32581 + Interview Questions in Mathematics Page 221 InterviewSolution

11001.	Question 100The actual length of a painting was 2 m. What is the length of the photograph if the scale used is 1 mm : 20 cm.
Answer» Question 100 The actual length of a painting was 2 m. What is the length of the photograph if the scale used is 1 mm : 20 cm.

Discussion

11002.	Question 1 (v) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. t2−15
Answer» Question 1 (v) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. $t^{2} - 15$

11002.

Question 1 (v) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. t2−15

Answer»

Question 1 (v)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$t^{2} - 15$

Discussion

11003.	Find two rational and two irrational numbers between 1.3 and 1.4
Answer» Find two rational and two irrational numbers between 1.3 and 1.4

Discussion

11004.	A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]
Answer» A conical tent is 10 m high and the radius of its base is 24 m. Find (i) Slant height of the tent. (ii) Cost of the canvas required to make the tent, if the cost of $1 m^{2}$ canvas is Rs 70. $[A s s u m e π = \frac{22}{7}]$

Discussion

11005.	solve for x : (x-2) (x-4) < 0
Answer» solve for x : (x-2) (x-4) < 0

Discussion

11006.	Find the rth term of an A.P., the sum of whose first n terms is 3n2 + 2n. [NCERT EXEMPLAR]
Answer» Find the rth term of an A.P., the sum of whose first n terms is 3n² + 2n. [NCERT EXEMPLAR]

Discussion

11007.	Find two consecutive positive odd numbers, the sum of whose squares is 74.
Answer» Find two consecutive positive odd numbers, the sum of whose squares is 74.

Discussion

11008.	If θ=30o,verify that: (i) tan 2 θ=2 tan θ1−tan2 θ (ii) sin 2θ=2 tan θ1+tan2 θ (iii) cos2 θ=1−tan2 θ1+tan2 θ (iv) cos3θ=4 cos3 θ−3 cos θ
Answer» If $θ = 30^{o}$ ,verify that: (i) $t a n 2 θ = \frac{2 t a n θ}{1 - t a n^{2} θ}$ (ii) $s i n 2 θ = \frac{2 t a n θ}{1 + t a n^{2} θ}$ (iii) $c o s 2 θ = \frac{1 - t a n^{2} θ}{1 + t a n^{2} θ}$ (iv) $c o s 3 θ = 4 c o s^{3} θ - 3 c o s θ$

11008.

If θ=30o,verify that: (i) tan 2 θ=2 tan θ1−tan2 θ (ii) sin 2θ=2 tan θ1+tan2 θ (iii) cos2 θ=1−tan2 θ1+tan2 θ (iv) cos3θ=4 cos3 θ−3 cos θ

Answer»

If $θ = 30^{o}$ ,verify that:

(i) $t a n 2 θ = \frac{2 t a n θ}{1 - t a n^{2} θ}$

(ii) $s i n 2 θ = \frac{2 t a n θ}{1 + t a n^{2} θ}$

(iii) $c o s 2 θ = \frac{1 - t a n^{2} θ}{1 + t a n^{2} θ}$

(iv) $c o s 3 θ = 4 c o s^{3} θ - 3 c o s θ$

Discussion

11009.	If the sum of first n terms of an A.P. is 12(3n2 + 7n), then find its nth term. Hence write its 20th term.
Answer» If the sum of first n terms of an A.P. is $\frac{1}{2}$ (3n² + 7n), then find its n^th term. Hence write its 20^th term.

Discussion

11010.	If a,b,c are in AP then show that 3a , 3b , 3c are in GP
Answer» If a,b,c are in AP then show that 3^a, 3^b , 3^c are in GP

Discussion

11011.	In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:x − 3y = 33x − 9y = 2
Answer» In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it: x − 3y = 3 3x − 9y = 2

Discussion

11012.	The ratio of the length of a rod and its shadow is 1: √3. The angle of elevation of the sun is
Answer» The ratio of the length of a rod and its shadow is 1: √3. The angle of elevation of the sun is

Discussion

11013.	Question 2A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6
Answer» Question 2 A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ? (a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6

11013.

Question 2A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6

Answer»

Question 2

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?

