3694 + Interview Questions in Maths in Class 10 Page 33 InterviewSolution

1601.	If alpha " and " beta are roots of x^2+5x-1=0 , " then find" (i) alpha^3 + beta^3(ii) alpha^2 + beta^2
Answer» ANSWER :(i)-140, (II) 27

Discussion

1602.	The maximumvolume of a cone that can be carved out of a solid hemisphere of radius ris3pir^2(b) (pir^3)/3(c) (pir^2)/3(d) 3pir^3
Answer» ANSWER :`(1)/(3) pi r ^(3) cm ^(3)`

Discussion

1603.	Which of the following is last link in the trading chain?
Answer» B2B B2C BC BB Answer :B

Discussion

1604.	From a solid cylinder of height 36 cm and radius 14 cm, a conical cavity of radius 7 cm and height 24 cm is drilled out. Find the volume and the total surface area of the remaining solid.
Answer» ANSWER :`20944 CM ^(3)`

Discussion

1605.	When x^(3)+3x^(2)-mx+4 is divided by x -2, the remainder is m + 3. Find the value of m.
Answer» ANSWER :m=7

Discussion

1606.	Find the area of the triangle formed by the points (2, 3), (6, 3) and (2, 6) by using Heron’s formula
Answer» ANSWER :6 UNITS

Discussion

1607.	Insert one arithmetic mean between 3 and 13.
Answer» ANSWER :8

Discussion

1608.	Which of the following are GP? If they are in G.P. Write next three terms? (i) 4,8,16,….. (ii) 1/3, -1/6, 1/12,……. (iii) 5,55,555,…….. (iv) -2, -6, -18,…….. (v) 1/2, 1/4, 1/6,……. (iv) 3,- -3^(2), 3^(3),…….. (vii) x,1,1/x,......... (x ne 0) (viii) 1/sqrt(2), -2, 4sqrt(2),.......... (ix) 0.4, 0.04, 0.004,........
Answer» Answer :(i) YES; 32,64, 128 , (II) Yes, `-1/24, 1/48, -1/96` (iii) No, (iv) Yes, `-54, -162, -148` (V) No (vi) Yes, `-81, 243, -729` , (vii) yes, `1/x^(2), 1/x^(3), 1/x^(4)`,…… (VIII) Yes, `-16, 32sqrt(2), -128`, (ix) Yes; 0.0004, 0.00004, 0.000004

Discussion

1609.	In winter, the temperature at a hill station from Monday to Friday is in A.P., The sum of the temperatures of Monday, Tuesday and Wednesday is zero and the sum of the temperature of Thursday and Friday is 15. Find the temperature of each of the five days.
Answer» ANSWER :₹812

Discussion

1610.	A manufacturer of wire produced 1400 m wire in the 5 th year and 1600 m in the 9th year. Assuming that the production increases uniformly by a fixed number every year, find (i) the production in the 12th year. (ii) in which year the production will be 1900 m? (iii) the total production in 9 years.
Answer» Answer :(i) 1750 m (II) `15^(th)`YEAR (iii) 12600 m

Discussion

1611.	Find the A.P. whose second term is 12 and 7th term exceeds the 4th by 15.
Answer» ANSWER :7,12,17,22

Discussion

1612.	Solve the following simultaneous equations graphically : x + y = 5 , x - y = 3
Answer» ANSWER :The solution of the GIVEN simultanousequationsis X = 4 , y = 1

Discussion

1613.	Rakhee invested 12500rs inshares of a company paying 6% dividend perannum. If she bought 50rs shares for 62.50rs each, find her income from the investment.
Answer» ANSWER :`600RS`

Discussion

1614.	Construct a triangle slmilar to a given triangle PQR with its sides equal to (2)/(3) of the corresponding sides of the triangle PQR (scale factor (2)/(3)).
Answer» ANSWER :`DELTA PQR`

Discussion

1615.	Point P is the centre of circle and AB is a diameter. Find the co-ordinate of centre of circle if A(22, 20) B(0.6)
Answer» ANSWER :12, 18

Discussion

1616.	(3x + 5) is a factor of the polynomial (a-1)x^(3)+(a+1)x^2-(2a+1)x-15. Find the value of 'a'. For this value of a'. Factorise the given polynomial completely
Answer» ANSWER :a=4; (3x+5) `(x^2-3)=(3x+5) (x+sqrt3) (x-sqrt3)`

Discussion

1617.	If "cosec"^(2) theta (1 + cos theta ) (1 - cos theta) = alphathen find the value of alpha.
Answer» ANSWER :`ALPHA` = 1

