24740 + Interview Questions in Mathematics Page 144 InterviewSolution

7151.	Find the values of a and bif 5+2√37+4√3=a+b√3
Answer» Find the values of $a$ and $b$ if $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

7151.

Find the values of a and bif 5+2√37+4√3=a+b√3

Answer»

Find the values of $a$ and $b$

if $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

7152.	Mode is:
Answer» Mode is:

Discussion

7153.	The diameter of the roller 1.5 m long is 84 cm if it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre. (m2)
Answer» The diameter of the roller $1.5 m$ long is $84 c m$ if it takes $100$ revolutions to level a playground, find the cost of levelling this ground at the rate of $50$ paise per square metre. $(m^{2})$

Discussion

7154.	If ax = by. Find the value of xy
Answer» If $a^{x}$ = $b^{y}$ . Find the value of $\frac{x}{y}$

Discussion

7155.	140.if tan(α +β )=1/2, tanα =1/3. find tanβ
Answer» 140.if tan(α +β )=1/2, tanα =1/3. find tanβ

Discussion

7156.	In a quadrilateral ABCD, show that (AB + BC + CD + DA) > (AC + BD).
Answer» In a quadrilateral ABCD, show that (AB + BC + CD + DA) > (AC + BD).

Discussion

7157.	Factorise:x2+76x+60
Answer» Factorise: $x^{2} + 7 \sqrt{6} x + 60$

Discussion

7158.	Which of the following is an irrational number?
Answer» Which of the following is an irrational number?

Discussion

7159.	If we know that one side of a rectangle is 8 cm, can we construct a unique rectangle?
Answer» If we know that one side of a rectangle is 8 cm, can we construct a unique rectangle?

Discussion

7160.	Which of the following are in inverse proportion?(i) The number of workers on a job and the time to complete the job.(ii) The time taken for a journey and the distance travelled in a uniform speed.(iii) Area of cultivated land and the crop harvested.(iv) The time taken for a fixed journey and the speed of the vehicle.(v) The population of a country and the area of land per person.
Answer» Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.

Discussion

7161.	Examine if the following are true statements:(i) The cube can cast a shadow in the shape of a rectangle.(ii) The cube can cast a shadow in the shape of a hexagon.
Answer» Examine if the following are true statements: (i) The cube can cast a shadow in the shape of a rectangle. (ii) The cube can cast a shadow in the shape of a hexagon.

Discussion

7162.	In the figure, if CP \|\| DQ, then the measure of x is
Answer» In the figure, if CP \|\| DQ, then the measure of x is

7162.

In the figure, if CP || DQ, then the measure of x is

Answer»

In the figure, if CP || DQ, then the measure of x is

Discussion

7163.	Which property do we use to construct a parallelogram given its sides and one diagonal?
Answer» Which property do we use to construct a parallelogram given its sides and one diagonal?

Discussion

7164.	Find 3x2y×4xy2×7x3y3
Answer» Find $3 x^{2} y \times 4 x y^{2} \times 7 x^{3} y^{3}$

Discussion

7165.	Question 6 (ii)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(ii) ar(DCB) = ar(ACB)
Answer» Question 6 (ii) In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (ii) ar(DCB) = ar(ACB)

Discussion

7166.	Find three different irrational numbers between the rational numbers 57 and 911.
Answer» Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$ .

Discussion

7167.	If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
Answer» If the volume of a right circular cone of height 9 cm is 48 $π$ cm³, find the diameter of its base.

Discussion

7168.	Question 5The point (3,4) is at a distance of(a) 3 from both the axes(b) 4 from both the axes(c) 4 from the X-axis and 3 from the Y-axis(d) 3 from the X-axis and from the Y-axis
Answer» Question 5 The point (3,4) is at a distance of (a) 3 from both the axes (b) 4 from both the axes (c) 4 from the X-axis and 3 from the Y-axis (d) 3 from the X-axis and from the Y-axis

Discussion

7169.	The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall in cm.40
Answer» $The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu . meters . Find the breadth of the wall in cm .$ 40

7169.