(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6

Discussion

11014.	The ratio between the radius of base and the height of a cylinder is 2 : 3. If its volume is 1617 cm3, the total surface area of the cylinder is _________.
Answer» The ratio between the radius of base and the height of a cylinder is 2 : 3. If its volume is 1617 cm³, the total surface area of the cylinder is _________.

Discussion

11015.	Find the quotient and remainder when:fx=x4-3x2+4x+5 is divided by gx=x2+1-x
Answer» Find the quotient and remainder when: $f (x) = x^{4} - 3 x^{2} + 4 x + 5$ is divided by $g (x) = x^{2} + 1 - x$

Discussion

11016.	The integer k for which the inequality x2−2(4k−1)x+15k2-2k−7>0 is valid for any x, is?
Answer» The integer k for which the inequality x²−2(4k−1)x+15k²-2k−7>0 is valid for any x, is?

11016.

The integer k for which the inequality x2−2(4k−1)x+15k2-2k−7>0 is valid for any x, is?

Answer»

The integer k for which the inequality

x²−2(4k−1)x+15k²-2k−7>0 is valid for any x, is?

Discussion

11017.	If α,β,γ are the zeroes of the cubic polynomial ax3+bx2+cx+d = 0, then α+β+γ equals to:
Answer» If $α, β, γ$ are the zeroes of the cubic polynomial a $x^{3}$ +b $x^{2}$ +cx+d = 0, then $α + β + γ$ equals to:

Discussion

11018.	The solution for the equations c1x + b1y + a1 = 0 and c2x + b2y + a2 = 0 is S1 : x = (b1a2–b2a1)(c1b2−c2b1) S2 : y = (c1a2–c2a1)(a1b2−a2b1)
Answer» The solution for the equations $c_{1}$ x + $b_{1}$ y + $a_{1}$ = 0 and $c_{2}$ x + $b_{2}$ y + $a_{2}$ = 0 is S1 : x = $\frac{(b_{1} a_{2} - b_{2} a_{1})}{(c_{1} b_{2} - c_{2} b_{1})}$ S2 : y = $\frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$

11018.

The solution for the equations c1x + b1y + a1 = 0 and c2x + b2y + a2 = 0 is S1 : x = (b1a2–b2a1)(c1b2−c2b1) S2 : y = (c1a2–c2a1)(a1b2−a2b1)

Answer»

The solution for the equations $c_{1}$ x + $b_{1}$ y + $a_{1}$ = 0 and $c_{2}$ x + $b_{2}$ y + $a_{2}$ = 0 is

S1 : x = $\frac{(b_{1} a_{2} - b_{2} a_{1})}{(c_{1} b_{2} - c_{2} b_{1})}$

S2 : y = $\frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$

Discussion

11019.	In an equilateral triangle ABC , D is a point on side BC, such that BD =1/3 BC. Prove that 9AD square = 7 AB square.
Answer» In an equilateral triangle ABC , D is a point on side BC, such that BD =1/3 BC. Prove that 9AD square = 7 AB square.

Discussion

11020.	A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.
Answer» A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Discussion

11021.	Solve for x, y and z in the given system of equations using Elimination :x=3z−52x+2z=y+167x−5z=3y+19
Answer» Solve for x, y and z in the given system of equations using Elimination : $x = 3 z - 5 2 x + 2 z = y + 16 7 x - 5 z = 3 y + 19$

Discussion

11022.	Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is.(a) 13 (b) 16 (c) 27 (d) 12
Answer» Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is. (a) $\frac{1}{3}$ (b) $\frac{1}{6}$ (c) $\frac{2}{7}$ (d) $\frac{1}{2}$

Discussion

11023.	Question 15A ladder against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p, so that is upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that pq=cos β−cos αsin α−sin β
Answer» Question 15 A ladder against a vertical wall at an inclination $α$ to the horizontal. Its foot is pulled away from the wall through a distance p, so that is upper end slides a distance q down the wall and then the ladder makes an angle $β$ to the horizontal. Show that $\frac{p}{q} = \frac{c o s β - c o s α}{s i n α - s i n β}$

Discussion

11024.	If 45, a, 2 are three consecutive terms of an A.P., then find the value of a.
Answer» If $\frac{4}{5}$ , a, 2 are three consecutive terms of an A.P., then find the value of a.

