32581 + Interview Questions in Mathematics Page 271 InterviewSolution

13501.	Find the middle term of the AP 10, 7, 4, ..., (−62). [CBSE 2009C]
Answer» Find the middle term of the AP 10, 7, 4, ..., (−62). [CBSE 2009C]

Discussion

13502.	Which of the following graph represents a quadratic polynomial which has sum of its zeroes is zero?
Answer» Which of the following graph represents a quadratic polynomial which has sum of its zeroes is zero?

Discussion

13503.	In the following figure, DE \|\| OQ and DF \|\| OR, show that EF \|\| QR.
Answer» In the following figure, DE \|\| OQ and DF \|\| OR, show that EF \|\| QR.

13503.

In the following figure, DE || OQ and DF || OR, show that EF || QR.

Answer»

In the following figure, DE || OQ and DF || OR, show that EF || QR.

Discussion

13504.	(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes. (ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper. (iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper. (iv) Write down the geometrical name of the figure AA'BB'. (v) Name two invariant points under reflection in the x-axis.
Answer» (i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes. (ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper. (iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper. (iv) Write down the geometrical name of the figure AA'BB'. (v) Name two invariant points under reflection in the x-axis.

13504.

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes. (ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper. (iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper. (iv) Write down the geometrical name of the figure AA'BB'. (v) Name two invariant points under reflection in the x-axis.

Answer»

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

Discussion

13505.	The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine its speed in kms per hour.
Answer» The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine its speed in kms per hour.

Discussion

13506.	In the given figure, if ∠ACE=43∘ and ∠CAF=62∘, then match the following correctly.ListIListIIA.∠ai.62∘B.∠cii.105∘C.∠biii.13∘
Answer» In the given figure, if $∠ A C E = 43^{\circ}$ and $∠ C A F = 62^{\circ}$ , then match the following correctly. $\begin{matrix} L i s t I & L i s t I I A . ∠ a & i {.62}^{\circ} B . ∠ c & i i . 105^{\circ} C . ∠ b & i i i . 13^{\circ} \end{matrix}$

Discussion

13507.	The mean of a discrete frequency distribution xi / fi, i = 1, 2, ......, n is given by(a) Σ fixiΣ fi(b) 1n∑i=1nfi xi(c) ∑i=1n fixi∑i=1n xi(d) ∑i=1nfixi∑1=1ni
Answer» The mean of a discrete frequency distribution x_i / f_i, i = 1, 2, ......, n is given by (a) $\frac{Σ f_{i} x_{i}}{Σ f_{i}}$ (b) $\frac{1}{n} \sum_{i = 1}^{n} f_{i} x_{i}$ (c) $\frac{\sum_{i = 1}^{n} f_{i} x_{i}}{\sum_{i = 1}^{n} x_{i}}$ (d) $\frac{\sum_{i = 1}^{n} f_{i} x_{i}}{\sum_{1 = 1}^{n} i}$

Discussion

13508.	Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angPTQ = 2 angOPQ.
Answer» Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angPTQ = 2 angOPQ.

Discussion

13509.	Find the sum of the integers between 50 and 500 which are divisible by 7
Answer» Find the sum of the integers between 50 and 500 which are divisible by 7

Discussion

13510.

Following is the Trial Balance of Shri Paras on 31st March, 2018: Particulars Dr. ₹ Particulars Cr. ₹ Sundry Debtors 1,45,000 Sundry Creditors 63,000 Drawings 52,450 Capital A/c 7,10,000 Insurancne 6,000 Returns Outward 5,000 Rent 10,000 Sales 10,00,000 General Expenses 20,000 Output CGST 20,000 Salaries 1,50,000 Output SGST 20,000 Patents and Patterns 75,000 Machinery 2,00,000 Freehold Land 1,00,000 Building 3,00,000 Stock (1st April, 2017) 57,600 Cash at Bank 26,300 Freight on Purchases 20,400 Carriage on Sales 32,000 Fuel and Power 47,300 Wages 1,04,800 Returns Inward 19,000 Purchases 4,06,750 Cash in Hand 5,400 Input IGST 40,000 18,18,000 18,18,000 Following adjustments are made:(a) Stock on 31st March, 2018 was valued at ₹ 68,000.(b) Provision for Doubtful Debts is to be made to the extent of 5% on Sundry Debtors.(c) Depreciate Machinery by 10%, Patents 20% and Building 5%.(d) Wages include a sum of ₹ 20,000 spent on constructiion of a cycle shed.(e) Salaries for the months of February and March, 2018 were not paid.(f) Insurance includes a premium of ₹ 1,700 on a policy expiring on 30th September, 2018.(g) General Manager is entitled to a commission of 10% on the net profit after charging his commission.You are required to prepare Final Accounts after giving effects to the adjustments.

