32581 + Interview Questions in Mathematics Page 245 InterviewSolution

12201.	Which of the following is a quadratic polynomial?
Answer» Which of the following is a quadratic polynomial?

Discussion

12202.	The probability that a non-leap year has 53 sundays, is(a) 27(b) 57(c) 67(d) 17
Answer» The probability that a non-leap year has 53 sundays, is (a) $\frac{2}{7}$ (b) $\frac{5}{7}$ (c) $\frac{6}{7}$ (d) $\frac{1}{7}$

Discussion

12203.	In each of the following, determine whether the given values are solutions of the given equation or not:(i) x2-3x+2=0, x=2, x=-1(ii) x2+x+1=0, x=0, x=1(iii) x2-33x+6=0, x=3, x=-23(iv) x+1x=136, x=56, x=43(v) 2x2-x+9=x2+4x+3, x=2, x=3(vi) x2-2x-4=0, x=-2, x=-22(vii) a2x2-3abx+2b2=0, x=ab, x=ba
Answer» In each of the following, determine whether the given values are solutions of the given equation or not: (i) $x^{2} - 3 x + 2 = 0, x = 2, x = - 1$ (ii) $x^{2} + x + 1 = 0, x = 0, x = 1$ (iii) $x^{2} - 3 \sqrt{3} x + 6 = 0, x = \sqrt{3}, x = - 2 \sqrt{3}$ (iv) $x + \frac{1}{x} = \frac{13}{6}, x = \frac{5}{6}, x = \frac{4}{3}$ (v) $2 x^{2} - x + 9 = x^{2} + 4 x + 3, x = 2, x = 3$ (vi) $x^{2} - \sqrt{2} x - 4 = 0, x = - \sqrt{2}, x = - 2 \sqrt{2}$ (vii) $a^{2} x^{2} - 3 a b x + 2 b^{2} = 0, x = \frac{a}{b}, x = \frac{b}{a}$

Discussion

12204.	The sum of squares of two consecutive odd positive integers is 394. Find them.
Answer» The sum of squares of two consecutive odd positive integers is 394. Find them.

Discussion

12205.	20. Water is flowing through a cylindrical pipe, of internal radius 1cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour
Answer» 20. Water is flowing through a cylindrical pipe, of internal radius 1cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour

Discussion

12206.	A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm.Determine the capacity of the tank.
Answer» A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm.Determine the capacity of the tank.

Discussion

12207.	Question 18 (i)A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.
Answer» Question 18 (i) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

Discussion

12208.	three solid cubes have a face diagonal of 4\surd2 cm each . three other solid cubes have a face diagonal of 8\surd2 cm each. all the cubes are melted together to form a cube. find the side of the cube formed
Answer» three solid cubes have a face diagonal of 4\surd2 cm each . three other solid cubes have a face diagonal of 8\surd2 cm each. all the cubes are melted together to form a cube. find the side of the cube formed

Discussion

12209.	A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be ₹55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Calculate the number of toys produced on that day. Select the possible answers.
Answer» A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be ₹55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Calculate the number of toys produced on that day. Select the possible answers.

Discussion

12210.	A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,(1) a red balloon(2) a blue balloon(3) a green balloon.
Answer» A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, (1) a red balloon (2) a blue balloon (3) a green balloon.

Discussion

12211.	A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Number of days0−66−1010−1414−2020−2828−3838−40Number of students111074431
Answer» A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. $\begin{matrix} Number of days & 0 - 6 & 6 - 10 & 10 - 14 & 14 - 20 & 20 - 28 & 28 - 38 & 38 - 40 Number of students & 11 & 10 & 7 & 4 & 4 & 3 & 1 \end{matrix}$

12211.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Number of days0−66−1010−1414−2020−2828−3838−40Number of students111074431

Answer»

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

$\begin{matrix} Number of days & 0 - 6 & 6 - 10 & 10 - 14 & 14 - 20 & 20 - 28 & 28 - 38 & 38 - 40 Number of students & 11 & 10 & 7 & 4 & 4 & 3 & 1 \end{matrix}$

Discussion

12212.

The following table gives the production yield per hectare of wheat of 100 farms of a village. Production yield in kg/hectare 50-55 55-60 60-65 65-70 70-75 75-80 Number of frames 2 8 12 24 38 16 Change the above distribution to more than type distribution and draw its ogive.

Answer» The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield in kg/hectare	50-55	55-60	60-65	65-70	70-75	75-80
Number of frames	2	8	12	24	38	16

Change the above distribution to more than type distribution and draw its ogive.

Discussion

12213.	Choose the correct answer in each of the following questions:If the nth term of the AP is (2n + 1) then the sum of its first three terms is (a) 6n + 3 (b) 15 (c) 12 (d) 21 [CBSE 2012]
Answer» Choose the correct answer in each of the following questions: If the nth term of the AP is (2n + 1) then the sum of its first three terms is (a) 6n + 3 (b) 15 (c) 12 (d) 21 [CBSE 2012]

Discussion

12214.	The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Answer» The sum of the first n terms of an A.P. is 4n² + 2n. Find the n^th term of this A.P.

Discussion

12215.	If tan θ = 1√7 then (cosec2 θ−sec2 θ)(cosec2 θ+sec2 θ) = ? (a) −23 (b) −34 (c) 23 (d) 24
Answer» If tan $θ$ = $\frac{1}{\sqrt{7}}$ then $\frac{(c o s e c^{2} θ - s e c^{2} θ)}{(c o s e c^{2} θ + s e c^{2} θ)}$ = ? (a) $\frac{- 2}{3}$ (b) $\frac{- 3}{4}$ (c) $\frac{2}{3}$ (d) $\frac{2}{4}$

12215.

If tan θ = 1√7 then (cosec2 θ−sec2 θ)(cosec2 θ+sec2 θ) = ? (a) −23 (b) −34 (c) 23 (d) 24

Answer»

If tan $θ$ = $\frac{1}{\sqrt{7}}$ then $\frac{(c o s e c^{2} θ - s e c^{2} θ)}{(c o s e c^{2} θ + s e c^{2} θ)}$ = ?

(a) $\frac{- 2}{3}$ (b) $\frac{- 3}{4}$ (c) $\frac{2}{3}$ (d) $\frac{2}{4}$

Discussion

12216.	Which of the following holds true in a Right angled triangle?
Answer» Which of the following holds true in a Right angled triangle?

Discussion

12217.	12. The perimeter of a certain sector of a circle is equal to half that of the circle of which it is a sector .The circular measure of one angle of the sector?
Answer» 12. The perimeter of a certain sector of a circle is equal to half that of the circle of which it is a sector .The circular measure of one angle of the sector?

Discussion

12218.	Find the mean deviation about the mean for the following data. Class interval0−1010−2020−3030−4040−5050−6060−70Frequency812108327
Answer» Find the mean deviation about the mean for the following data. $\begin{matrix} C l a s s i n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 F r e q u e n c y & 8 & 12 & 10 & 8 & 3 & 2 & 7 \end{matrix}$

Discussion

12219.	In an AP, where the first term is 7 and the common difference is 4, ___ term of the AP will be five times the first term.Represent this situation in the form of an equation, where a = first term, an = nth term and d is the common difference.
Answer» In an AP, where the first term is 7 and the common difference is 4, ___ term of the AP will be five times the first term. Represent this situation in the form of an equation, where $a$ = first term, $a_{n}$ = $n^{t h}$ term and $d$ is the common difference.

Discussion

12220.	If G be the centroid of a triangle ABC, prove that:AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
Answer» If G be the centroid of a triangle ABC, prove that: AB² + BC² + CA² = 3 (GA² + GB² + GC²)

Discussion

12221.	Question 2If the sum of the circumference of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R then:(A) R1+R2=R(B) R1+R2>R(C) R1+R2<R(D) Nothing definite can be said about the relation among R1,R2 and R
Answer» Question 2 If the sum of the circumference of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle of radius R then: (A) $R_{1} + R_{2} = R$ (B) $R_{1} + R_{2} > R$ (C) $R_{1} + R_{2} < R$ (D) Nothing definite can be said about the relation among $R_{1}, R_{2} a n d R$

Discussion

12222.	Define distance and displacement.
Answer» Define distance and displacement.

Discussion

12223.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x+1x=3, x≠0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x + \frac{1}{x} = 3, x \neq 0$

Discussion

12224.	A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
Answer» A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.

Discussion

12225.	A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket. [CBSE 2012]
Answer» A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket. [CBSE 2012]

Discussion

12226.	The sum of two natural numbers is 9 and the sum of their reciprocal is 12. Find the numbers.
Answer» The sum of two natural numbers is 9 and the sum of their reciprocal is $\frac{1}{2}$ . Find the numbers.

Discussion

12227.	A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?
Answer» A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?

Discussion

12228.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2+6x-a2+2a-8=0 [CBSE 2015]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x^{2} + 6 x - (a^{2} + 2 a - 8) = 0$ [CBSE 2015]

Discussion

12229.	Which of the following is a solution of x+5y−18=0?
Answer» Which of the following is a solution of $x + 5 y - 18 = 0 ?$

Discussion

12230.	The value of k for which the system of equations has a unique solution, iskx − y = 26x − 2y = 3(a) =3(b) ≠3(c) ≠0(d) =0
Answer» The value of k for which the system of equations has a unique solution, is kx − y = 2 6x − 2y = 3 (a) =3 (b) ≠3 (c) ≠0 (d) =0

Discussion

12231.	Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Answer» Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

12231.

Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Answer»

Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Discussion

12232.	The following table shows the age distribution of patients of malaria in a village during a particular month: Age (in years)5−1415−2425−3435−4445−5455−64Number of cases6112123145
Answer» The following table shows the age distribution of patients of malaria in a village during a particular month: $\begin{matrix} Age (in years) & 5 - 14 & 15 - 24 & 25 - 34 & 35 - 44 & 45 - 54 & 55 - 64 Number of cases & 6 & 11 & 21 & 23 & 14 & 5 \end{matrix}$

Discussion

12233.

The following table gives production yield per hectare of wheat of 100 farms of a village: Production yield in kg per hectare: 50−55 55−60 60−65 65−70 70−75 75−80 Number of farms: 2 8 12 24 38 16 Draw 'less than' ogive and 'more than' ogive.

Answer» The following table gives production yield per hectare of wheat of 100 farms of a village:

Production yield in kg per hectare:	50−55	55−60	60−65	65−70	70−75	75−80
Number of farms:	2	8	12	24	38	16

Draw 'less than' ogive and 'more than' ogive.

Discussion

12234.	Reduce x2−16x2+8x+16 into its simpest form.
Answer» Reduce $\frac{x^{2} - 16}{x^{2} + 8 x + 16}$ into its simpest form.

Discussion

12235.	In the adjoining figure, if ∠QPR=67∘ and ∠SPR=72∘, then ∠QRS is equal to
Answer» In the adjoining figure, if $∠ Q P R = 67^{\circ}$ and $∠ S P R = 72^{\circ}$ , then $∠ Q R S$ is equal to

12235.

In the adjoining figure, if ∠QPR=67∘ and ∠SPR=72∘, then ∠QRS is equal to

Answer»

In the adjoining figure, if $∠ Q P R = 67^{\circ}$ and $∠ S P R = 72^{\circ}$ , then $∠ Q R S$ is equal to

Discussion

12236.	ABCD is a parallelogram. If the radius of the circle is 4cm, then the length of the diagonal AC is ___.
Answer» ABCD is a parallelogram. If the radius of the circle is 4cm, then the length of the diagonal AC is ___.

Discussion

12237.

Extracts of Trial Balance as at 31st March, 2017: Dr. (₹) Cr. (₹) Sundry Debtors (including Dewan for dishonoured bill of ₹ 20,000) 4,80,000 – Provision for Doubtful Debts – 24,000 Bad Debts 10,000 – Adjustments:(i) 34th of Dewan's bill is irrecoverable.(ii) Create a provision of 6% on Sundry Debtors.Show the effect on Profit and Loss Account and Balance Sheet.

Answer» Extracts of Trial Balance as at 31st March, 2017:

	Dr. (₹)	Cr. (₹)
Sundry Debtors (including Dewan for dishonoured bill of ₹ 20,000)	4,80,000	–
Provision for Doubtful Debts	–	24,000
Bad Debts	10,000	–

Adjustments:

(i)

\frac{3}{4} th

of Dewan's bill is irrecoverable.

(ii) Create a provision of 6% on Sundry Debtors.

Show the effect on Profit and Loss Account and Balance Sheet.

Discussion

12238.	Question 7The diameter of the moon is approximately one-fourth of the diameter of the earth.Find the ratio of their surface area.
Answer» Question 7 The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

12238.

Question 7The diameter of the moon is approximately one-fourth of the diameter of the earth.Find the ratio of their surface area.

Answer»

Question 7

The diameter of the moon is approximately one-fourth of the diameter of the earth.

Find the ratio of their surface area.

Discussion

12239.	The monthly consumption of electricity (in units) of some families of a locality is given in the follwoing frequency distribution. Monthly consumption(in units)140−160160−180180−200200−240220−240240−260260−280Number of families381540503010 Prepare a 'more than type'ogive for the given frequency distribution:
Answer» The monthly consumption of electricity (in units) of some families of a locality is given in the follwoing frequency distribution. $\begin{matrix} M o n t h l y c o n s u m p t i o n (i n u n i t s) & 140 - 160 & 160 - 180 & 180 - 200 & 200 - 240 & 220 - 240 & 240 - 260 & 260 - 280 N u m b e r o f f a m i l i e s & 3 & 8 & 15 & 40 & 50 & 30 & 10 \end{matrix}$ Prepare a 'more than type'ogive for the given frequency distribution:

12239.

The monthly consumption of electricity (in units) of some families of a locality is given in the follwoing frequency distribution. Monthly consumption(in units)140−160160−180180−200200−240220−240240−260260−280Number of families381540503010 Prepare a 'more than type'ogive for the given frequency distribution:

Answer»

The monthly consumption of electricity (in units) of some families of a locality is given in the follwoing frequency distribution.

$\begin{matrix} M o n t h l y c o n s u m p t i o n (i n u n i t s) & 140 - 160 & 160 - 180 & 180 - 200 & 200 - 240 & 220 - 240 & 240 - 260 & 260 - 280 N u m b e r o f f a m i l i e s & 3 & 8 & 15 & 40 & 50 & 30 & 10 \end{matrix}$

Prepare a 'more than type'ogive for the given frequency distribution:

Discussion

12240.	Show that :tan48∘tan23∘tan42∘tan67∘=1
Answer» Show that : $t a n 48^{\circ} t a n 23^{\circ} t a n 42^{\circ} t a n 67^{\circ} = 1$

Discussion

12241.	The value of [(sec A + tan A) (1−sin A)] is equal to(a) tan2 A(b) sin2 A(c) cos A(d) sin A
Answer» The value of [(sec A + tan A) (1−sin A)] is equal to (a) tan² A (b) sin² A (c) cos A (d) sin A

Discussion

12242.	The equation of the normal(s) to y=x3−3x, which is parallel to 2x+18y=9 is/are
Answer» The equation of the normal(s) to $y = x^{3} - 3 x$ , which is parallel to $2 x + 18 y = 9$ is/are

Discussion

12243.	Volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height. (π= 3.14)
Answer» Volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height. ( $π$ = 3.14)

Discussion

12244.	A circle of radius 3 cm, with centre O is drawn circumscribing a ΔABC. What is the sum of OA + OB + OC?
Answer» A circle of radius 3 cm, with centre O is drawn circumscribing a $Δ$ ABC. What is the sum of OA + OB + OC?

Discussion

12245.	The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___.
Answer» The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___.

Discussion

12246.	Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3)
Answer» Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3)

Discussion

12247.	How we can find the sum of nth term.What is the equation?
Answer» How we can find the sum of nth term.What is the equation?

Discussion

12248.	If two positive integers a and b are written as a = x3y2 and b = xy3 ; x , y are prime numbers , then HCF(a,b) is(a) xy (b) xy2 (c) x3y3 (d) x2y2
Answer» If two positive integers a and b are written as $a = x^{3} y^{2}$ and $b = x y^{3}; x, y$ are prime numbers , then HCF(a,b) is (a) xy (b) xy² (c) x³y³ (d) x²y²

Discussion

12249.	Divide 4xy5xyz by 4z3xy
Answer» Divide $\frac{4 x y}{5 x y z} b y \frac{4 z}{3 x y}$

Discussion

12250.	A6,1 , B(8,2) and C(9, 4) are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of ∆ 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 , find the area of $∆$ ADE.

Discussion

Explore topic-wise InterviewSolutions in .

Which of the following is a quadratic polynomial?

The probability that a non-leap year has 53 sundays, is(a) 27(b) 57(c) 67(d) 17

In each of the following, determine whether the given values are solutions of the given equation or not:(i) x2-3x+2=0, x=2, x=-1(ii) x2+x+1=0, x=0, x=1(iii) x2-33x+6=0, x=3, x=-23(iv) x+1x=136, x=56, x=43(v) 2x2-x+9=x2+4x+3, x=2, x=3(vi) x2-2x-4=0, x=-2, x=-22(vii) a2x2-3abx+2b2=0, x=ab, x=ba

The sum of squares of two consecutive odd positive integers is 394. Find them.

20. Water is flowing through a cylindrical pipe, of internal radius 1cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour

A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm.Determine the capacity of the tank.

Question 18 (i)A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

three solid cubes have a face diagonal of 4\surd2 cm each . three other solid cubes have a face diagonal of 8\surd2 cm each. all the cubes are melted together to form a cube. find the side of the cube formed

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,(1) a red balloon(2) a blue balloon(3) a green balloon.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Number of days0−66−1010−1414−2020−2828−3838−40Number of students111074431

The following table gives the production yield per hectare of wheat of 100 farms of a village. Production yield in kg/hectare 50-55 55-60 60-65 65-70 70-75 75-80 Number of frames 2 8 12 24 38 16 Change the above distribution to more than type distribution and draw its ogive.

Choose the correct answer in each of the following questions:If the nth term of the AP is (2n + 1) then the sum of its first three terms is (a) 6n + 3 (b) 15 (c) 12 (d) 21 [CBSE 2012]

The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.

If tan θ = 1√7 then (cosec2 θ−sec2 θ)(cosec2 θ+sec2 θ) = ? (a) −23 (b) −34 (c) 23 (d) 24

Which of the following holds true in a Right angled triangle?

12. The perimeter of a certain sector of a circle is equal to half that of the circle of which it is a sector .The circular measure of one angle of the sector?

Find the mean deviation about the mean for the following data. Class interval0−1010−2020−3030−4040−5050−6060−70Frequency812108327

In an AP, where the first term is 7 and the common difference is 4, ___ term of the AP will be five times the first term.Represent this situation in the form of an equation, where a = first term, an = nth term and d is the common difference.

If G be the centroid of a triangle ABC, prove that:AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)

Question 2If the sum of the circumference of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R then:(A) R1+R2=R(B) R1+R2&gt;R(C) R1+R2&lt;R(D) Nothing definite can be said about the relation among R1,R2 and R

Define distance and displacement.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x+1x=3, x≠0

A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket. [CBSE 2012]

The sum of two natural numbers is 9 and the sum of their reciprocal is 12. Find the numbers.

A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2+6x-a2+2a-8=0 [CBSE 2015]

Which of the following is a solution of x+5y−18=0?

The value of k for which the system of equations has a unique solution, iskx − y = 26x − 2y = 3(a) =3(b) ≠3(c) ≠0(d) =0

Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

The following table shows the age distribution of patients of malaria in a village during a particular month: Age (in years)5−1415−2425−3435−4445−5455−64Number of cases6112123145

The following table gives production yield per hectare of wheat of 100 farms of a village: Production yield in kg per hectare: 50−55 55−60 60−65 65−70 70−75 75−80 Number of farms: 2 8 12 24 38 16 Draw 'less than' ogive and 'more than' ogive.

Reduce x2−16x2+8x+16 into its simpest form.

In the adjoining figure, if ∠QPR=67∘ and ∠SPR=72∘, then ∠QRS is equal to

ABCD is a parallelogram. If the radius of the circle is 4cm, then the length of the diagonal AC is ___.

Question 7The diameter of the moon is approximately one-fourth of the diameter of the earth.Find the ratio of their surface area.

Show that :tan48∘tan23∘tan42∘tan67∘=1

The value of [(sec A + tan A) (1−sin A)] is equal to(a) tan2 A(b) sin2 A(c) cos A(d) sin A

The equation of the normal(s) to y=x3−3x, which is parallel to 2x+18y=9 is/are

Volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height. (π= 3.14)

A circle of radius 3 cm, with centre O is drawn circumscribing a ΔABC. What is the sum of OA + OB + OC?

The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___.

Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3)

How we can find the sum of nth term.What is the equation?

If two positive integers a and b are written as a = x3y2 and b = xy3 ; x , y are prime numbers , then HCF(a,b) is(a) xy (b) xy2 (c) x3y3 (d) x2y2

Divide 4xy5xyz by 4z3xy

A6,1 , B(8,2) and C(9, 4) are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of ∆ ADE.

Question 2If the sum of the circumference of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R then:(A) R1+R2=R(B) R1+R2>R(C) R1+R2<R(D) Nothing definite can be said about the relation among R1,R2 and R