Discussion

11025.	In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.
Answer» In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

Discussion

11026.	Find the volume of the cylinder whose radius is 5 cm and height is 28 cm.
Answer» Find the volume of the cylinder whose radius is 5 cm and height is 28 cm.

Discussion

11027.	If D is a point on the side BC of a triangle ABC such that ∠ADC=∠BAC then, CA2 = _____.
Answer» If D is a point on the side BC of a triangle ABC such that $∠ A D C = ∠ B A C$ then, $C A^{2}$ = _____.

Discussion

11028.	A man spends Rs.2210 and saves 15% of his income. Find his income.
Answer» A man spends Rs.2210 and saves 15% of his income. Find his income.

Discussion

11029.	9. Two tangent segments BC and BD are drawn to a circle with centre O such that angle CBD =120^° . Prove that OB =2BC
Answer» 9. Two tangent segments BC and BD are drawn to a circle with centre O such that angle CBD =120^° . Prove that OB =2BC

Discussion

11030.	Find five rational numbers between 2/3and 4/5
Answer» Find five rational numbers between 2/3and 4/5

Discussion

11031.	Using prime factorization, find the HCF and LCM of:(i) 8, 9, 25(ii) 12, 15, 21(iii) 17, 23, 29(iv) 24, 36, 40(v) 30, 72, 432(vi) 21, 28, 36
Answer» Using prime factorization, find the HCF and LCM of: (i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29 (iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36

Discussion

11032.	Show that 3+2 is an irrational number.
Answer» Show that $3 + \sqrt{2}$ is an irrational number.

Discussion

11033.	If A=[0110], then A4=__________________
Answer» If $A = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}]$ , then $A^{4}$ =__________________

Discussion

11034.	If the product of zeros of the polynomial f(x) ax3 − 6x2 + 11x − 6 is 4, then a =(a) 32(b) -32(c) 23(d) -23
Answer» If the product of zeros of the polynomial f(x) ax³ − 6x² + 11x − 6 is 4, then a = (a) $\frac{3}{2}$ (b) $- \frac{3}{2}$ (c) $\frac{2}{3}$ (d) $- \frac{2}{3}$

Discussion

11035.	x^2+1/x^2=5 Check whether it is a quadratic or not
Answer» x^2+1/x^2=5 Check whether it is a quadratic or not

Discussion

11036.	In the figure below, the lines AB, BC, CA touch the circle at P, Q, R.Prove that the perimeter of the triangle is 2(AP + BQ + CR)
Answer» In the figure below, the lines AB, BC, CA touch the circle at P, Q, R. Prove that the perimeter of the triangle is 2(AP + BQ + CR)

11036.

In the figure below, the lines AB, BC, CA touch the circle at P, Q, R.Prove that the perimeter of the triangle is 2(AP + BQ + CR)

Answer»

In the figure below, the lines AB, BC, CA touch the circle at P, Q, R.

Prove that the perimeter of the triangle is 2(AP + BQ + CR)

Discussion

11037.	A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.
Answer» A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

Discussion

11038.	Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are -
Answer» Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are -

Discussion

11039.	The units' digit of a two digit number is thrice its tens digit. If 36 is added to the number, the digits interchange their place. Find the number.
Answer» The units' digit of a two digit number is thrice its tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

Discussion

11040.	If A = {2, 3, 5, 6}, B = {4, 8, 15, 17} and a R b ⇒ a divides b. Find domain and range of the relation R.
Answer» If A = {2, 3, 5, 6}, B = {4, 8, 15, 17} and a R b $\Rightarrow$ a divides b. Find domain and range of the relation R.

Discussion

11041.	Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).
Answer» Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).

Discussion

11042.	The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides (in cm).
Answer» The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides (in cm).