Discussion

1618.	At one side of a road, there os a house and on the other side there is a tower. House and tower are on the same horizontal plane. The angle of depression of the top and foot of the house, from the top of the tower are 30^(@)" and "45^(@) respectively. If the height of the house is 10 m, then find the distance between the house and the tower.
Answer» ANSWER :23.66 m

Discussion

1619.	A man buys a 80rs share in a company which pays 20% dividend. He buysthe share at such a price that his profit is 16% on his investment. At what price did he buy the share ?
Answer» ANSWER :`100RS`

Discussion

1620.	Shri Shantilal has purchased 150 shares of FV 100, for MV of 120. Company has paid divident at 7%. Find the rate of return on his investment.
Answer» ANSWER :`THEREFORE` RATE of RETURN on INVESTMENT is 5.83%.

Discussion

1621.	Calculate the ratio in which the line segment A(6, 5) and B(4, -3) is divided by the line y = 2.
Answer» ANSWER :`3:5`

Discussion

1622.	If the mid-point of the line segment joining the points A(3, 4), B(k, 6) is P(x, y) and x + y - 10 = 0, find the value of k.
Answer» ANSWER :` K = 7 `

Discussion

1623.	From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30^(@). A flag is hoisted at the top of building and the angle ofelevation of the top of the flagstaff from P is 45^(@). Find the length of the flagstaff and the distance of the building from the point? (You may take sqrt3=1.732)
Answer» ANSWER :`17.32 m`

Discussion

1624.	Fill in the blank using the correct word given in the bracket. Two polygons of the same number of sides are similar, if their corresponding sides are ........... . (equal, proportional)
Answer» ANSWER :PROPORTIONAL.

Discussion

1625.	If sin theta + cos theta =sqrt(3), thenprovethat tantheta + cos theta = 1 .
Answer» Solution :`sin theta + COS theta = sqrt(3)RARR 9SIN theta +sintheta)^(2) = 3` `rArr 1+ 2 sin theta cos theta = 3 rArr sin thetacos theta = 1` `therefore TAN theta + cottheta= (sin theta)/(cos theta) +(cos theta)/(sint theta) = 1`

Discussion

1626.	Cards marked with number 3, 4, 5, .... 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected cards bears a perfect square number.
Answer» ANSWER :Total cards = 50 – 3 + 1 = 48 perfect squares are 4, 9, 16, 25, 36, 49 Required PROBABILITY `=(6)/(48)=(1)/(8)`

Discussion

1627.	Sum of the areas of two squares is 468 m^(2). If the difference of their perimeters is 24 m, find the sides of the two squares.
Answer» ANSWER :18M; 12M

Discussion

1628.	Write the coefficientspresent in the polynomial of degree 5 .
Answer» ANSWER :COEFFICIENTS in polynomial of degree 5 are 1,5,-6,-2, and 8.

Discussion

1629.	(B) Solve any four of the following subquestions : Draw a circle with centre O and radius 3.2 cm . Marka point X on the circle . Draw a tangent passing through point Xto the without using the centre .
Answer» ANSWER :K=0

Discussion

1630.	Two dice are thrown simultaneously. Find the probability that : the total of the numbers on the dice is greater than 9.
Answer» ANSWER :`1/6`

Discussion

1631.	Find n if the nth term of the following A.P. is 66:3, 6,9,12……..
Answer» ANSWER :n=22

Discussion

1632.	A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : green ball ?
Answer» ANSWER :`1/3`

Discussion

1633.	A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : (ii) black ball ?
Answer» ANSWER :`1/3`

Discussion

1634.	A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : (i) red ball ?
Answer» ANSWER :`1/3`

Discussion

1635.	Solve the following pair of linear equation using elimination method. 3x + 2y = 11 2x + 3y = 4
Answer» ANSWER :THEREFORE, the REQUIRED solution is X = 5,y = -2.

Discussion

1636.	In triangle PQR, The value of y is
Answer» `4sqrt(3)` `6sqrt(3)` `5sqrt(3)` `SQRT(3)` ANSWER :C

Discussion

1637.	Find the area of the trianglevertices are (-5, -1), (3, -5), (5, 2)
Answer» ANSWER :32 SQ. UNITS

Discussion

1638.	Construct a triangle similar to a given triangle ABCsuch that each of its sides is (2)/(3)rd of the corresponding sides of the triangle ABC. It is given that AB=4cm, BC=5cm and AC=6cm .
Answer» Solution :Steps of Construction: 1. Take BC=5cm and construction `DeltaABC` with BA=4 cm and CA=6 cm. 2. Divide BC into THREE EQUAL PARTS. 3. Let C' be a point on BC such that `BC'=(2)/(3)BC`. 4. Draw A'C' parallel to AC through C' intersecting BA at A' . `DeltaAB'C'` is the required triangle.

