24740 + Interview Questions in Mathematics Page 151 InterviewSolution

7501.	The linear equation 5x+12y=48 cuts the x-axis at
Answer» The linear equation $5 x + 12 y = 48$ cuts the x-axis at

Discussion

7502.	Factorise:2x2-x+18
Answer» Factorise: $2 x^{2} - x + \frac{1}{8}$

Discussion

7503.	State which statement is/are true of the following figure.
Answer» State which statement is/are true of the following figure.

Discussion

7504.	Question 5 Write True or False and justify your answer : In the figure, ABCD and EFGD are two parallelograms and G is the midpoint of CD. Then, ar(ΔDPC)=ar12(EFGD).
Answer» Question 5 Write True or False and justify your answer : In the figure, ABCD and EFGD are two parallelograms and G is the midpoint of CD. Then, $a r (Δ D P C) = a r \frac{1}{2} (E F G D)$ .

Discussion

7505.	Question 2Find three rational numbers between(i) -1 and -2(ii) 0.1 and 0.11(iii) 57 and 67(iv) 14 and 15Thinking processUse the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x<y and n =3
Answer» Question 2 Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) $\frac{5}{7}$ and $\frac{6}{7}$ (iv) $\frac{1}{4}$ and $\frac{1}{5}$ Thinking process Use the concept that three numbers between x and y are x+d, x+2d and x+3d , where $d = \frac{y - x}{n + 1}, x < y$ and n =3

Discussion

7506.	The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS. Statement 1: SX=XY Statement 2: XY=QY
Answer» The figure shows a parallelogram $P Q R S,$ in which, $A$ is the mid point of $P Q$ and $B$ is the mid point of $R S .$ Statement 1: $S X = X Y$ Statement 2: $X Y = Q Y$

7506.

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS. Statement 1: SX=XY Statement 2: XY=QY

Answer»

The figure shows a parallelogram $P Q R S,$ in which, $A$ is the mid point of $P Q$ and $B$ is the mid point of $R S .$

Statement 1: $S X = X Y$

Statement 2: $X Y = Q Y$

Discussion

7507.	Consider a circle with center O. Let AB, BC CD be three chords of the circle such that O lies inside the quadrilateral ABCD (one need not join DA). Let BC = CD= 2AB. Also, let E be a point on minor arc BC such that
Answer» Consider a circle with center O. Let AB, BC CD be three chords of the circle such that O lies inside the quadrilateral ABCD (one need not join DA). Let BC = CD= 2AB. Also, let E be a point on minor arc BC such that

Discussion

7508.	(i) In the given figure, if AB \|\| CD, find the value of x.(ii) In the given figure, If AB \|\| CD, find the value of x.(iii) In the given figure, AB \|\| CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.
Answer» (i) In the given figure, if AB \|\| CD, find the value of x. (ii) In the given figure, If AB \|\| CD, find the value of x. (iii) In the given figure, AB \|\| CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.

7508.

(i) In the given figure, if AB || CD, find the value of x.(ii) In the given figure, If AB || CD, find the value of x.(iii) In the given figure, AB || CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.

Answer» (i) In the given figure, if AB || CD, find the value of x.

(ii) In the given figure, If AB || CD, find the value of x.

(iii) In the given figure, AB || CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.

Discussion

7509.	If an+1+bn+1an+bn represents arithmetic mean, geometric mean, harmonic mean between two distinct positive numbers a and b for n=α,β,γ respectively, then the equation whose roots are α,2β,γ is
Answer» If $\frac{a^{n + 1} + b^{n + 1}}{a^{n} + b^{n}}$ represents arithmetic mean, geometric mean, harmonic mean between two distinct positive numbers $a$ and $b$ for $n = α, β, γ$ respectively, then the equation whose roots are $α, 2 β, γ$ is

Discussion

7510.	23. Prove by contradiction method that there are infinitly many prime numbers.
Answer» 23. Prove by contradiction method that there are infinitly many prime numbers.

