the customer for ₹ 8200. If VAT is 6%, find the VAT paid by Ross.

Question 1 (iii) Without actually performing the long division, state whether 64455 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 82(v)Given below is a frequency distribution table. Read it and answer the questions that follow.Class intervalFrequency10−20520−301030−40440−501550−6012Which interval has the lowest frequency ?

A particle describes a horizontal circle of radius r on the smooth surface of an inverted cone asshown. The height of plane of circle above vertex is h. The speed of particle should be -\sqrt{rg} -\sqrt{2rg} -\sqrt{gh} -\sqrt{2gh}

The LCM of (x−1)3(x+8) and (x−1)(x+8)2 is:

In a rhombus ABCD, if ∠CDO = 48°, then find ∠OAB.

Water in a canal 1.5 m wide and 6 m deep is flowing with a speed of 10km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?

What is the probability that a number selected at random from the numbers 3, 4, 5, ....9 is a multiple of 4?

Find the angle subtended at the centre of a circle of radius 'a' by an arc of length (aπ/4) cm.

Find the capacity (in litres) of a conical vessel with radius 7 cm, slant height 25 cm.[Assume π=227]

Question 3 (iii)For the following A.Ps, write the first term and the common difference.(iii) 13,53,93,133……

ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB=3.6 cm,AC=2.4 cm and AD=2.1 cm, then AE = ______.

Question 2In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41,39,48,52, 46, 62,54, 40, 96,52,98, 40,42,52, 60Find the mean,median and mode of this data.

The LCM of two numbers is 1200. Which of the following cannot be their HCF?(a) 600(b) 500(c) 400(d) 200

The value of tan 1° tan 2° tan 3° _________ tan 89° is _________.

Question 6 Draw a triangle ABC with side BC=7 cm,∠B=45∘,∠A=105∘. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the approximate volume of the toy.

Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor is blue?

Which of the following numbers is irrational?(a) 49(b) 12508(c) 8(d) 246

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

Rukshar painted the outside of the cabinet of measure 1m×2m×1.5m. How much surface area did she cover if she painted all except the bottom of the cabinet?

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show thatab=cos α-cos βsin β-sin α

In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)

The value of tan 1° tan 2° tan 3° _ tan 89° is _.