Answer» Following is the Trial Balance of Shri Paras on 31^st March, 2018:

Particulars	Dr. ₹	Particulars	Cr. ₹
Sundry Debtors	1,45,000	Sundry Creditors	63,000
Drawings	52,450	Capital A/c	7,10,000
Insurancne	6,000	Returns Outward	5,000
Rent	10,000	Sales	10,00,000
General Expenses	20,000	Output CGST	20,000
Salaries	1,50,000	Output SGST	20,000
Patents and Patterns	75,000
Machinery	2,00,000
Freehold Land	1,00,000
Building	3,00,000
Stock (1st April, 2017)	57,600
Cash at Bank	26,300
Freight on Purchases	20,400
Carriage on Sales	32,000
Fuel and Power	47,300
Wages	1,04,800
Returns Inward	19,000
Purchases	4,06,750
Cash in Hand	5,400
Input IGST	40,000
	18,18,000		18,18,000

Following adjustments are made:

(a) Stock on 31st March, 2018 was valued at ₹ 68,000.

(b) Provision for Doubtful Debts is to be made to the extent of 5% on Sundry Debtors.

(c) Depreciate Machinery by 10%, Patents 20% and Building 5%.

(d) Wages include a sum of ₹ 20,000 spent on constructiion of a cycle shed.

(e) Salaries for the months of February and March, 2018 were not paid.

(f) Insurance includes a premium of ₹ 1,700 on a policy expiring on 30th September, 2018.

(g) General Manager is entitled to a commission of 10% on the net profit after charging his commission.

You are required to prepare Final Accounts after giving effects to the adjustments.

Discussion

13511.

The table below shows the number of employees of an office, classified according to the income-tax paid by them. Income Tax (Rupees) Number of Employees 1000 − 2000 2000 − 3000 3000 − 4000 4000 − 5000 5000 − 6000 6000 − 7000 7000 − 8000 8000 − 9000 8 10 15 18 22 8 6 3 Compute the median income-tax.

Answer»

The table below shows the number of employees of an office, classified according to the income-tax paid by them.

Income Tax

(Rupees)

Number of Employees

1000 − 2000

2000 − 3000

3000 − 4000

4000 − 5000

5000 − 6000

6000 − 7000

7000 − 8000

8000 − 9000

8

10

15

18

22

8

6

3

Compute the median income-tax.

Discussion

13512.	The 3rd term of an arithmetic sequence is 10 and its 8th term is 25. What is its 4th term? And the 13th term?
Answer» The 3^rd term of an arithmetic sequence is 10 and its 8^th term is 25. What is its 4^th term? And the 13^th term?

Discussion

13513.	Question 3A 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» Question 3 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

13514.	A biology aptitude test of 50 students was recorded as follows: Marks50−6060−7070−8080−9090−100No. of students4814195 Draw a histogram from the above data using a graph paper and find the mode value.
Answer» A biology aptitude test of 50 students was recorded as follows: $\begin{matrix} M a r k s & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 N o . o f s t u d e n t s & 4 & 8 & 14 & 19 & 5 \end{matrix}$ Draw a histogram from the above data using a graph paper and find the mode value.

13514.

A biology aptitude test of 50 students was recorded as follows: Marks50−6060−7070−8080−9090−100No. of students4814195 Draw a histogram from the above data using a graph paper and find the mode value.

Answer»

A biology aptitude test of 50 students was recorded as follows:

$\begin{matrix} M a r k s & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 N o . o f s t u d e n t s & 4 & 8 & 14 & 19 & 5 \end{matrix}$

Draw a histogram from the above data using a graph paper and find the mode value.