The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall in cm.40

Answer»

$The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu . meters . Find the breadth of the wall in cm .$

40

Discussion

7170.	Which of the following options can be a solution of 6x ≡ 3(mod 13).
Answer» Which of the following options can be a solution of $6 x$ $\equiv$ $3 (mod 13)$ .

Discussion

7171.	The value of x for which \|x−2\|+\|x−8\|=10 is
Answer» The value of x for which $\| x - 2 \| + \| x - 8 \| = 10$ is

Discussion

7172.	if sides of a triangle are in the ratio 1:2: square root of 5, what will be the ration of their angles opposite to the corresponding sides?
Answer» if sides of a triangle are in the ratio 1:2: square root of 5, what will be the ration of their angles opposite to the corresponding sides?

Discussion

7173.	Question 14(i)50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :Distance (inm)0−2020−4040−6060−8080−100Number of students 6 11 17 12 4Construct a cumulative frequency table.
Answer» Question 14(i) 50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below : $\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$ Construct a cumulative frequency table.

Discussion

7174.	Prove that a2 + b2 + c2 −ab−bc−ca is always non-negative for all values of a, b, and c.
Answer» Prove that a² + b² + c² −ab−bc−ca is always non-negative for all values of a, b, and c.

Discussion

7175.	Question 110State whether the statements are True or False.Diagonals of a rhombus are equal and perpendicular to each other.
Answer» Question 110 State whether the statements are True or False. Diagonals of a rhombus are equal and perpendicular to each other.

Discussion

7176.	If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.
Answer» If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

Discussion

7177.	Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?
Answer» Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?

Discussion

7178.	Simplify √12121
Answer» Simplify $\sqrt{\frac{12}{121}}$

Discussion

7179.	Which of the following statements are true ? (i) A line segment has no definite length. (ii) A ray has no end point. (iii) A line has a definite length. (iv) A line ↔AB is the same as line ↔BA. (v) A ray →AB is the same as ray →BA. (vi) Two distinct points always determine a unique line. (vii) Three lines are concurrent if they have a common point. (viii) Two distinct lines cannot have more than one point in common. (ix) Two intersecting lines cannot both be parallel to the same line. (x) Open half-line is the same thing as ray. (xi) Two lines may intersect in two points. (xii) Two lines are parallel only when they have no point in common.
Answer» Which of the following statements are true ? (i) A line segment has no definite length. (ii) A ray has no end point. (iii) A line has a definite length. (iv) A line $\leftrightarrow A B$ is the same as line $\leftrightarrow B A$ . (v) A ray $\to A B$ is the same as ray $\to B A$ . (vi) Two distinct points always determine a unique line. (vii) Three lines are concurrent if they have a common point. (viii) Two distinct lines cannot have more than one point in common. (ix) Two intersecting lines cannot both be parallel to the same line. (x) Open half-line is the same thing as ray. (xi) Two lines may intersect in two points. (xii) Two lines are parallel only when they have no point in common.

7179.

Which of the following statements are true ? (i) A line segment has no definite length. (ii) A ray has no end point. (iii) A line has a definite length. (iv) A line ↔AB is the same as line ↔BA. (v) A ray →AB is the same as ray →BA. (vi) Two distinct points always determine a unique line. (vii) Three lines are concurrent if they have a common point. (viii) Two distinct lines cannot have more than one point in common. (ix) Two intersecting lines cannot both be parallel to the same line. (x) Open half-line is the same thing as ray. (xi) Two lines may intersect in two points. (xii) Two lines are parallel only when they have no point in common.

Answer»

Which of the following statements are true ?

(i) A line segment has no definite length.

(ii) A ray has no end point.

(iii) A line has a definite length.

(iv) A line $\leftrightarrow A B$ is the same as line $\leftrightarrow B A$ .

(v) A ray $\to A B$ is the same as ray $\to B A$ .

(vi) Two distinct points always determine a unique line.

(vii) Three lines are concurrent if they have a common point.

(viii) Two distinct lines cannot have more than one point in common.