Discussion

7511.	Question 1 (v) Without actually performing the long division, state whether 29343 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Question 1 (v) Without actually performing the long division, state whether $\frac{29}{343}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

7512.	If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.
Answer» If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

Discussion

7513.	How to find the irrational numbers between two given numbers
Answer» How to find the irrational numbers between two given numbers

Discussion

7514.	The perimeter of a right triangle is 60 cm and it's hypotenuse is 25 cm l. Find the area of the triangle
Answer» The perimeter of a right triangle is 60 cm and it's hypotenuse is 25 cm l. Find the area of the triangle

Discussion

7515.	In the given figure, if l1 \|\| l2, what is x + y in terms of w and z?(a) 180 − w + z(b) 180 + w − z(c) 180 − w − z(d) 180 + w + z
Answer» In the given figure, if l₁ \|\| l₂, what is x + y in terms of w and z? (a) 180 − w + z (b) 180 + w − z (c) 180 − w − z (d) 180 + w + z

Discussion

7516.	The largest value in the range of f(x)=2(a-x)(x+\sqrt{x^2+b^2}), x∈ R is (1) a^2+2b^2 (2) 2a^2+b^2 (3) a^2+b^2 (4) a^2-b^2
Answer» The largest value in the range of f(x)=2(a-x)(x+\sqrt{x^2+b^2}), x∈ R is (1) a^2+2b^2 (2) 2a^2+b^2 (3) a^2+b^2 (4) a^2-b^2

Discussion

7517.	In figure lines l1 and l2 intersect at O, forming angles as shown in the figure.If a=35∘, find the values of b, c and d. [3 MARKS]
Answer» In figure lines $l_{1}$ and $l_{2}$ intersect at O, forming angles as shown in the figure.If $a = 35^{\circ}$ , find the values of b, c and d. [3 MARKS]

7517.

In figure lines l1 and l2 intersect at O, forming angles as shown in the figure.If a=35∘, find the values of b, c and d. [3 MARKS]

Answer»

In figure lines $l_{1}$ and $l_{2}$ intersect at O, forming angles as shown in the figure.If $a = 35^{\circ}$ , find the values of b, c and d. [3 MARKS]

Discussion

7518.	Question 1 (iv)Does the following figure lie on the same base and between the same parallels? If yes,write the common base and two parallels.
Answer» Question 1 (iv) Does the following figure lie on the same base and between the same parallels? If yes,write the common base and two parallels.

Discussion

7519.	prove that a positive integer n is prime number if no prime p less than or equal to root n divides n
Answer» prove that a positive integer n is prime number if no prime p less than or equal to root n divides n

Discussion

7520.	The width of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. Find the upper class limit of the highest class.
Answer» The width of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. Find the upper class limit of the highest class.

Discussion

7521.	In the adjoining figure, the value of ∠A+∠B+∠C+∠D+∠E+∠F in degrees is ___
Answer» In the adjoining figure, the value of $∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F$ in degrees is ___

7521.

In the adjoining figure, the value of ∠A+∠B+∠C+∠D+∠E+∠F in degrees is ___

Answer»

In the adjoining figure, the value of $∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F$ in degrees is

___

Discussion

7522.	P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. If AD = 10 cm, then CD =(a) 5 cm(b) 6 cm(c) 8 cm(d) 10 cm
Answer» P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. If AD = 10 cm, then CD = (a) 5 cm (b) 6 cm (c) 8 cm (d) 10 cm

Discussion

7523.

Vardhman commenced business on 1st April, 2018, with a capital of ₹ 50,000. He immediately purchased furniture of ₹ 20,000. During the year he received from his uncle a gift of ₹ 3,000 and he borrowed from his father a sum of ₹ 5,000. He had withdrawn ₹ 600 per month for his household expenses. He had no Bank account and all dealings were in cash. He did not maintain any books but following information is given : ₹ Sales (including cash sales ₹ 30,000) 1,00,000 Purchases (including cash purchases ₹ 10,000) 75,000 Carriage inwards 700 Wages 300 Discount allowed to debtors 800 Salaries 6,200 Bad-Debts written off 1,500 Trade expenses 1,200 Advertisements 2,200 He used goods worth ₹ 1,300 for personal purposes and paid ₹ 500 to his son for examination and college fees.On 31st March, 2019, his Debtors were worth ₹ 21,000 and Creditors ₹ 15,000. Stock in trade was valued at ₹ 10,000. Furniture to be depreciated by 10% p.a.Prepare Trading and Profit and Loss Account for the year ended on 31st March, 2019, and Balance Sheet as at 31st March, 2019.