Discussion

13515.	If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is ______ ___
Answer» If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is ______ ___

Discussion

13516.	1. if f(x) is a cubic polynomial then f(4) is equal to
Answer» 1. if f(x) is a cubic polynomial then f(4) is equal to

Discussion

13517.	Question 6A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.
Answer» Question 6 A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

Discussion

13518.	Fill in the missing number −C2B−3A2A?−B−3C−A−2B
Answer» Fill in the missing number $\begin{matrix} - C & 2 B & - 3 A 2 A & ? & - B - 3 C & - A & - 2 B \end{matrix}$

13518.

Fill in the missing number −C2B−3A2A?−B−3C−A−2B

Answer»

Fill in the missing number

$\begin{matrix} - C & 2 B & - 3 A 2 A & ? & - B - 3 C & - A & - 2 B \end{matrix}$

Discussion

13519.	In the given figure, PA and PB are tangents to the given circle such that PA = 5 and \angle APB = 60^o The length of chord AB is (a) 5√2 cm (b) 5 cm (a) 5√3 cm (a) 7.5 cm
Answer» In the given figure, PA and PB are tangents to the given circle such that PA = 5 and \angle APB = 60^o The length of chord AB is (a) $5 \sqrt{2}$ cm (b) 5 cm (a) $5 \sqrt{3}$ cm (a) 7.5 cm

13519.

In the given figure, PA and PB are tangents to the given circle such that PA = 5 and \angle APB = 60^o The length of chord AB is (a) 5√2 cm (b) 5 cm (a) 5√3 cm (a) 7.5 cm

Answer»

In the given figure, PA and PB are tangents to the given circle such that PA = 5 and \angle APB = 60^o The length of chord AB is

(a) $5 \sqrt{2}$ cm (b) 5 cm

(a) $5 \sqrt{3}$ cm (a) 7.5 cm

Discussion

13520.	The length of a line segment AB is 10 units.if the coordinate of extermity are (2,-3) and the abscissa of the other extremity is 10 then the sum of all possible value of the ordinate of the other extremity is
Answer» The length of a line segment AB is 10 units.if the coordinate of extermity are (2,-3) and the abscissa of the other extremity is 10 then the sum of all possible value of the ordinate of the other extremity is

Discussion

13521.	If A and B are two square matrices of the same order such that B = -A-1BA, then (A+B)2 = ______________.
Answer» If A and B are two square matrices of the same order such that B = -A^-1BA, then (A+B)² = ______________.

Discussion

13522.	Find the remainder when the polynomial 4x3+12x2+11x+3 is divided by x+1
Answer» Find the remainder when the polynomial $4 x^{3} + 12 x^{2} + 11 x + 3$ is divided by $x + 1$

Discussion

13523.	Question 11 If the sum of the first n terms of an AP is 4n−n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the 10th and the nth terms.
Answer» Question 11 If the sum of the first n terms of an AP is $4 n - n^{2}$ , what is the first term $(t h a t i s S_{1})$ ? What is the sum of first two terms? What is the second term? Similarly find the $3^{r d}$ , the $10^{t h}$ and the $n^{t h}$ terms.

Discussion

13524.	Prove that semi vertical angle of given surface area and maximum value of a cone is sin inverse 1/3.(count total surface)
Answer» Prove that semi vertical angle of given surface area and maximum value of a cone is sin inverse 1/3.(count total surface)

Discussion

13525.	A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm
Answer» A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

13525.

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Answer»

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Discussion

13526.	If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that ab-cbc-aca-b=1.
Answer» If p^th, q^th and r^thterms of an A.P. and G.P. are both a, b and c respectively, show that $a^{b - c} b^{c - a} c^{a - b} = 1$ .

