32581 + Interview Questions in Mathematics Page 162 InterviewSolution

8051.	Match the following to their roots.
Answer» Match the following to their roots.

Discussion

8052.	If 1+2 is a root of a quadratic equation will rational coefficients, write its other root.
Answer» If $1 + \sqrt{2}$ is a root of a quadratic equation will rational coefficients, write its other root.

Discussion

8053.	In a ∆ABC, right angled at A, if tan C=3, find the value of sin B cos C + cos B sin C.
Answer» In a ∆ABC, right angled at A, if $\tan C = \sqrt{3}$ , find the value of sin B cos C + cos B sin C.

Discussion

8054.	Question 74Fill in the blanks to make the statements true.In a rhombus, diagonals intersect at ___ angles.
Answer» Question 74 Fill in the blanks to make the statements true. In a rhombus, diagonals intersect at ___ angles.

Discussion

8055.	If p1 and p2 are two odd prime numbers such that p1 > p2, then p12-p22 is(a) an even number(b) an odd number(c) an odd prime number(d) a prime number
Answer» If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then $p_{1}^{2} - p_{2}^{2}$ is (a) an even number (b) an odd number (c) an odd prime number (d) a prime number

Discussion

8056.	The value of cos248° – sin212° is ___________.
Answer» The value of cos²48° – sin²12° is ___________.

Discussion

8057.	A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.
Answer» A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.

Discussion

8058.	Find the sum : 34 + 32 + 30 + .... + 10
Answer» Find the sum : 34 + 32 + 30 + .... + 10

Discussion

8059.	Écrivez sous chacun des dessins ci-dessous la phrase qui correspond au temps qu'il fait.
Answer» Écrivez sous chacun des dessins ci-dessous la phrase qui correspond au temps qu'il fait.

Discussion

8060.	In the diagram the smaller circle is drawn such that it passes through the Centre of the larger and touches the larger circle. What is the radius of the smaller circle if the diameter of the larger circle is D?
Answer» In the diagram the smaller circle is drawn such that it passes through the Centre of the larger and touches the larger circle. What is the radius of the smaller circle if the diameter of the larger circle is D?

8060.

In the diagram the smaller circle is drawn such that it passes through the Centre of the larger and touches the larger circle. What is the radius of the smaller circle if the diameter of the larger circle is D?

Answer»

In the diagram the smaller circle is drawn such that it passes through the Centre of the larger and touches the larger circle. What is the radius of the smaller circle if the diameter of the larger circle is D?

Discussion

8061.	A football league scores on an average 1.3 goals per match. What is the total goals scored in 22 matches?
Answer» A football league scores on an average 1.3 goals per match. What is the total goals scored in 22 matches?

8061.

A football league scores on an average 1.3 goals per match. What is the total goals scored in 22 matches?

Answer»

A football league scores on an average 1.3 goals per match.

What is the total goals scored in 22 matches?

Discussion

8062.	A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use π=227)
Answer» A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use $π = \frac{22}{7}$ )

8062.

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use π=227)

Answer»

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use $π = \frac{22}{7}$ )

Discussion

8063.	In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .
Answer» In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

8063.

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

Answer»

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

Discussion

8064.	The catalogue price of a color T.V is ₹ 50,000. The shopkeeper gives a discount of 8 % on the listed price. He gives a further off - season discount of 5 % on the balance. But sales tax at 10 % is charged on the remaining amount. Find: (i) the sales tax amount a customer has to pay (ii) the final price he has to pay for the color T.V
Answer» The catalogue price of a color T.V is ₹ 50,000. The shopkeeper gives a discount of 8 % on the listed price. He gives a further off - season discount of 5 % on the balance. But sales tax at 10 % is charged on the remaining amount. Find: (i) the sales tax amount a customer has to pay (ii) the final price he has to pay for the color T.V

8064.

The catalogue price of a color T.V is ₹ 50,000. The shopkeeper gives a discount of 8 % on the listed price. He gives a further off - season discount of 5 % on the balance. But sales tax at 10 % is charged on the remaining amount. Find: (i) the sales tax amount a customer has to pay (ii) the final price he has to pay for the color T.V

Answer»

The catalogue price of a color T.V is ₹ 50,000. The shopkeeper gives a discount of 8 % on the listed price. He gives a further off - season discount of 5 % on the balance. But sales tax at 10 % is charged on the remaining amount. Find:

(i) the sales tax amount a customer has to pay

(ii) the final price he has to pay for the color T.V

Discussion

8065.	The areas of two similar triangles are 25 cm2 and 36 cm2 respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.
Answer» The areas of two similar triangles are 25 cm² and 36 cm² respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.

