32581 + Interview Questions in Mathematics Page 39 InterviewSolution

1901.	A(0, 0), B(6, 0), C(4, 2), D(2, 2) are the vertices of trapezium ABCD. E and F are the midpoints of AD and BC respectively then, EF =?.
Answer» A(0, 0), B(6, 0), C(4, 2), D(2, 2) are the vertices of trapezium ABCD. E and F are the midpoints of AD and BC respectively then, EF =?.

1901.

A(0, 0), B(6, 0), C(4, 2), D(2, 2) are the vertices of trapezium ABCD. E and F are the midpoints of AD and BC respectively then, EF =?.

Answer»

A(0, 0), B(6, 0), C(4, 2), D(2, 2) are the vertices of trapezium ABCD.

E and F are the midpoints of AD and BC respectively then, EF =?.

1902.	In the given figure, there are two circles with the centres O and O' touching each other internally at P. TangentsTQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR
Answer» In the given figure, there are two circles with the centres O and O' touching each other internally at P. TangentsTQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR

Discussion

1903.	If the points (1,1) , (-1,-1) and (-√3,k) are vertices of an equilateral triangle, find the values of k.
Answer» If the points (1,1) , (-1,-1) and (-√3,k) are vertices of an equilateral triangle, find the values of k.

Discussion

1904.

JournalWithout Goods and Services Tax (GST)Following transactions of Ramesh for April,2018 are given below. Journalise them. 2018 April 1 April 2 April 3 April 4 April 13 April 20 April 24 April 28 April 28 April 30 April 30 April 30 Ramesh started business with cash Paid into bank Bought goods for cash Drew cash from bank for office use Sold goods to Krishna on credit Bought goods from Shyam on credit Received from Krishna Allowed him discount Paid cash to Shyam Discount received Krishna returned goods Cash sales for the month Paid rent Paid salary ₹ 1,00,000 20,000 50,000 10,000 15,000 22,500 12,500 500 21,500 1,000 2,000 80,000 5,000 10,000

Answer» Journal

Without Goods and Services Tax (GST)

Following transactions of Ramesh for April,2018 are given below. Journalise them.

2018

April 1

April 2

April 3

April 4

April 13

April 20

April 24

April 28

April 28

April 30

April 30

April 30

Ramesh started business with cash

Paid into bank

Bought goods for cash

Drew cash from bank for office use

Sold goods to Krishna on credit

Bought goods from Shyam on credit

Received from Krishna

Allowed him discount

Paid cash to Shyam

Discount received

Krishna returned goods

Cash sales for the month

Paid rent

Paid salary

₹

1,00,000

20,000

50,000

10,000

15,000

22,500

12,500

500

21,500

1,000

2,000

80,000

5,000

10,000

Discussion

1905.	In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options. At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (8)?
Answer» In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options. At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (8)?

Discussion

1906.	In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back to the pole and continues the same way until all the flags are on the pole. Find the total distance covered.
Answer» In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back to the pole and continues the same way until all the flags are on the pole. Find the total distance covered.

Discussion

1907.	Find the average price of the rice mixture (in Rs.) if 3 kgs of rice at Rs.10/kg and 5 kgs at Rs.18/kg are mixed together.
Answer» Find the average price of the rice mixture (in Rs.) if 3 kgs of rice at Rs.10/kg and 5 kgs at Rs.18/kg are mixed together.

Discussion

1908.	If the tth term of an AP is s and sth term of the same AP is t, then an is
Answer» If the $t^{t h}$ term of an AP is s and $s^{t h}$ term of the same AP is t, then $a_{n}$ is

Discussion

1909.	A solid metallic cuboid of dimensions (9 m × 8 m × 2 m) is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed.
Answer» A solid metallic cuboid of dimensions (9 m × 8 m × 2 m) is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed.

Discussion

1910.	If –2 is one of the zeroes of the cubic polynomial x3 + 2x2 + 9x – 18, then the other two zeroes are
Answer» If –2 is one of the zeroes of the cubic polynomial x3 + 2x2 + 9x – 18, then the other two zeroes are

Discussion

1911.	The sum of the zeros of the quadratic polynomial 2x2 – 3k is ________.
Answer» The sum of the zeros of the quadratic polynomial 2x² – 3k is ________.