Discussion

11043.	Question2 (ii)Are the following statements ‘True’ or False’? Justify your answer.ii) If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial
Answer» Question2 (ii) Are the following statements ‘True’ or False’? Justify your answer. ii) If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial

Discussion

11044.	In figure, BC is the diameter of the circle and ∠ABC=380 then ∠BAP is
Answer» In figure, BC is the diameter of the circle and $∠ A B C = 38^{0}$ then $∠ B A P$ is

Discussion

11045.	Question 1 (iii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(iii) 5t2+12t+7
Answer» Question 1 (iii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (iii) $5 t^{2} + 12 t + 7$

Discussion

11046.	If the vertices of ∆ABC be A(1, −3), B(4, p) and C(−9, 7) and its area is 15 square units, find the values of p.
Answer» If the vertices of $∆ A B C$ be A(1, −3), B(4, p) and C(−9, 7) and its area is 15 square units, find the values of p.

Discussion

11047.	29. If A(9,9),(1,-3) are the end points of hypotenus of a right angled isosceles triangle, then the vertex is. A) (8,-2) B) (-8,2) C) (8,-8) D) (0,0)
Answer» 29. If A(9,9),(1,-3) are the end points of hypotenus of a right angled isosceles triangle, then the vertex is. A) (8,-2) B) (-8,2) C) (8,-8) D) (0,0)

Discussion

11048.	The value of x in log2 (x+2)=3 is
Answer» The value of $x$ in $l o g_{2} (x + 2) = 3$ is

Discussion

11049.	Question 2(v) Express the following numbers in usual form: 5.8×1012
Answer» Question 2(v) Express the following numbers in usual form: $5.8 \times 10^{12}$

Discussion

11050.

Following are the transactions of R.Singh & Co., Kanpur (UP) for the month of July, 2018. You are required to Journalise them: 2018 July 1 July 1 July 1 July 2 July 5 July 6 July 11 July 12 July 16 July 20 July 23 July 26 July 28 July 31 Started business with cash Cash paid into bank Bought stationery of ₹ 300 plus CGST and SGST 6% each Bought goods of ₹ 21,000 plus CGST and SGST 6% each Sold goods of ₹ 7,500 plus CGST and SGST 6% each Bought office furniture of ₹ 5,000 plus CGST and SGST 6% each from Banerjee Bros. Sold goods of ₹ 10,000 plus CGST and SGST 6% each to Mahendra Received cheque from Mahendra for the amount due Sold goods of ₹ 5,000 plus CGST and SGST 6% each to Ramesh & Co. Bought goods of ₹ 20,000 plus IGST 12% from S. Seth & Bros., Delhi Bought goods of ₹ 2,250 plus IGST 12 % for cash from S. Narain & Co., Ludhiana (Punjab) Ramesh & Co. paid on account Paid to S. Seth & Bros. by cheque in full settlement Rent is due to S. Sharma but not yet paid. ₹ 80,000 50,000 2,500 22,000 1,000

Answer» Following are the transactions of R.Singh & Co., Kanpur (UP) for the month of July, 2018. You are required to Journalise them:

2018

July 1

July 1

July 1

July 2

July 5

July 6

July 11

July 12

July 16

July 20

July 23

July 26

July 28

July 31

Started business with cash

Cash paid into bank

Bought stationery of ₹ 300 plus CGST and SGST 6% each

Bought goods of ₹ 21,000 plus CGST and SGST 6% each

Sold goods of ₹ 7,500 plus CGST and SGST 6% each

Bought office furniture of ₹ 5,000 plus CGST and SGST 6% each from Banerjee Bros.

Sold goods of ₹ 10,000 plus CGST and SGST 6% each to Mahendra

Received cheque from Mahendra for the amount due

Sold goods of ₹ 5,000 plus CGST and SGST 6% each to Ramesh & Co.

Bought goods of ₹ 20,000 plus IGST 12% from S. Seth & Bros., Delhi

Bought goods of ₹ 2,250 plus IGST 12 % for cash from S. Narain & Co., Ludhiana (Punjab)

Ramesh & Co. paid on account

Paid to S. Seth & Bros. by cheque in full settlement

Rent is due to S. Sharma but not yet paid.

₹ 80,000

50,000

2,500

22,000

1,000

Discussion

Explore topic-wise InterviewSolutions in .

Question 100The actual length of a painting was 2 m. What is the length of the photograph if the scale used is 1 mm : 20 cm.

Question 1 (v) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. t2−15

Find two rational and two irrational numbers between 1.3 and 1.4

A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]

solve for x : (x-2) (x-4) &lt; 0

Find the rth term of an A.P., the sum of whose first n terms is 3n2 + 2n. [NCERT EXEMPLAR]

Find two consecutive positive odd numbers, the sum of whose squares is 74.