Answer» Vardhman commenced business on 1st April, 2018, with a capital of ₹ 50,000. He immediately purchased furniture of ₹ 20,000. During the year he received from his uncle a gift of ₹ 3,000 and he borrowed from his father a sum of ₹ 5,000. He had withdrawn ₹ 600 per month for his household expenses. He had no Bank account and all dealings were in cash. He did not maintain any books but following information is given :

	₹
Sales (including cash sales ₹ 30,000)	1,00,000
Purchases (including cash purchases ₹ 10,000)	75,000
Carriage inwards	700
Wages	300
Discount allowed to debtors	800
Salaries	6,200
Bad-Debts written off	1,500
Trade expenses	1,200
Advertisements	2,200

He used goods worth ₹ 1,300 for personal purposes and paid ₹ 500 to his son for examination and college fees.

On 31st March, 2019, his Debtors were worth ₹ 21,000 and Creditors ₹ 15,000. Stock in trade was valued at ₹ 10,000. Furniture to be depreciated by 10% p.a.

Prepare Trading and Profit and Loss Account for the year ended on 31st March, 2019, and Balance Sheet as at 31st March, 2019.

Discussion

7524.	In the following figures, ABCD is a parallelogram. A circle through A, B, C intersects CD or CD produced at E. Prove that AE = AD.
Answer» In the following figures, ABCD is a parallelogram. A circle through A, B, C intersects CD or CD produced at E. Prove that AE = AD.

Discussion

7525.	If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary rise to maintain the same standard of living if the CPI is 400?
Answer» If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary rise to maintain the same standard of living if the CPI is 400?

Discussion

7526.	Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?
Answer» Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

Discussion

7527.	In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? (a) 12AB (b) 12CD (c) 12(AB+CD) (d) 12(AB−CD)
Answer» In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? (a) $\frac{1}{2} A B$ (b) $\frac{1}{2} C D$ (c) $\frac{1}{2} (A B + C D)$ (d) $\frac{1}{2} (A B - C D)$

7527.

In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? (a) 12AB (b) 12CD (c) 12(AB+CD) (d) 12(AB−CD)

Answer»

In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ?

(a) $\frac{1}{2} A B$

(b) $\frac{1}{2} C D$

(c) $\frac{1}{2} (A B + C D)$

(d) $\frac{1}{2} (A B - C D)$

Discussion

7528.	The volume of a 4 inches wide and 3 inches high box is 36 cubic inches, what is its length?
Answer» The volume of a 4 inches wide and 3 inches high box is 36 cubic inches, what is its length?

Discussion

7529.	An equilateral triangle ABC is inscribed in a circle of radius 8 cm, which is centered at O, as shown below. Then the length of the side of this triangle is equal to
Answer» An equilateral triangle ABC is inscribed in a circle of radius 8 cm, which is centered at O, as shown below. Then the length of the side of this triangle is equal to

7529.

An equilateral triangle ABC is inscribed in a circle of radius 8 cm, which is centered at O, as shown below. Then the length of the side of this triangle is equal to

Answer»

An equilateral triangle ABC is inscribed in a circle of radius 8 cm, which is centered at O, as shown below. Then the length of the side of this triangle is equal to

Discussion

7530.	In ∆ LMN, LM = 7.2 cm, ∠M = 105° , MN = 6.4 cm , then draw ∆ LMN and construct its circumcircle.
Answer» In $∆$ LMN, LM = 7.2 cm, $∠$ M = $105^{°}$ , MN = 6.4 cm , then draw $∆$ LMN and construct its circumcircle.

Discussion

7531.	In the following figure, PQRS is a square of side 4 cm. Find the area of the shaded square.
Answer» In the following figure, PQRS is a square of side 4 cm. Find the area of the shaded square.