Discussion

1912.	Find the angle of elevation of the sun when the shadow of a 10m long pole is 10√3 m.
Answer» Find the angle of elevation of the sun when the shadow of a 10m long pole is 10 $\sqrt{3}$ m.

Discussion

1913.	The nth term of a sequence is (2n -1). Find the 15th term of the sequence.
Answer» The nth term of a sequence is (2n -1). Find the 15th term of the sequence.

Discussion

1914.	If 1+cot2 θ=(√3+2√2−1)2, find the value of 1tan θ+sin θ1+cos θ
Answer» If $1 + c o t^{2} θ = {(\sqrt{3 + 2 \sqrt{2}} - 1)}^{2}$ , find the value of $\frac{1}{t a n θ} + \frac{s i n θ}{1 + c o s θ}$

Discussion

1915.	{ Show that the points }A(1,2),B(-1,-16) and }C(0,-7) lie on the graph of linear equation }}{y=9x-7
Answer» { Show that the points }A(1,2),B(-1,-16) and }C(0,-7) lie on the graph of linear equation }}{y=9x-7

Discussion

1916.	Which of the given line segments is a radius of the given circle?
Answer» Which of the given line segments is a radius of the given circle?

Discussion

1917.	From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30^° and 45^° respectively. Findthe distance between the cars. \lbrack Use \sqrt{3 } = 1.732\rbrack
Answer» From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30^° and 45^° respectively. Findthe distance between the cars. \lbrack Use \sqrt{3 } = 1.732\rbrack

Discussion

1918.	Find the acute angle (θ) at which sinθ and tanθ are equal.
Answer» Find the acute angle $(θ)$ at which $s i n θ a n d t a n θ$ are equal.

Discussion

1919.	Find the mean of the following data, using direct method: Class0−1010−2020−3030−4040−5050−60Frequency7561282
Answer» Find the mean of the following data, using direct method: $\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Frequency & 7 & 5 & 6 & 12 & 8 & 2 \end{matrix}$

Discussion

1920.	A circle is inscribed in an equilateral triangle of side √3s units. Which of the following is the area of the square constructed with a diameter of the circle as a side (in sq. units)?
Answer» A circle is inscribed in an equilateral triangle of side $\sqrt{3} s$ units. Which of the following is the area of the square constructed with a diameter of the circle as a side (in sq. units)?

Discussion

1921.	If the roots of the equations a2+b2x2-2ba+cx+b2+c2=0 are equal, then(a) 2b = a + c(b) b2 = ac(c) b=2aca+c(d) b = ac
Answer» If the roots of the equations $(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0$ are equal, then (a) 2b = a + c (b) b² = ac (c) $b = \frac{2 a c}{a + c}$ (d) b = ac

Discussion

1922.	For determining median from ogive curves , S1 : one can use less than type curve.S2 : one can use more than type curve.
Answer» For determining median from ogive curves , S1 : one can use less than type curve. S2 : one can use more than type curve.

1922.

For determining median from ogive curves , S1 : one can use less than type curve.S2 : one can use more than type curve.

Answer»

For determining median from ogive curves ,

S1 : one can use less than type curve.

S2 : one can use more than type curve.

Discussion

1923.	Find the 8th term from the end of the A.P. 7,10,13,...,184
Answer» Find the 8th term from the end of the A.P. 7,10,13,...,184

Discussion

1924.	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

1925.	If θ is a positive acute such that sec θ = cosec 60°, find the value of 2 cos2 θ − 1.
Answer» If θ is a positive acute such that sec θ = cosec 60°, find the value of 2 cos² θ − 1.

Discussion

1926.	In the given figure ∠ABC=46∘, then ∠BAC is equal to
Answer» In the given figure $∠ A B C = 46^{\circ},$ then $∠ B A C$ is equal to

Discussion

1927.	Question 3 If ΔABC∼ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true? (A) BC.EF = AC.FD (B) AB.EF = AC.DE (C) BC.DE = AB.EF (D) BC.DE = AB.FD
Answer» Question 3 If $Δ A B C \sim Δ E D F a n d Δ A B C$ is not similar to $Δ D E F$ , then which of the following is not true? (A) BC.EF = AC.FD (B) AB.EF = AC.DE (C) BC.DE = AB.EF (D) BC.DE = AB.FD

Discussion

1928.	When a die is thrown 10 times, the following outcomes are noted 1, 3, 2, 1, 5, 6, 3, 4, 1, 5 S1: The empirical probability of getting a 1 is 16 S2: The theoretical probability of getting a 1 is 16
Answer» When a die is thrown 10 times, the following outcomes are noted 1, 3, 2, 1, 5, 6, 3, 4, 1, 5 S1: The empirical probability of getting a 1 is $\frac{1}{6}$ S2: The theoretical probability of getting a 1 is $\frac{1}{6}$

1928.