Discussion

13527.	Mark the correct alternative in the following question:If P=3x3+3x2+3x+3 and Q=3x2-3x+3, then P-Q=a 3x3 b 3x3+6x2+6x+6 c 6x2+6x+6 d 3x3+6x
Answer» Mark the correct alternative in the following question: $If P = 3 x^{3} + 3 x^{2} + 3 x + 3 and Q = 3 x^{2} - 3 x + 3, then P - Q = (a) 3 x^{3} (b) 3 x^{3} + 6 x^{2} + 6 x + 6 (c) 6 x^{2} + 6 x + 6 (d) 3 x^{3} + 6 x$

Discussion

13528.	The zeroes of mn(x2+1)=(m2+n2)x are:
Answer» The zeroes of $m n (x^{2} + 1) = (m^{2} + n^{2}) x$ are:

Discussion

13529.	Question 4In the formula ¯x=a+h(∑fiui∑fi), for finding the mean of grouped frequency distribution ui is equal to(a) xi+ah(b) xi+a(c) xi+ah(a) a−xih
Answer» Question 4 In the formula $¯ x = a + h (\frac{\sum f_{i} u_{i}}{\sum f_{i}}),$ for finding the mean of grouped frequency distribution $u_{i}$ is equal to (a) $\frac{x_{i} + a}{h}$ (b) $x_{i} + a$ (c) $\frac{x_{i} + a}{h}$ (a) $\frac{a - x_{i}}{h}$

Discussion

13530.	Question 11 A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60∘. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30∘. Find the height of the tower and the width of the canal.
Answer» Question 11 A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the canal.

Discussion

13531.	Let a,b are roots of x^2-4x+A=0, c and d are roots of x^2-36x+B=0. If a,b,c,d are in increasing G.P then evaluate A,B.
Answer» Let a,b are roots of x^2-4x+A=0, c and d are roots of x^2-36x+B=0. If a,b,c,d are in increasing G.P then evaluate A,B.

Discussion

13532.	The ratio of the surface area of a cube of volume 64 cm3 to the surface area of 64 cubes of volume 1 cm3 is:
Answer» The ratio of the surface area of a cube of volume $64 c m^{3}$ to the surface area of 64 cubes of volume $1 c m^{3}$ is:

Discussion

13533.	Observe the given pattern and identify what comes next?
Answer» Observe the given pattern and identify what comes next?

Discussion

13534.	Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y + 5 = 0, whose distance from the point(3, 2) is 7/5. [NCERT EXEMPLAR]
Answer» Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y + 5 = 0, whose distance from the point(3, 2) is 7/5. [NCERT EXEMPLAR]

Discussion

13535.	The volume of a sphere is 4851 cm3. Find its curved surface area.
Answer» The volume of a sphere is 4851 cm³. Find its curved surface area.

Discussion

13536.	What is the finalises form of the equation 5x2 – 6x – 2 = 0 by the method of completion of squares?
Answer» What is the finalises form of the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completion of squares?

Discussion

13537.	A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take π=227)
Answer» A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take $π = \frac{22}{7}$ )

Discussion

13538.	A circular swimming pool has protection bars installed along the circumference of 220 meters. Find the radius of the swimming pool.
Answer» A circular swimming pool has protection bars installed along the circumference of 220 meters. Find the radius of the swimming pool.

Discussion

13539.	Find the length of the diagonal of a square of side 12 m.
Answer» Find the length of the diagonal of a square of side 12 m.

Discussion

13540.	Solve the following systems of equations:2x+5y=160x+40y=19, x≠0, y≠0
Answer» Solve the following systems of equations: $\frac{2}{x} + \frac{5}{y} = 1 \frac{60}{x} + \frac{40}{y} = 19, x \neq 0, y \neq 0$

Discussion

13541.	Without using trigonometric tables, prove that: (i) cos 81∘−sin 9∘=0 (ii) tan 71∘−cot 19∘=0 (iii) cosec 80∘−sec 10∘=0 (iv) cosec272∘−tan218∘=1 (v) cos275∘+cos215∘=1 (vi) tan266∘−cot224∘=0 (vii) sin248∘+sin∘42∘=1 (viii) cos257∘=sin233∘=0 (ix) (sin 65∘+cos25∘)(sin 65∘−cos 25∘)=0
Answer» Without using trigonometric tables, prove that: (i) $c o s 81^{\circ} - s i n 9^{\circ} = 0$ (ii) $t a n 71^{\circ} - c o t 19^{\circ} = 0$ (iii) $c o s e c 80^{\circ} - s e c 10^{\circ} = 0$ (iv) $c o s e c^{2} 72^{\circ} - t a n^{2} 18^{\circ} = 1$ (v) $c o s^{2} 75^{\circ} + c o s^{2} 15^{\circ} = 1$ (vi) $t a n^{2} 66^{\circ} - c o t^{2} 24^{\circ} = 0$ (vii) $s i n^{2} 48^{\circ} + s i n^{\circ} 42^{\circ} = 1$ (viii) $c o s^{2} 57^{\circ} = s i n^{2} 33^{\circ} = 0$ (ix) $(s i n 65^{\circ} + c o s 25^{\circ}) (s i n 65^{\circ} - c o s 25^{\circ}) = 0$

13541.

Without using trigonometric tables, prove that: (i) cos 81∘−sin 9∘=0 (ii) tan 71∘−cot 19∘=0 (iii) cosec 80∘−sec 10∘=0 (iv) cosec272∘−tan218∘=1 (v) cos275∘+cos215∘=1 (vi) tan266∘−cot224∘=0 (vii) sin248∘+sin∘42∘=1 (viii) cos257∘=sin233∘=0 (ix) (sin 65∘+cos25∘)(sin 65∘−cos 25∘)=0

Answer»

Without using trigonometric tables, prove that:

(i) $c o s 81^{\circ} - s i n 9^{\circ} = 0$ (ii) $t a n 71^{\circ} - c o t 19^{\circ} = 0$

(iii) $c o s e c 80^{\circ} - s e c 10^{\circ} = 0$ (iv) $c o s e c^{2} 72^{\circ} - t a n^{2} 18^{\circ} = 1$

(v) $c o s^{2} 75^{\circ} + c o s^{2} 15^{\circ} = 1$ (vi) $t a n^{2} 66^{\circ} - c o t^{2} 24^{\circ} = 0$

(vii) $s i n^{2} 48^{\circ} + s i n^{\circ} 42^{\circ} = 1$ (viii) $c o s^{2} 57^{\circ} = s i n^{2} 33^{\circ} = 0$

(ix) $(s i n 65^{\circ} + c o s 25^{\circ}) (s i n 65^{\circ} - c o s 25^{\circ}) = 0$

Discussion

13542.	The value of 2+12+12+... is
Answer» The value of $2 + \frac{1}{2 + \frac{1}{2 + . . .}}$ is

Discussion

13543.	A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?
Answer» A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

Discussion

13544.	Question 1 (x)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(x) 7y2–113y−23
Answer» Question 1 (x) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (x) $7 y^{2} - \frac{11}{3} y - \frac{2}{3}$

Discussion

13545.	If alpha and beta are zeros of quadratic polynomial find f(x)=6x^2+x-2.
Answer» If alpha and beta are zeros of quadratic polynomial find f(x)=6x^2+x-2.

Discussion

13546.	8x^2+7x+3=0 ->qaudratic equation or not ? but if 8x^2+7x+3=other number except 0 ->still it will be a quadratic equation or not?
Answer» 8x^2+7x+3=0 ->qaudratic equation or not ? but if 8x^2+7x+3=other number except 0 ->still it will be a quadratic equation or not?

Discussion

13547.	Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).
Answer» Taylor purchased a rectangular plot of area $634 m^{2}$ . The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).

Discussion

13548.	Solve each of the following systems of equations by the method of cross-multiplication :x + 2y + 1 = 02x − 3y − 12 = 0
Answer» Solve each of the following systems of equations by the method of cross-multiplication : x + 2y + 1 = 0 2x − 3y − 12 = 0

Discussion

13549.

A (1, 3) and B (–1, 1). i) AB cuts the -axis at the point C. Write down the coordinate of C. ii) If the line joining (–1, k) and (3, 0) intersects AB at right angles, find the value of k.

Answer»

A (1, 3) and B (–1, 1).

i) AB cuts the -axis at the point C. Write down the coordinate of C.

ii) If the line joining (–1, k) and (3, 0) intersects AB at right angles,

find the value of k.

Discussion

13550.	In an A.P., the sum of first ten terms is -150 and the sum of its next ten terms is -550 Find the A.P.
Answer» In an A.P., the sum of first ten terms is -150 and the sum of its next ten terms is -550 Find the A.P.

Discussion

Explore topic-wise InterviewSolutions in .

Find the middle term of the AP 10, 7, 4, ..., (−62). [CBSE 2009C]

Which of the following graph represents a quadratic polynomial which has sum of its zeroes is zero?