If θ=30o,verify that: (i) tan 2 θ=2 tan θ1−tan2 θ (ii) sin 2θ=2 tan θ1+tan2 θ (iii) cos2 θ=1−tan2 θ1+tan2 θ (iv) cos3θ=4 cos3 θ−3 cos θ

If the sum of first n terms of an A.P. is 12(3n2 + 7n), then find its nth term. Hence write its 20th term.

If a,b,c are in AP then show that 3a , 3b , 3c are in GP

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:x − 3y = 33x − 9y = 2

The ratio of the length of a rod and its shadow is 1: √3. The angle of elevation of the sun is

Question 2A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6

The ratio between the radius of base and the height of a cylinder is 2 : 3. If its volume is 1617 cm3, the total surface area of the cylinder is _________.

Find the quotient and remainder when:fx=x4-3x2+4x+5 is divided by gx=x2+1-x

The integer k for which the inequality x2−2(4k−1)x+15k2-2k−7&gt;0 is valid for any x, is?

If α,β,γ are the zeroes of the cubic polynomial ax3+bx2+cx+d = 0, then α+β+γ equals to:

The solution for the equations c1x + b1y + a1 = 0 and c2x + b2y + a2 = 0 is S1 : x = (b1a2–b2a1)(c1b2−c2b1) S2 : y = (c1a2–c2a1)(a1b2−a2b1)

In an equilateral triangle ABC , D is a point on side BC, such that BD =1/3 BC. Prove that 9AD square = 7 AB square.

A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Solve for x, y and z in the given system of equations using Elimination :x=3z−52x+2z=y+167x−5z=3y+19

Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is.(a) 13 (b) 16 (c) 27 (d) 12

Question 15A ladder against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p, so that is upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that pq=cos β−cos αsin α−sin β

If 45, a, 2 are three consecutive terms of an A.P., then find the value of a.

In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

Find the volume of the cylinder whose radius is 5 cm and height is 28 cm.

If D is a point on the side BC of a triangle ABC such that ∠ADC=∠BAC then, CA2 = _____.

A man spends Rs.2210 and saves 15% of his income. Find his income.

9. Two tangent segments BC and BD are drawn to a circle with centre O such that angle CBD =120^° . Prove that OB =2BC

Find five rational numbers between 2/3and 4/5

Using prime factorization, find the HCF and LCM of:(i) 8, 9, 25(ii) 12, 15, 21(iii) 17, 23, 29(iv) 24, 36, 40(v) 30, 72, 432(vi) 21, 28, 36

Show that 3+2 is an irrational number.

If A=[0110], then A4=__________________

If the product of zeros of the polynomial f(x) ax3 − 6x2 + 11x − 6 is 4, then a =(a) 32(b) -32(c) 23(d) -23

x^2+1/x^2=5 Check whether it is a quadratic or not

In the figure below, the lines AB, BC, CA touch the circle at P, Q, R.Prove that the perimeter of the triangle is 2(AP + BQ + CR)

A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are -

The units' digit of a two digit number is thrice its tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

If A = {2, 3, 5, 6}, B = {4, 8, 15, 17} and a R b ⇒ a divides b. Find domain and range of the relation R.

Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides (in cm).

Question2 (ii)Are the following statements ‘True’ or False’? Justify your answer.ii) If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial

In figure, BC is the diameter of the circle and ∠ABC=380 then ∠BAP is

Question 1 (iii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(iii) 5t2+12t+7

If the vertices of ∆ABC be A(1, −3), B(4, p) and C(−9, 7) and its area is 15 square units, find the values of p.

29. If A(9,9),(1,-3) are the end points of hypotenus of a right angled isosceles triangle, then the vertex is. A) (8,-2) B) (-8,2) C) (8,-8) D) (0,0)

The value of x in log2 (x+2)=3 is

Question 2(v) Express the following numbers in usual form: 5.8×1012

solve for x : (x-2) (x-4) < 0

The integer k for which the inequality x2−2(4k−1)x+15k2-2k−7>0 is valid for any x, is?