(ix) Two intersecting lines cannot both be parallel to the same line.

(x) Open half-line is the same thing as ray.

(xi) Two lines may intersect in two points.

(xii) Two lines are parallel only when they have no point in common.

Discussion

7180.	The maximum resul†an t of 2 vector A and B(A≥ B) is n times their least resul†an t. If θ be the angle between the two vectors and their resul†an t is half of the sum of vector. Then show that Cosθ= -n^2+2/2(n^2-1
Answer» The maximum resul†an t of 2 vector A and B(A≥ B) is n times their least resul†an t. If θ be the angle between the two vectors and their resul†an t is half of the sum of vector. Then show that Cosθ= -n^2+2/2(n^2-1

Discussion

7181.	20. AD is an altitude of an equilateral triangle ABC . On AD as base , another equilateral triangle ADE is drawn . Prove that Ar(ΔABE):Ar(ΔABC)=3:4
Answer» 20. AD is an altitude of an equilateral triangle ABC . On AD as base , another equilateral triangle ADE is drawn . Prove that Ar(ΔABE):Ar(ΔABC)=3:4

Discussion

7182.	41, 43, 127, 99, 71, 92, 71, 58, 57
Answer» 41, 43, 127, 99, 71, 92, 71, 58, 57

Discussion

7183.	If ΔABC ≅ ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:(a) BC = PQ(b) AC = PR(c) AB = PQ(d) QR = BC
Answer» If ΔABC $≅$ ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true: (a) BC = PQ (b) AC = PR (c) AB = PQ (d) QR = BC

Discussion

7184.	What is the marks scored by most number of students?
Answer» What is the marks scored by most number of students?

Discussion

7185.	Question 3Solve the following pair of linear equations by the substitution and cross-multiplication methods:8x +5y = 93x +2y = 4
Answer» Question 3 Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x +5y = 9 3x +2y = 4

Discussion

7186.	Find, which of the following points lie on the line x - 2y + 5 = 0 :(i) (1, 3) (ii) (0, 5)(iii) (-5, 0) (iv) (5, 5)(v) (2, -1.5) (vi) (-2, -1.5)
Answer» Find, which of the following points lie on the line x - 2y + 5 = 0 : (i) (1, 3) (ii) (0, 5) (iii) (-5, 0) (iv) (5, 5) (v) (2, -1.5) (vi) (-2, -1.5)

7186.

Find, which of the following points lie on the line x - 2y + 5 = 0 :(i) (1, 3) (ii) (0, 5)(iii) (-5, 0) (iv) (5, 5)(v) (2, -1.5) (vi) (-2, -1.5)

Answer»

Find, which of the following points lie on the line x - 2y + 5 = 0 :

(i) (1, 3) (ii) (0, 5)

(iii) (-5, 0) (iv) (5, 5)

(v) (2, -1.5) (vi) (-2, -1.5)

Discussion

7187.	If a brick has length, breadth and height in the ratio 1 : 2 : 3 and the total surface area of the brick is 792 m2, then the volume of the brick is _______.
Answer» If a brick has length, breadth and height in the ratio 1 : 2 : 3 and the total surface area of the brick is 792 $m^{2}$ , then the volume of the brick is _______.

Discussion

7188.	If z is any complex numbers satisfying Iz - 3 - 2il 2, then theminimum value of \vert2z - 6 + 5i\rbrack is
Answer» If z is any complex numbers satisfying Iz - 3 - 2il 2, then theminimum value of \vert2z - 6 + 5i\rbrack is

Discussion

7189.