In the following figure, DE || OQ and DF || OR, show that EF || QR.

The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine its speed in kms per hour.

In the given figure, if ∠ACE=43∘ and ∠CAF=62∘, then match the following correctly.ListIListIIA.∠ai.62∘B.∠cii.105∘C.∠biii.13∘

The mean of a discrete frequency distribution xi / fi, i = 1, 2, ......, n is given by(a) Σ fixiΣ fi(b) 1n∑i=1nfi xi(c) ∑i=1n fixi∑i=1n xi(d) ∑i=1nfixi∑1=1ni

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angPTQ = 2 angOPQ.

Find the sum of the integers between 50 and 500 which are divisible by 7

The 3rd term of an arithmetic sequence is 10 and its 8th term is 25. What is its 4th term? And the 13th term?

A biology aptitude test of 50 students was recorded as follows: Marks50−6060−7070−8080−9090−100No. of students4814195 Draw a histogram from the above data using a graph paper and find the mode value.

If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is ______ ___

1. if f(x) is a cubic polynomial then f(4) is equal to

Question 6A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

Fill in the missing number −C2B−3A2A?−B−3C−A−2B

In the given figure, PA and PB are tangents to the given circle such that PA = 5 and \angle APB = 60^o The length of chord AB is (a) 5√2 cm (b) 5 cm (a) 5√3 cm (a) 7.5 cm

The length of a line segment AB is 10 units.if the coordinate of extermity are (2,-3) and the abscissa of the other extremity is 10 then the sum of all possible value of the ordinate of the other extremity is

If A and B are two square matrices of the same order such that B = -A-1BA, then (A+B)2 = ______________.

Find the remainder when the polynomial 4x3+12x2+11x+3 is divided by x+1

Question 11 If the sum of the first n terms of an AP is 4n−n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the 10th and the nth terms.

Prove that semi vertical angle of given surface area and maximum value of a cone is sin inverse 1/3.(count total surface)

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that ab-cbc-aca-b=1.

Mark the correct alternative in the following question:If P=3x3+3x2+3x+3 and Q=3x2-3x+3, then P-Q=a 3x3 b 3x3+6x2+6x+6 c 6x2+6x+6 d 3x3+6x

The zeroes of mn(x2+1)=(m2+n2)x are:

Question 4In the formula ¯x=a+h(∑fiui∑fi), for finding the mean of grouped frequency distribution ui is equal to(a) xi+ah(b) xi+a(c) xi+ah(a) a−xih

Let a,b are roots of x^2-4x+A=0, c and d are roots of x^2-36x+B=0. If a,b,c,d are in increasing G.P then evaluate A,B.

The ratio of the surface area of a cube of volume 64 cm3 to the surface area of 64 cubes of volume 1 cm3 is:

Observe the given pattern and identify what comes next?

Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y + 5 = 0, whose distance from the point(3, 2) is 7/5. [NCERT EXEMPLAR]

The volume of a sphere is 4851 cm3. Find its curved surface area.

What is the finalises form of the equation 5x2 – 6x – 2 = 0 by the method of completion of squares?

A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take π=227)

A circular swimming pool has protection bars installed along the circumference of 220 meters. Find the radius of the swimming pool.

Find the length of the diagonal of a square of side 12 m.

Solve the following systems of equations:2x+5y=160x+40y=19, x≠0, y≠0

The value of 2+12+12+... is

A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

Question 1 (x)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(x) 7y2–113y−23

If alpha and beta are zeros of quadratic polynomial find f(x)=6x^2+x-2.

8x^2+7x+3=0 ->qaudratic equation or not ? but if 8x^2+7x+3=other number except 0 ->still it will be a quadratic equation or not?

Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).

Solve each of the following systems of equations by the method of cross-multiplication :x + 2y + 1 = 02x − 3y − 12 = 0

A (1, 3) and B (–1, 1). i) AB cuts the -axis at the point C. Write down the coordinate of C. ii) If the line joining (–1, k) and (3, 0) intersects AB at right angles, find the value of k.

In an A.P., the sum of first ten terms is -150 and the sum of its next ten terms is -550 Find the A.P.

If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is ____ _