Discussion

1639.	Mohit, Rajiv and Geeta live in the same city. Mohit sells an article to Rajiv for Rs. 50,000 and Rajiv sells the same article to Geeta at a profit of Rs. 6,000. If all the transactions are under GST system at the rate of 12% , find : the state - government tax (SGST) paid by Rajiv.
Answer» ANSWER :360

Discussion

1640.	The marks obtained by 200 students in an examination are given below. :Draw a less than ogive for the above distribution and use less than ogive to find median.
Answer» ANSWER :57

Discussion

1641.	A dealer sells anarticle for Rs. 24 and gains as much percent as the cost price of thearticle. Find the cost price of the article.
Answer» ANSWER :RS 20

Discussion

1642.	Solve the following equations : (2x)/(3)+(y)/(2)=3 (x)/(2)-(2y)/(3)=(1)/(6).
Answer» ANSWER :`x=3 and y=2.`

Discussion

1643.	Which terms of the GP: (i) 2,8,32,…… is 512? (ii) sqrt(3), 3,3sqrt(3),…………… is 729? (iii) 1/3, 1/9, 1/27,…………. Is 1/(2187) ?
Answer» Answer :(i) 5, (II) 12, (III) 7

Discussion

1644.	If a= (x+y)/( z) , b= (y+z)/( x) and c= (z+ x)/( y), then the value of (1)/( a+1) div (1)/( b+1) + (1)/(c+1) is equal to
Answer» `3` `2` `1` `-3` ANSWER :C

Discussion

1645.	A train covered a certain distance at a uniform speed. If the train would have been 10 km/hr faster, it would have taken 2 hours less than the scheduled time. And, if the train were solwer by 10 km/hr, it would have taken 3 hours more than the scheduled time. Find the distance. covered by train.
Answer» ANSWER :The actual SPEED of the train is 50 km/hr and TIME taken is 12 HRS and distance covered by the train is 600 km.

Discussion

1646.	Find the roots of the quadratic equations by factorisation: 2x^(2)-x+(1)/(8)=0
Answer» ANSWER :`(1)/(4); (1)/(4)`

Discussion

1647.	If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha^2 + beta^2
Answer» ANSWER :13

Discussion

1648.	Find the values of 'a' and ''b so that the polynomial x^3+ax^2+bx-45 has (x-1) and (x+5) as its factors. For the value sof 'a' and 'b', as obtained above, factorise the given polynomial completely.
Answer» ANSWER :(x-1) (x+9) (x+5)

Discussion

1649.	If 'white' is called 'blue', 'blue' is called 'red', red is called 'yellow', 'yellow' is called 'green', 'green' is called 'black', 'black' is called 'violet' and 'violet' is called 'orange', what would be the colour of human blood?
Answer» Red Green Violet Yellow ANSWER :D

Discussion

1650.	Use the substitution x=3y+1 to solve for y, if 5(3y+1)^(2)+6(3y+1)-8=0.
Answer» ANSWER :`y=-1`, or y= `-(1)/(15)`

Discussion

Explore topic-wise InterviewSolutions in .

If alpha " and " beta are roots of x^2+5x-1=0 , " then find" (i) alpha^3 + beta^3(ii) alpha^2 + beta^2

The maximumvolume of a cone that can be carved out of a solid hemisphere of radius ris3pir^2(b) (pir^3)/3(c) (pir^2)/3(d) 3pir^3

Which of the following is last link in the trading chain?

From a solid cylinder of height 36 cm and radius 14 cm, a conical cavity of radius 7 cm and height 24 cm is drilled out. Find the volume and the total surface area of the remaining solid.

When x^(3)+3x^(2)-mx+4 is divided by x -2, the remainder is m + 3. Find the value of m.

Find the area of the triangle formed by the points (2, 3), (6, 3) and (2, 6) by using Heron’s formula

Insert one arithmetic mean between 3 and 13.

In winter, the temperature at a hill station from Monday to Friday is in A.P., The sum of the temperatures of Monday, Tuesday and Wednesday is zero and the sum of the temperature of Thursday and Friday is 15. Find the temperature of each of the five days.

A manufacturer of wire produced 1400 m wire in the 5 th year and 1600 m in the 9th year. Assuming that the production increases uniformly by a fixed number every year, find (i) the production in the 12th year. (ii) in which year the production will be 1900 m? (iii) the total production in 9 years.

Find the A.P. whose second term is 12 and 7th term exceeds the 4th by 15.

Solve the following simultaneous equations graphically : x + y = 5 , x - y = 3

Rakhee invested 12500rs inshares of a company paying 6% dividend perannum. If she bought 50rs shares for 62.50rs each, find her income from the investment.