Discussion

8066.	The Directors of Super Star Ltd. invited applications for 2,00,000 Equity Shares of ₹ 10 each to be issued at 20% premium. The money payable per shares was: on application ₹ 5, on allotment ₹ 4 (including premium of ₹ 2), first call ₹ 2 and final call ₹ 1.Applications were received for 2,40,000 shares and allotment was made as:(i) to applicants for 1,00,000 shares— in full,(ii) to applicants for 80,000 shares—60,000 shares,(iii) to applicants for 60,000 shares—40,000 shares.Applicants of 1,000 shares falling in Category(i) and applicants of 1,200 shares falling in Category(ii) failed to pay allotment money. These shares were forfeited on failure to pay first call. Holders of 1,200 shares falling in Category(iii) failed to pay the first and final call and these shares were forfeited after final call.1,300 shares[1,000 of Category(i) and 300 of Category (ii)] were reissued at ₹ 8 per share as fully paid-up.Journalise the above transactions. Prepare Cash book and Balance Sheet.
Answer» The Directors of Super Star Ltd. invited applications for 2,00,000 Equity Shares of ₹ 10 each to be issued at 20% premium. The money payable per shares was: on application ₹ 5, on allotment ₹ 4 (including premium of ₹ 2), first call ₹ 2 and final call ₹ 1. Applications were received for 2,40,000 shares and allotment was made as: (i) to applicants for 1,00,000 shares $—$ in full, (ii) to applicants for 80,000 shares $—$ 60,000 shares, (iii) to applicants for 60,000 shares $—$ 40,000 shares. Applicants of 1,000 shares falling in Category (i) and applicants of 1,200 shares falling in Category (ii) failed to pay allotment money. These shares were forfeited on failure to pay first call. Holders of 1,200 shares falling in Category (iii) failed to pay the first and final call and these shares were forfeited after final call. 1,300 shares[1,000 of Category(i) and 300 of Category (ii)] were reissued at ₹ 8 per share as fully paid-up. Journalise the above transactions. Prepare Cash book and Balance Sheet.

Discussion

8067.	the length of chord of contact of the tangents drawn from the point (-2,-1) to the parabola y2=12x is
Answer» the length of chord of contact of the tangents drawn from the point (-2,-1) to the parabola y2=12x is

Discussion

8068.	The square of a positive integer cannot be of the form(k is an integer) A. 3K+1 B.4K+1 C.5K+1 D.5K+4 Give reason..
Answer» The square of a positive integer cannot be of the form(k is an integer) A. 3K+1 B.4K+1 C.5K+1 D.5K+4 Give reason..

Discussion

8069.	14.Let A, b,c are be the real numbers then the following system of equations in x,y,z
Answer» 14.Let A, b,c are be the real numbers then the following system of equations in x,y,z

Discussion

8070.	if the 9th term of A.P is 0 ,then the ratio of the 29th and 19th term will be
Answer» if the 9th term of A.P is 0 ,then the ratio of the 29th and 19th term will be

Discussion

8071.	A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find the i) number of shares he has in company and ii) dividend percent per share
Answer» A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find the i) number of shares he has in company and ii) dividend percent per share

Discussion

8072.	Prove that n^2-n is divisible by 2 for any positive integer n.
Answer» Prove that n^2-n is divisible by 2 for any positive integer n.

Discussion

8073.	Find other zeroes of the polynomial p(x) = 2x4 + 7x3 − 19x2 − 14x + 30 if two of its zeroes are 2 and -2.
Answer» Find other zeroes of the polynomial p(x) = 2x⁴ + 7x³ − 19x² − 14x + 30 if two of its zeroes are $\sqrt{2}$ and $\sqrt{- 2}$ .