On 31st March, 2017 the following Trial Balance of Sh. Ajay Oswal was taken out. Prepare Trading and Profit & Loss Account for the year and Balance Sheet at that date after making the following adjustments:-(i) Stock on 31st March, 2017 was valued ₹ 26,000.(ii) General Manager is entitled to a Commission of 5% on Net Profits after charging such Commission.(iii) ₹ 2,000 paid for Salary & Wages have been included in Sundry Debtors.(iv) Increase Bad-debts by ₹ 800 and create provision for Doubtful Debts at 10%.(v) General Expenses include insurance premium paid up to 30th June, 2017 ₹ 3,000 per annum.(vi) ₹ 600 out of the Advertisement Expenses are to be carried forward to the next year.(vii) Charge one-fourth of 'Salaries and Wages' to Trading A/c.(viii) Accrued Income ₹ 2,500. Dr. (₹) Cr. (₹) Capital 3,00,000 Income Tax 8,000 - Stock on 1-4-2016 16,000 - Return Inwards 5,600 - Carriage Inwards 8,200 - Deposit with PNB 15,000 - Return Outwards - 4,100 Carriage Outwards 3,700 - Loan to Mr. Malik 18% p.a. given on 1-7-2016 10,000 - Interest on the above - 900 Rent 13,000 - Outstanding Rent - 1,000 Purchases 1,48,000 - Debtors 75,800 - Goodwill 25,000 - Land and Buildings 2,00,000 - Furniture 15,000 - Salaries & Wages 38,000 - Creditors - 26,200 Advertisement Expenses 3,000 - Provision for Doubtful Debts - 3,500 Bad-Debts 2,000 Patents and Patterns 6,000 Cash in hand 8,900 Sales - 2,70,000 General Expenses 4,500 - 6,05,700 6,05,700

Answer» On 31st March, 2017 the following Trial Balance of Sh. Ajay Oswal was taken out. Prepare Trading and Profit & Loss Account for the year and Balance Sheet at that date after making the following adjustments:-

(i) Stock on 31st March, 2017 was valued ₹ 26,000.

(ii) General Manager is entitled to a Commission of 5% on Net Profits after charging such Commission.

(iii) ₹ 2,000 paid for Salary & Wages have been included in Sundry Debtors.

(iv) Increase Bad-debts by ₹ 800 and create provision for Doubtful Debts at 10%.

(v) General Expenses include insurance premium paid up to 30th June, 2017 ₹ 3,000 per annum.

(vi) ₹ 600 out of the Advertisement Expenses are to be carried forward to the next year.

(vii) Charge one-fourth of 'Salaries and Wages' to Trading A/c.

(viii) Accrued Income ₹ 2,500.

	Dr. (₹)	Cr. (₹)
Capital		3,00,000
Income Tax	8,000	-
Stock on 1-4-2016	16,000	-
Return Inwards	5,600	-
Carriage Inwards	8,200	-
Deposit with PNB	15,000	-
Return Outwards	-	4,100
Carriage Outwards	3,700	-
Loan to Mr. Malik 18% p.a. given on 1-7-2016	10,000	-
Interest on the above	-	900
Rent	13,000	-
Outstanding Rent	-	1,000
Purchases	1,48,000	-
Debtors	75,800	-
Goodwill	25,000	-
Land and Buildings	2,00,000	-
Furniture	15,000	-
Salaries & Wages	38,000	-
Creditors	-	26,200
Advertisement Expenses	3,000	-
Provision for Doubtful Debts	-	3,500
Bad-Debts	2,000
Patents and Patterns	6,000
Cash in hand	8,900
Sales	-	2,70,000
General Expenses	4,500	-

	6,05,700	6,05,700

Discussion

7190.	The top view of the area occupied by a famous airport is given. This airport has three runways (paths where the planes take off or land) and many taxiways (paths that planes use to get to the runways).R1: 3x + 16y = 112 T1: 11y - 2x = 22R2: 6x + 5y = 30 T2: 3x + 16y = -kR3: 3x + 16y = 24The three runways, R1, R2, and R3, are shown in pink, and two of the taxiways, T1 and T2 are shown in blue.The point where R2 intersects T1 is:[1 mark]
Answer» The top view of the area occupied by a famous airport is given. This airport has three runways (paths where the planes take off or land) and many taxiways (paths that planes use to get to the runways). R1: 3x + 16y = 112 T1: 11y - 2x = 22 R2: 6x + 5y = 30 T2: 3x + 16y = -k R3: 3x + 16y = 24 The three runways, R1, R2, and R3, are shown in pink, and two of the taxiways, T1 and T2 are shown in blue. The point where R2 intersects T1 is: [1 mark]