Construct a triangle slmilar to a given triangle PQR with its sides equal to (2)/(3) of the corresponding sides of the triangle PQR (scale factor (2)/(3)).

Point P is the centre of circle and AB is a diameter. Find the co-ordinate of centre of circle if A(22, 20) B(0.6)

(3x + 5) is a factor of the polynomial (a-1)x^(3)+(a+1)x^2-(2a+1)x-15. Find the value of 'a'. For this value of a'. Factorise the given polynomial completely

If "cosec"^(2) theta (1 + cos theta ) (1 - cos theta) = alphathen find the value of alpha.

A man buys a 80rs share in a company which pays 20% dividend. He buysthe share at such a price that his profit is 16% on his investment. At what price did he buy the share ?

Shri Shantilal has purchased 150 shares of FV 100, for MV of 120. Company has paid divident at 7%. Find the rate of return on his investment.

Calculate the ratio in which the line segment A(6, 5) and B(4, -3) is divided by the line y = 2.

If the mid-point of the line segment joining the points A(3, 4), B(k, 6) is P(x, y) and x + y - 10 = 0, find the value of k.

Fill in the blank using the correct word given in the bracket. Two polygons of the same number of sides are similar, if their corresponding sides are ........... . (equal, proportional)

If sin theta + cos theta =sqrt(3), thenprovethat tantheta + cos theta = 1 .

Cards marked with number 3, 4, 5, .... 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected cards bears a perfect square number.

Sum of the areas of two squares is 468 m^(2). If the difference of their perimeters is 24 m, find the sides of the two squares.

Write the coefficientspresent in the polynomial of degree 5 .

(B) Solve any four of the following subquestions : Draw a circle with centre O and radius 3.2 cm . Marka point X on the circle . Draw a tangent passing through point Xto the without using the centre .

Two dice are thrown simultaneously. Find the probability that : the total of the numbers on the dice is greater than 9.

Find n if the nth term of the following A.P. is 66:3, 6,9,12……..

A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : green ball ?

A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : (ii) black ball ?

A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. Mohit takes out a ball from the bag, without looking into it. What is the probability that the ball drawn is : (i) red ball ?

Solve the following pair of linear equation using elimination method. 3x + 2y = 11 2x + 3y = 4

In triangle PQR, The value of y is

Find the area of the trianglevertices are (-5, -1), (3, -5), (5, 2)

Construct a triangle similar to a given triangle ABCsuch that each of its sides is (2)/(3)rd of the corresponding sides of the triangle ABC. It is given that AB=4cm, BC=5cm and AC=6cm .

Mohit, Rajiv and Geeta live in the same city. Mohit sells an article to Rajiv for Rs. 50,000 and Rajiv sells the same article to Geeta at a profit of Rs. 6,000. If all the transactions are under GST system at the rate of 12% , find : the state - government tax (SGST) paid by Rajiv.

The marks obtained by 200 students in an examination are given below. :Draw a less than ogive for the above distribution and use less than ogive to find median.

A dealer sells anarticle for Rs. 24 and gains as much percent as the cost price of thearticle. Find the cost price of the article.

Solve the following equations : (2x)/(3)+(y)/(2)=3 (x)/(2)-(2y)/(3)=(1)/(6).

Which terms of the GP: (i) 2,8,32,…… is 512? (ii) sqrt(3), 3,3sqrt(3),…………… is 729? (iii) 1/3, 1/9, 1/27,…………. Is 1/(2187) ?

If a= (x+y)/( z) , b= (y+z)/( x) and c= (z+ x)/( y), then the value of (1)/( a+1) div (1)/( b+1) + (1)/(c+1) is equal to

A train covered a certain distance at a uniform speed. If the train would have been 10 km/hr faster, it would have taken 2 hours less than the scheduled time. And, if the train were solwer by 10 km/hr, it would have taken 3 hours more than the scheduled time. Find the distance. covered by train.

Find the roots of the quadratic equations by factorisation: 2x^(2)-x+(1)/(8)=0

If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha^2 + beta^2

Find the values of 'a' and ''b so that the polynomial x^3+ax^2+bx-45 has (x-1) and (x+5) as its factors. For the value sof 'a' and 'b', as obtained above, factorise the given polynomial completely.

If 'white' is called 'blue', 'blue' is called 'red', red is called 'yellow', 'yellow' is called 'green', 'green' is called 'black', 'black' is called 'violet' and 'violet' is called 'orange', what would be the colour of human blood?

Use the substitution x=3y+1 to solve for y, if 5(3y+1)^(2)+6(3y+1)-8=0.