Discussion

7532.	Rationalize the denominator of 12−√3
Answer» Rationalize the denominator of $\frac{1}{2 - \sqrt{3}}$

Discussion

7533.	What fraction of the given image is dehighlighted?
Answer» What fraction of the given image is dehighlighted?

Discussion

7534.	For √3x2 to be irrational, x should be
Answer» For $\sqrt{3} x^{2}$ to be irrational, x should be

Discussion

7535.	AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of ∠FEB. If ∠LEB = 35°, then ∠CFQ will be(a) 55°(b) 70°(c) 110°(d) 130°
Answer» AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of ∠FEB. If ∠LEB = 35°, then ∠CFQ will be (a) 55° (b) 70° (c) 110° (d) 130°

Discussion

7536.	Find the zeroes of the polynomial x²-2x-1.
Answer» Find the zeroes of the polynomial x²-2x-1.

Discussion

7537.	A(6,1) B(8,2) and C(9,4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, then find the area of Δ ADE.
Answer» A(6,1) B(8,2) and C(9,4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, then find the area of $Δ$ ADE.

Discussion

7538.	A rectangular sheet of paper 30cm×18cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling, it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.
Answer» A rectangular sheet of paper $30 c m \times 18 c m$ can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling, it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.

Discussion

7539.	Question 6 (ii) A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. (ii) How much of tape is needed for all the 12 edges?
Answer» Question 6 (ii) A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. (ii) How much of tape is needed for all the 12 edges?

Discussion

7540.	35. If the curve ax+bxy+cxy+dy=0 intersects the given line (which passes through a point P) at three points A, B & C, then find PA.PB.PC (product of distance of A,B & C from P).The coordinates of P are (1,1).
Answer» 35. If the curve ax+bxy+cxy+dy=0 intersects the given line (which passes through a point P) at three points A, B & C, then find PA.PB.PC (product of distance of A,B & C from P).The coordinates of P are (1,1).

Discussion

7541.	Find product of 2xy²z,7xyz,8xyz²
Answer» Find product of 2xy²z,7xyz,8xyz²

Discussion

7542.	Find the percentage increase in the area of a triangle if each side is increased by N times.
Answer» Find the percentage increase in the area of a triangle if each side is increased by N times.

Discussion

7543.	A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Answer» A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Discussion

7544.	The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 150 times. What is the probability that the forecast is correct on any given day?
Answer» The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 150 times. What is the probability that the forecast is correct on any given day?

Discussion

7545.	On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m (∠ACB) and m (∠ABC).
Answer» On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m (∠ACB) and m (∠ABC).

Discussion

7546.	Equation of the circle which touches the coordinate axes and passes through the point (2,1) is
Answer» Equation of the circle which touches the coordinate axes and passes through the point (2,1) is

Discussion

7547.	Which of the following lines passes through the origin?
Answer» Which of the following lines passes through the origin?

Discussion

7548.	Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:x2+3x+1,3x4+5x3−7x2+2x+2
Answer» Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

7548.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:x2+3x+1,3x4+5x3−7x2+2x+2

Answer»

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

Discussion

7549.	Question 7O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ΔOCD is an isosceles triangle.
Answer» Question 7 O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that $Δ O C D$ is an isosceles triangle.

Discussion

7550.	If x=0.¯¯¯¯¯¯18, which of the following statements are true?(i) 100x=18.¯¯¯¯¯¯18 (ii) 100x−x=17.¯¯¯¯¯¯18(iii) 99x=18
Answer» If $x = 0. ¯ ¯¯¯¯ ¯ 18$ , which of the following statements are true? (i) $100 x = 18. ¯ ¯¯¯¯ ¯ 18$ (ii) $100 x - x = 17. ¯ ¯¯¯¯ ¯ 18$ (iii) $99 x = 18$

Discussion

Explore topic-wise InterviewSolutions in .

The linear equation 5x+12y=48 cuts the x-axis at

Factorise:2x2-x+18

State which statement is/are true of the following figure.

Question 5 Write True or False and justify your answer : In the figure, ABCD and EFGD are two parallelograms and G is the midpoint of CD. Then, ar(ΔDPC)=ar12(EFGD).

Question 2Find three rational numbers between(i) -1 and -2(ii) 0.1 and 0.11(iii) 57 and 67(iv) 14 and 15Thinking processUse the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x&lt;y and n =3

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS. Statement 1: SX=XY Statement 2: XY=QY

Consider a circle with center O. Let AB, BC CD be three chords of the circle such that O lies inside the quadrilateral ABCD (one need not join DA). Let BC = CD= 2AB. Also, let E be a point on minor arc BC such that

(i) In the given figure, if AB || CD, find the value of x.(ii) In the given figure, If AB || CD, find the value of x.(iii) In the given figure, AB || CD, If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, find x.