Discussion

8074.	3. equation of astraigt line passing through 1,1 and at a distance of 3 units from-2,3. is
Answer» 3. equation of astraigt line passing through 1,1 and at a distance of 3 units from-2,3. is

Discussion

8075.	15. Monica has a piece of canvas whose area is 818 metres square . She uses it to have a conical tent made with the base radius of 10 metre. Assuming that all the stitching margins and the wastage incurred while cutting amounts to approximately 1.6 metres square .Find the volume of the tank that can be made with it. Click here to view details:
Answer» 15. Monica has a piece of canvas whose area is 818 metres square . She uses it to have a conical tent made with the base radius of 10 metre. Assuming that all the stitching margins and the wastage incurred while cutting amounts to approximately 1.6 metres square .Find the volume of the tank that can be made with it. Click here to view details:

Discussion

8076.	Two dice are thrown. The events A,B and C are as follows:A: getting an even number on the first die.B: getting an odd number on the first die.C: getting the sum of the numbers on the dice ≤5i. Describe the event A′ii. Describe the event not Biii. Describe the event A or Biv. Describe the event A and Bv. Describe the event A but not Cvi. Describe the event B or C vii. Describe the event B and Cviii. Describe the event A ∩B′ ∩ C′
Answer» Two dice are thrown. The events $A, B and C$ are as follows: $A :$ getting an even number on the first die. $B :$ getting an odd number on the first die. $C :$ getting the sum of the numbers on the dice $\leq 5$ $i .$ Describe the event $A^{'}$ $i i .$ Describe the event not $B$ $i i i .$ Describe the event $A or B$ $i v .$ Describe the event $A and B$ $v .$ Describe the event $A but not C$ $v i .$ Describe the event $B or C$ $v i i .$ Describe the event $B and C$ $v i i i .$ Describe the event $A \cap B^{'} \cap C^{'}$

Discussion

8077.	What is the probability that a die thrown randomly on the rectangular region will land inside the circle with diameter 1 m?
Answer» What is the probability that a die thrown randomly on the rectangular region will land inside the circle with diameter 1 m?

Discussion

8078.	Fill In The Blanks In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat patato chips. If a child is selected at random, the probability that he/she does not like eat patato chips, is _________.
Answer» Fill In The Blanks In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat patato chips. If a child is selected at random, the probability that he/she does not like eat patato chips, is _________.

Discussion

8079.	A tower is built on a river of width 80 m. One can see the top of the tower at an angle of elevation of 55∘ and 65∘ from either banks of the river. The height of tower measured from the water level is [Tan 65∘=2.14, Tan 55∘=1.43]
Answer» A tower is built on a river of width 80 m. One can see the top of the tower at an angle of elevation of $55^{\circ}$ and $65^{\circ}$ from either banks of the river. The height of tower measured from the water level is $[T a n 65^{\circ} = 2.14, T a n 55^{\circ} = 1.43]$

Discussion

8080.	In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm2, then find the lengths of sides AB and AC.
Answer» In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of $Δ$ ABC = 21 $c m^{2}$ , then find the lengths of sides AB and AC.

8080.

In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm2, then find the lengths of sides AB and AC.

Answer»

In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of $Δ$ ABC = 21 $c m^{2}$ , then find the lengths of sides AB and AC.

Discussion

8081.	During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h=−16t2+24t+1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?
Answer» During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h = - 16 t^{2} + 24 t + 1$ , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Discussion

8082.	A hemisphere the diameter of whose base is equal to the side of a cube is placed upon the upper face of the cube if the side of the cube is 14 cm find the total surface area of the solid combination
Answer» A hemisphere the diameter of whose base is equal to the side of a cube is placed upon the upper face of the cube if the side of the cube is 14 cm find the total surface area of the solid combination

Discussion

8083.	Who invented similarities of triangles
Answer» Who invented similarities of triangles

Discussion

8084.	If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to(a) 60°(b) 70°(c) 80°(d) 90°
Answer» If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to (a) 60° (b) 70° (c) 80° (d) 90°

Discussion

8085.	A jeweller has two bars of 18 carat gold and 12 carat gold .how much each must be melted together to obtain a bar of 16 carat gold weighing 120 grams ?
Answer» A jeweller has two bars of 18 carat gold and 12 carat gold .how much each must be melted together to obtain a bar of 16 carat gold weighing 120 grams ?

Discussion

8086.	25. Determine all function f:R-'0,1' to R, which satisfy the equation f(x)+f(1/1-x)=2(1-2x)/x(1-x) valid for all x not equal to 0and1
Answer» 25. Determine all function f:R-'0,1' to R, which satisfy the equation f(x)+f(1/1-x)=2(1-2x)/x(1-x) valid for all x not equal to 0and1

Discussion

8087.	Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)
Answer» Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

Discussion

8088.	Five cards − the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.(i) What is the probability that the card is the queen?(ii) If the queen is drawn and put a side, what is the probability that the second card picked up is (a) an ace? (b) a queen?
Answer» Five cards − the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is the queen? (ii) If the queen is drawn and put a side, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Discussion

8089.	Question 5 (v)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(v) (cosA−sinA+1)(cosA+sinA−1)=cosecA+cotA, using the identity cosec2A=1+cot2A.
Answer» Question 5 (v) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (v) $\frac{(c o s A - s i n A + 1)}{(c o s A + s i n A - 1)} = c o s e c A + c o t A$ , using the identity $c o s e c^{2} A = 1 + c o t^{2} A$ .