Discussion

7191.	The median of the variables x+4,x−72,x−52, x−3,x−2,x+12,x−12 and x+5, where x>0, is:
Answer» The median of the variables $x + 4, x - \frac{7}{2}, x - \frac{5}{2}$ , $x - 3, x - 2, x + \frac{1}{2}, x - \frac{1}{2}$ and $x + 5$ , where $x > 0$ , is:

Discussion

7192.	The area of an isosceles trapezium is 34cm2 and the length of one of the parallel sides is 10 cm and Its height is 4 cm. Find the length of the other parallel side.
Answer» The area of an isosceles trapezium is $34 c m^{2}$ and the length of one of the parallel sides is 10 cm and Its height is 4 cm. Find the length of the other parallel side.

Discussion

7193.	In the given figure, O is the centre of the circle. If ∠ABD=35∘ and ∠BAC=70∘, find ∠ACB.
Answer» In the given figure, O is the centre of the circle. If $∠$ ABD=35 $^{\circ}$ and $∠$ BAC=70 $^{\circ}$ , find $∠$ ACB.

7193.

In the given figure, O is the centre of the circle. If ∠ABD=35∘ and ∠BAC=70∘, find ∠ACB.

Answer»

In the given figure, O is the centre of the circle. If $∠$ ABD=35 $^{\circ}$ and $∠$ BAC=70 $^{\circ}$ , find $∠$ ACB.

Discussion

7194.	A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30∘ to the ground whereas for elder children she wants to have a steep slide at a height of 3 m and inclined at an angle of 60∘ to the ground. What should be the length of the slide in each case?
Answer» A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of $30^{\circ}$ to the ground whereas for elder children she wants to have a steep slide at a height of 3 m and inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide in each case?

Discussion

7195.	Which among the following is a cubic polynomial?
Answer» Which among the following is a cubic polynomial?

Discussion

7196.	If A=x3,B=4x2+x−1,C=x+1, then find (A-B)(A-C)
Answer» If $A = x^{3}, B = 4 x^{2} + x - 1, C = x + 1$ , then find (A-B)(A-C)

Discussion

7197.	If x+y-z=4, 3x+ 3y+ z=12,(x+3y)^2 -z^{2 }=36, then find the value ofx.
Answer» If x+y-z=4, 3x+ 3y+ z=12,(x+3y)^2 -z^{2 }=36, then find the value ofx.

Discussion

7198.	Question 5 (iii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income(in Rs)Vehicles per family012Above 2Less than 7000101602507000−10000030527210000−13000153529113000−160002469592516000 or more15798288 Suppose a family is chosen, find the probability that the family chosen is (iii) earning less than Rs7000 per month and does not own any vehicle.
Answer» Question 5 (iii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: $\begin{matrix} Monthly income(in Rs) & Vehicles per family 0 & 1 & 2 & A b o v e 2 Less than 7000 & 10 & 160 & 25 & 0 7000 - 10000 & 0 & 305 & 27 & 2 10000 - 13000 & 1 & 535 & 29 & 1 13000 - 16000 & 2 & 469 & 59 & 25 16000 or more & 1 & 579 & 82 & 88 \end{matrix}$ Suppose a family is chosen, find the probability that the family chosen is (iii) earning less than Rs7000 per month and does not own any vehicle.

Discussion

7199.	Find the locus of a point which moves such that the sum of its distances from points a(0,0,-alpha) and b(0,0,alpha) is a constant equal to 2a
Answer» Find the locus of a point which moves such that the sum of its distances from points a(0,0,-alpha) and b(0,0,alpha) is a constant equal to 2a

Discussion

7200.

If one angle of a Parallelogram is 90 degrees, then it is a ______.

Answer»

If one angle of a Parallelogram is 90 degrees, then it is a ______.

Discussion

Explore topic-wise InterviewSolutions in .