When a die is thrown 10 times, the following outcomes are noted 1, 3, 2, 1, 5, 6, 3, 4, 1, 5 S1: The empirical probability of getting a 1 is 16 S2: The theoretical probability of getting a 1 is 16

Answer»

When a die is thrown 10 times, the following outcomes are noted

1, 3, 2, 1, 5, 6, 3, 4, 1, 5

S1: The empirical probability of getting a 1 is $\frac{1}{6}$

S2: The theoretical probability of getting a 1 is $\frac{1}{6}$

Discussion

1929.	(a) If A = {p, q, r, s), B = (s, t, u) and C = (s, t, u, v, w}Find (i) A ∪ (B ∪ C) (ii) (A ∪ B) ∪ C (iii) A ∩ (B ∩ C) (iv) (A ∩ B) ∩ C(b) If A = {1, 4, 9, 16}, B = {3, 4, 5} and C = {3, 9, 12}Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ C (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ C(c) If A = {5, 7, 9}, B = {7, 9, 11} and C = {9, 11}Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ (A ∪ C), (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ (A ∩ C)
Answer» (a) If A = {p, q, r, s), B = (s, t, u) and C = (s, t, u, v, w} Find (i) A ∪ (B ∪ C) (ii) (A ∪ B) ∪ C (iii) A ∩ (B ∩ C) (iv) (A ∩ B) ∩ C (b) If A = {1, 4, 9, 16}, B = {3, 4, 5} and C = {3, 9, 12} Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ C (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ C (c) If A = {5, 7, 9}, B = {7, 9, 11} and C = {9, 11} Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ (A ∪ C), (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ (A ∩ C)

1929.

(a) If A = {p, q, r, s), B = (s, t, u) and C = (s, t, u, v, w}Find (i) A ∪ (B ∪ C) (ii) (A ∪ B) ∪ C (iii) A ∩ (B ∩ C) (iv) (A ∩ B) ∩ C(b) If A = {1, 4, 9, 16}, B = {3, 4, 5} and C = {3, 9, 12}Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ C (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ C(c) If A = {5, 7, 9}, B = {7, 9, 11} and C = {9, 11}Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ (A ∪ C), (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ (A ∩ C)

Answer»

(a) If A = {p, q, r, s), B = (s, t, u) and C = (s, t, u, v, w}

Find (i) A ∪ (B ∪ C) (ii) (A ∪ B) ∪ C (iii) A ∩ (B ∩ C) (iv) (A ∩ B) ∩ C

(b) If A = {1, 4, 9, 16}, B = {3, 4, 5} and C = {3, 9, 12}

Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ C (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ C

(c) If A = {5, 7, 9}, B = {7, 9, 11} and C = {9, 11}

Verify (i) A ∪ (B ∪ C) = (A ∪ B) ∪ (A ∪ C), (ii) A ∩ (B ∩ C) = (A ∩ B) ∩ (A ∩ C)

Discussion

1930.	64. The equation of the parabola with latus rectum joining the points ( 3 , 5 ) and ( 3 , -3) is __________.
Answer» 64. The equation of the parabola with latus rectum joining the points ( 3 , 5 ) and ( 3 , -3) is __________.

Discussion

1931.	Question 177(iii)Find x.2x+2x+2x=192
Answer» Question 177(iii) Find x. $2^{x} + 2^{x} + 2^{x} = 192$

1931.

Question 177(iii)Find x.2x+2x+2x=192

Answer»

Question 177(iii)

Find x.

$2^{x} + 2^{x} + 2^{x} = 192$

Discussion

1932.	TP and TQ are tangents drawn to a circle with centre O. Show that .
Answer» TP and TQ are tangents drawn to a circle with centre O. Show that .

Discussion

1933.	If sinθ cosθ=12,then what is the value of sin6θ+cos6θ ?
Answer» If $s i n θ c o s θ = \frac{1}{2}$ ,then what is the value of $s i n^{6} θ + c o s^{6} θ$ ?

Discussion

1934.	The sum 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.
Answer» The sum 4^th and 8^th terms of an A.P. is 24 and the sum of 6^th and 10^th terms is 44. Find the A.P.

Discussion

1935.	Question 1 (iii)Solve the following pairs of equations by reducing them to a pair of linear equations:4x+3y=143x−4y=23
Answer» Question 1 (iii) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{4}{x} + 3 y = 14$ $\frac{3}{x} - 4 y = 23$

Discussion

1936.	The sum of the series 15,25,35,...,795 is
Answer» The sum of the series $\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, . . ., \frac{79}{5}$ is

Discussion

1937.	Mark the correct alternative in each of the following:If a digit is chosen at random from the digit 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is(a) 49(b) 59(c) 19(d) 23
Answer» Mark the correct alternative in each of the following: If a digit is chosen at random from the digit 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is (a) $\frac{4}{9}$ (b) $\frac{5}{9}$ (c) $\frac{1}{9}$ (d) $\frac{2}{3}$

Discussion

1938.	Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?
Answer» Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?

Discussion

1939.	In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?
Answer» In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

1939.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Answer»

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Discussion

1940.	△ABC ∼ △DEF such that ar(△ABC) = 64 cm2 and ar(△DEF) = 169 cm2 If BC = 4 cm, find EF
Answer» △ABC ∼ △DEF such that ar(△ABC) = 64 cm² and ar(△DEF) = 169 cm² If BC = 4 cm, find EF

Discussion

1941.	The area of the triangle formed by the lines x = 3, y = 4 and x = y is(a) ½ sq. unit(b) 1 sq. unit(c) 2 sq. unit(d) None of these
Answer» The area of the triangle formed by the lines x = 3, y = 4 and x = y is (a) ½ sq. unit (b) 1 sq. unit (c) 2 sq. unit (d) None of these

Discussion

1942.	Find a pair of numbers with sum 4 and product 2.
Answer» Find a pair of numbers with sum 4 and product 2.

Discussion

1943.	The sum of first m terms of an AP is (4m2−m). If its nth term is 107, find the value of n. Also, find the 21st term of this AP.
Answer» The sum of first m terms of an AP is $(4 m^{2} - m)$ . If its nth term is 107, find the value of n. Also, find the 21st term of this AP.

Discussion

1944.	If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
Answer» If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

Discussion

1945.	If the equation (1+m2)x2+2mcx+(c2-a2)=0 has equal roots, prove that c2=a2(1+m2).
Answer» If the equation (1+m²)x²+2mcx+(c²-a²)=0 has equal roots, prove that c²=a²(1+m²).

Discussion

1946.	area bounded by curve y=[cosA+cosB+cosC] ,y=[ 5sinA/2 sinB/2 sinC/2] where [.] represents GIF and A,B,C are angles of a triangle and the curve y-\|x-4\|=0 is
Answer» area bounded by curve y=[cosA+cosB+cosC] ,y=[ 5sinA/2 sinB/2 sinC/2] where [.] represents GIF and A,B,C are angles of a triangle and the curve y-\|x-4\|=0 is

Discussion

1947.	What is the difference between lemma and axiom?
Answer» What is the difference between lemma and axiom?

Discussion

1948.	The range of probability is
Answer» The range of probability is

Discussion

1949.	the value of quadratic polynomial is zero only at x=-2 and -1. if p(1)=6, then p(3) is
Answer» the value of quadratic polynomial is zero only at x=-2 and -1. if p(1)=6, then p(3) is

Discussion

1950.	If axn is a zero degree polynomial in x, what can be said about a?
Answer» If $a x^{n}$ is a zero degree polynomial in $x$ , what can be said about $a$ ?

Discussion

Explore topic-wise InterviewSolutions in .

A(0, 0), B(6, 0), C(4, 2), D(2, 2) are the vertices of trapezium ABCD. E and F are the midpoints of AD and BC respectively then, EF =?.

In the given figure, there are two circles with the centres O and O' touching each other internally at P. TangentsTQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR

If the points (1,1) , (-1,-1) and (-√3,k) are vertices of an equilateral triangle, find the values of k.

Find the average price of the rice mixture (in Rs.) if 3 kgs of rice at Rs.10/kg and 5 kgs at Rs.18/kg are mixed together.

If the tth term of an AP is s and sth term of the same AP is t, then an is

A solid metallic cuboid of dimensions (9 m × 8 m × 2 m) is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed.

If –2 is one of the zeroes of the cubic polynomial x3 + 2x2 + 9x – 18, then the other two zeroes are

The sum of the zeros of the quadratic polynomial 2x2 – 3k is ________.

Find the angle of elevation of the sun when the shadow of a 10m long pole is 10√3 m.

The nth term of a sequence is (2n -1). Find the 15th term of the sequence.

If 1+cot2 θ=(√3+2√2−1)2, find the value of 1tan θ+sin θ1+cos θ

{ Show that the points }A(1,2),B(-1,-16) and }C(0,-7) lie on the graph of linear equation }}{y=9x-7

Which of the given line segments is a radius of the given circle?

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30^° and 45^° respectively. Findthe distance between the cars. \lbrack Use \sqrt{3 } = 1.732\rbrack

Find the acute angle (θ) at which sinθ and tanθ are equal.

Find the mean of the following data, using direct method: Class0−1010−2020−3030−4040−5050−60Frequency7561282

A circle is inscribed in an equilateral triangle of side √3s units. Which of the following is the area of the square constructed with a diameter of the circle as a side (in sq. units)?

If the roots of the equations a2+b2x2-2ba+cx+b2+c2=0 are equal, then(a) 2b = a + c(b) b2 = ac(c) b=2aca+c(d) b = ac

For determining median from ogive curves , S1 : one can use less than type curve.S2 : one can use more than type curve.

Find the 8th term from the end of the A.P. 7,10,13,...,184

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

If θ is a positive acute such that sec θ = cosec 60°, find the value of 2 cos2 θ − 1.

In the given figure ∠ABC=46∘, then ∠BAC is equal to

Question 3 If ΔABC∼ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true? (A) BC.EF = AC.FD (B) AB.EF = AC.DE (C) BC.DE = AB.EF (D) BC.DE = AB.FD

When a die is thrown 10 times, the following outcomes are noted 1, 3, 2, 1, 5, 6, 3, 4, 1, 5 S1: The empirical probability of getting a 1 is 16 S2: The theoretical probability of getting a 1 is 16

64. The equation of the parabola with latus rectum joining the points ( 3 , 5 ) and ( 3 , -3) is __________.

Question 177(iii)Find x.2x+2x+2x=192

TP and TQ are tangents drawn to a circle with centre O. Show that .

If sinθ cosθ=12,then what is the value of sin6θ+cos6θ ?

The sum 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.

Question 1 (iii)Solve the following pairs of equations by reducing them to a pair of linear equations:4x+3y=143x−4y=23

The sum of the series 15,25,35,...,795 is

Mark the correct alternative in each of the following:If a digit is chosen at random from the digit 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is(a) 49(b) 59(c) 19(d) 23

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?

In the figure; P and Q are the points of intersection of two circles with centres O &amp; O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

△ABC ∼ △DEF such that ar(△ABC) = 64 cm2 and ar(△DEF) = 169 cm2 If BC = 4 cm, find EF

The area of the triangle formed by the lines x = 3, y = 4 and x = y is(a) ½ sq. unit(b) 1 sq. unit(c) 2 sq. unit(d) None of these

Find a pair of numbers with sum 4 and product 2.

The sum of first m terms of an AP is (4m2−m). If its nth term is 107, find the value of n. Also, find the 21st term of this AP.

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

If the equation (1+m​​​​​​2)x​​​​​​2+2mcx+(c​2-a2)=0 has equal roots, prove that c​​​​​​2=a​​​​​​2(1+m​​​​​​2).

area bounded by curve y=[cosA+cosB+cosC] ,y=[ 5sinA/2 sinB/2 sinC/2] where [.] represents GIF and A,B,C are angles of a triangle and the curve y-|x-4|=0 is

What is the difference between lemma and axiom?

The range of probability is

the value of quadratic polynomial is zero only at x=-2 and -1. if p(1)=6, then p(3) is

If axn is a zero degree polynomial in x, what can be said about a?

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

If the equation (1+m2)x2+2mcx+(c2-a2)=0 has equal roots, prove that c2=a2(1+m2).