Discussion

8090.	A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs 20 per litre and the cost of metal sheet used if it costs Rs 10 per 100 cm2 [Use π=3.14.]
Answer» A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs 20 per litre and the cost of metal sheet used if it costs Rs 10 per 100 $c m^{2}$ $[U s e π = 3.14.]$

Discussion

8091.	If k is the zero of both the polynomials x2−6x+8 and x3−5x2+6x, then value of k is
Answer» If k is the zero of both the polynomials $x^{2} - 6 x + 8$ and $x^{3} - 5 x^{2} + 6 x$ , then value of k is

Discussion

8092.	Using division algorithm, find the quotient and remainder on dividing f(x) by g(x) where f(x)=6x3+13x2+x−2 and g(x)=2x+1.
Answer» Using division algorithm, find the quotient and remainder on dividing f(x) by g(x) where $f (x) = 6 x^{3} + 13 x^{2} + x - 2 a n d g (x) = 2 x + 1.$

Discussion

8093.	In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.
Answer» In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Discussion

8094.	Find three consecutive terms which are in AP . Whose sum is 24 and product is 440
Answer» Find three consecutive terms which are in AP . Whose sum is 24 and product is 440

Discussion

8095.	The area of circular playground is 22176 m2 . Find the cost of fencing this ground at the rate of ₹ 50 per metre.
Answer» The area of circular playground is 22176 m² . Find the cost of fencing this ground at the rate of ₹ 50 per metre.

Discussion

8096.	If α,β be the zeros of the polynomial 2x2+5x+k such that α2+β2+αβ=214 then k = ? (a) 3 (b) -3 (c) -2 (d) 2
Answer» If $α, β$ be the zeros of the polynomial $2 x^{2} + 5 x + k$ such that $α^{2} + β^{2} + α β = \frac{21}{4}$ then k = ? (a) 3 (b) -3 (c) -2 (d) 2

8096.

If α,β be the zeros of the polynomial 2x2+5x+k such that α2+β2+αβ=214 then k = ? (a) 3 (b) -3 (c) -2 (d) 2

Answer»

If $α, β$ be the zeros of the polynomial $2 x^{2} + 5 x + k$ such that $α^{2} + β^{2} + α β = \frac{21}{4}$ then k = ?

(a) 3 (b) -3 (c) -2 (d) 2

Discussion

8097.	Question 4 A football player scored the following number of goals in the 10 matches. 1, 3, 2, 5, 8, 6, 1, 4, 7 and 9. Since the number of matches is 10 ( an even number), Median=5th observation + 6th observation2=8+62=7 Is it the correct answer and why?
Answer» Question 4 A football player scored the following number of goals in the 10 matches. 1, 3, 2, 5, 8, 6, 1, 4, 7 and 9. Since the number of matches is 10 ( an even number), $Median = \frac{5th observation + 6th observation}{2} = \frac{8 + 6}{2} = 7$ Is it the correct answer and why?

Discussion

8098.	cos70∘sin20∘+cos59∘sin31∘−8sin230∘ is equal to\N
Answer» $\frac{c o s 70^{\circ}}{s i n 20^{\circ}} + \frac{c o s 59^{\circ}}{s i n 31^{\circ}} - 8 s i n^{2} 30^{\circ}$ is equal to \N

Discussion

8099.

Weight of 60 eggs were recorded as given below: Weight (in grams) 75−79 80−84 85−89 90−94 95−99 100−104 105−109 Number of eggs 4 9 13 17 12 3 2 Calculate their mean weight to the nearest gram.

Answer» Weight of 60 eggs were recorded as given below:

Weight (in grams)	75−79	80−84	85−89	90−94	95−99	100−104	105−109
Number of eggs	4	9	13	17	12	3	2

Calculate their mean weight to the nearest gram.

Discussion

8100.	cot A-cos Acot A+cos A=cosec A-1cosec A+1
Answer» $\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{cosec A - 1}{cosec A + 1}$

Discussion

Explore topic-wise InterviewSolutions in .

Match the following to their roots.

If 1+2 is a root of a quadratic equation will rational coefficients, write its other root.

In a ∆ABC, right angled at A, if tan C=3, find the value of sin B cos C + cos B sin C.

Question 74Fill in the blanks to make the statements true.​​​​​​​In a rhombus, diagonals intersect at ___ angles.

If p1 and p2 are two odd prime numbers such that p1 > p2, then p12-p22 is(a) an even number(b) an odd number(c) an odd prime number(d) a prime number

The value of cos248° – sin212° is ___________.

A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.

Find the sum : 34 + 32 + 30 + .... + 10

Écrivez sous chacun des dessins ci-dessous la phrase qui correspond au temps qu'il fait.

In the diagram the smaller circle is drawn such that it passes through the Centre of the larger and touches the larger circle. What is the radius of the smaller circle if the diameter of the larger circle is D?

A football league scores on an average 1.3 goals per match. What is the total goals scored in 22 matches?

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

The areas of two similar triangles are 25 cm2 and 36 cm2 respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.

the length of chord of contact of the tangents drawn from the point (-2,-1) to the parabola y2=12x is

The square of a positive integer cannot be of the form(k is an integer) A. 3K+1 B.4K+1 C.5K+1 D.5K+4 Give reason..

14.Let A, b,c are be the real numbers then the following system of equations in x,y,z

if the 9th term of A.P is 0 ,then the ratio of the 29th and 19th term will be

A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find the i) number of shares he has in company and ii) dividend percent per share

Prove that n^2-n is divisible by 2 for any positive integer n.

Find other zeroes of the polynomial p(x) = 2x4 + 7x3 − 19x2 − 14x + 30 if two of its zeroes are 2 and -2.

3. equation of astraigt line passing through 1,1 and at a distance of 3 units from-2,3. is

What is the probability that a die thrown randomly on the rectangular region will land inside the circle with diameter 1 m?

Fill In The Blanks In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat patato chips. If a child is selected at random, the probability that he/she does not like eat patato chips, is _________.

A tower is built on a river of width 80 m. One can see the top of the tower at an angle of elevation of 55∘ and 65∘ from either banks of the river. The height of tower measured from the water level is [Tan 65∘=2.14, Tan 55∘=1.43]

In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm2, then find the lengths of sides AB and AC.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h=−16t2+24t+1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

A hemisphere the diameter of whose base is equal to the side of a cube is placed upon the upper face of the cube if the side of the cube is 14 cm find the total surface area of the solid combination

Who invented similarities of triangles

If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to(a) 60°(b) 70°(c) 80°(d) 90°

A jeweller has two bars of 18 carat gold and 12 carat gold .how much each must be melted together to obtain a bar of 16 carat gold weighing 120 grams ?

25. Determine all function f:R-'0,1' to R, which satisfy the equation f(x)+f(1/1-x)=2(1-2x)/x(1-x) valid for all x not equal to 0and1

Question 5 (v)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(v) (cosA−sinA+1)(cosA+sinA−1)=cosecA+cotA, using the identity cosec2A=1+cot2A.

If k is the zero of both the polynomials x2−6x+8 and x3−5x2+6x, then value of k is

Using division algorithm, find the quotient and remainder on dividing f(x) by g(x) where f(x)=6x3+13x2+x−2 and g(x)=2x+1.

In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Find three consecutive terms which are in AP . Whose sum is 24 and product is 440

The area of circular playground is 22176 m2 . Find the cost of fencing this ground at the rate of ₹ 50 per metre.

If α,β be the zeros of the polynomial 2x2+5x+k such that α2+β2+αβ=214 then k = ? (a) 3 (b) -3 (c) -2 (d) 2

Question 4 A football player scored the following number of goals in the 10 matches. 1, 3, 2, 5, 8, 6, 1, 4, 7 and 9. Since the number of matches is 10 ( an even number), Median=5th observation + 6th observation2=8+62=7 Is it the correct answer and why?

cos70∘sin20∘+cos59∘sin31∘−8sin230∘ is equal to\N

Weight of 60 eggs were recorded as given below: Weight (in grams) 75−79 80−84 85−89 90−94 95−99 100−104 105−109 Number of eggs 4 9 13 17 12 3 2 Calculate their mean weight to the nearest gram.

cot A-cos Acot A+cos A=cosec A-1cosec A+1

Question 74Fill in the blanks to make the statements true.In a rhombus, diagonals intersect at ___ angles.