If an+1+bn+1an+bn represents arithmetic mean, geometric mean, harmonic mean between two distinct positive numbers a and b for n=α,β,γ respectively, then the equation whose roots are α,2β,γ is

23. Prove by contradiction method that there are infinitly many prime numbers.

Question 1 (v) Without actually performing the long division, state whether 29343 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

How to find the irrational numbers between two given numbers

The perimeter of a right triangle is 60 cm and it's hypotenuse is 25 cm l. Find the area of the triangle

In the given figure, if l1 || l2, what is x + y in terms of w and z?(a) 180 − w + z(b) 180 + w − z(c) 180 − w − z(d) 180 + w + z

The largest value in the range of f(x)=2(a-x)(x+\sqrt{x^2+b^2}), x∈ R is (1) a^2+2b^2 (2) 2a^2+b^2 (3) a^2+b^2 (4) a^2-b^2

In figure lines l1 and l2 intersect at O, forming angles as shown in the figure.If a=35∘, find the values of b, c and d. [3 MARKS]

Question 1 (iv)Does the following figure lie on the same base and between the same parallels? If yes,write the common base and two parallels.

prove that a positive integer n is prime number if no prime p less than or equal to root n divides n

The width of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. Find the upper class limit of the highest class.

In the adjoining figure, the value of ∠A+∠B+∠C+∠D+∠E+∠F in degrees is ___

P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. If AD = 10 cm, then CD =(a) 5 cm(b) 6 cm(c) 8 cm(d) 10 cm

In the following figures, ABCD is a parallelogram. A circle through A, B, C intersects CD or CD produced at E. Prove that AE = AD.

If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary rise to maintain the same standard of living if the CPI is 400?

In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ? (a) 12AB (b) 12CD (c) 12(AB+CD) (d) 12(AB−CD)

The volume of a 4 inches wide and 3 inches high box is 36 cubic inches, what is its length?

An equilateral triangle ABC is inscribed in a circle of radius 8 cm, which is centered at O, as shown below. Then the length of the side of this triangle is equal to

In ∆ LMN, LM = 7.2 cm, ∠M = 105° , MN = 6.4 cm , then draw ∆ LMN and construct its circumcircle.

In the following figure, PQRS is a square of side 4 cm. Find the area of the shaded square.

Rationalize the denominator of 12−√3

What fraction of the given image is dehighlighted?

For √3x2 to be irrational, x should be

AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of ∠FEB. If ∠LEB = 35°, then ∠CFQ will be(a) 55°(b) 70°(c) 110°(d) 130°

Find the zeroes of the polynomial x²-2x-1.

A(6,1) B(8,2) and C(9,4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, then find the area of Δ ADE.

A rectangular sheet of paper 30cm×18cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling, it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.

Question 6 (ii) A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. (ii) How much of tape is needed for all the 12 edges?

35. If the curve ax+bxy+cxy+dy=0 intersects the given line (which passes through a point P) at three points A, B & C, then find PA.PB.PC (product of distance of A,B & C from P).The coordinates of P are (1,1).

Find product of 2xy²z,7xyz,8xyz²

Find the percentage increase in the area of a triangle if each side is increased by N times.

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 150 times. What is the probability that the forecast is correct on any given day?

On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m (∠ACB) and m (∠ABC).

Equation of the circle which touches the coordinate axes and passes through the point (2,1) is

Which of the following lines passes through the origin?

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:x2+3x+1,3x4+5x3−7x2+2x+2

Question 7O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ΔOCD is an isosceles triangle.

If x=0.¯¯¯¯¯¯18, which of the following statements are true?(i) 100x=18.¯¯¯¯¯¯18 (ii) 100x−x=17.¯¯¯¯¯¯18(iii) 99x=18

Question 2Find three rational numbers between(i) -1 and -2(ii) 0.1 and 0.11(iii) 57 and 67(iv) 14 and 15Thinking processUse the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x<y and n =3