Find the values of a and bif 5+2√37+4√3=a+b√3

Mode is:

The diameter of the roller 1.5 m long is 84 cm if it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre. (m2)

If ax = by. Find the value of xy

140.if tan(α +β )=1/2, tanα =1/3. find tanβ

In a quadrilateral ABCD, show that (AB + BC + CD + DA) > (AC + BD).

Factorise:x2+76x+60

Which of the following is an irrational number?

If we know that one side of a rectangle is 8 cm, can we construct a unique rectangle?

Examine if the following are true statements:(i) The cube can cast a shadow in the shape of a rectangle.(ii) The cube can cast a shadow in the shape of a hexagon.

In the figure, if CP || DQ, then the measure of x is

Which property do we use to construct a parallelogram given its sides and one diagonal?

Find 3x2y×4xy2×7x3y3

Question 6 (ii)In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:(ii) ar(DCB) = ar(ACB)

Find three different irrational numbers between the rational numbers 57 and 911.

If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.

Question 5The point (3,4) is at a distance of(a) 3 from both the axes(b) 4 from both the axes(c) 4 from the X-axis and 3 from the Y-axis(d) 3 from the X-axis and from the Y-axis

The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall in cm.40

Which of the following options can be a solution of 6x ≡ 3(mod 13).

The value of x for which |x−2|+|x−8|=10 is

if sides of a triangle are in the ratio 1:2: square root of 5, what will be the ration of their angles opposite to the corresponding sides?

Question 14(i)50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :Distance (inm)0−2020−4040−6060−8080−100Number of students 6 11 17 12 4Construct a cumulative frequency table.

Prove that a2 + b2 + c2 −ab−bc−ca is always non-negative for all values of a, b, and c.

Question 110State whether the statements are True or False.Diagonals of a rhombus are equal and perpendicular to each other.

If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?

Simplify √12121

The maximum resul†an t of 2 vector A and B(A≥ B) is n times their least resul†an t. If θ be the angle between the two vectors and their resul†an t is half of the sum of vector. Then show that Cosθ= -n^2+2/2(n^2-1

20. AD is an altitude of an equilateral triangle ABC . On AD as base , another equilateral triangle ADE is drawn . Prove that Ar(ΔABE):Ar(ΔABC)=3:4

41, 43, 127, 99, 71, 92, 71, 58, 57

If ΔABC ≅ ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:(a) BC = PQ(b) AC = PR(c) AB = PQ(d) QR = BC

What is the marks scored by most number of students?

Question 3Solve the following pair of linear equations by the substitution and cross-multiplication methods:8x +5y = 93x +2y = 4

Find, which of the following points lie on the line x - 2y + 5 = 0 :(i) (1, 3) (ii) (0, 5)(iii) (-5, 0) (iv) (5, 5)(v) (2, -1.5) (vi) (-2, -1.5)

If a brick has length, breadth and height in the ratio 1 : 2 : 3 and the total surface area of the brick is 792 m2, then the volume of the brick is _______.

If z is any complex numbers satisfying Iz - 3 - 2il 2, then theminimum value of \vert2z - 6 + 5i\rbrack is

The median of the variables x+4,x−72,x−52, x−3,x−2,x+12,x−12 and x+5, where x&gt;0, is:

The area of an isosceles trapezium is 34cm2 and the length of one of the parallel sides is 10 cm and Its height is 4 cm. Find the length of the other parallel side.

In the given figure, O is the centre of the circle. If ∠ABD=35∘ and ∠BAC=70∘, find ∠ACB.

Which among the following is a cubic polynomial?

If A=x3,B=4x2+x−1,C=x+1, then find (A-B)(A-C)

If x+y-z=4, 3x+ 3y+ z=12,(x+3y)^2 -z^{2 }=36, then find the value ofx.

Find the locus of a point which moves such that the sum of its distances from points a(0,0,-alpha) and b(0,0,alpha) is a constant equal to 2a

If one angle of a Parallelogram is 90 degrees, then it is a ______.

The median of the variables x+4,x−72,x−52, x−3,x−2,x+12,x−12 and x+5, where x>0, is: