32581 + Interview Questions in Mathematics Page 78 InterviewSolution

3851.	If 2 and -2 are two zeros of the polynomial (x4+x3−34x2−4x+120), find all the zeros of the given polynomial.
Answer» If 2 and -2 are two zeros of the polynomial $(x^{4} + x^{3} - 34 x^{2} - 4 x + 120)$ , find all the zeros of the given polynomial.

Discussion

3852.	Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?
Answer» Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

Discussion

3853.	In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.
Answer» In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

Discussion

3854.

A and B are partners sharing profits in the ratio of 3 : 2. They admit C as a new partner from 1st April, 2019. They have decided to share future profits in the ratio of 4 : 3 : 3. The Balance Sheet as at 31st March, 2019 is given below: Liabilities ₹ Assets ₹ A's Capital 1,76,000 Goodwill 34,000 B's Capital 2,54,000 4,30,000 Land and Building 60,000 Workmen Compensation Reserve 20,000 Investment (Market value ₹ 45,000) 50,000 Investments Fluctuation Reserve 10,000 Debtors 1,00,000 Employee's Provident Fund 34,000 Less: Provision for Doubtful Debts 10,000 90,000 C's Loan 3,00,000 Stock 3,00,000 Bank Balance 2,50,000 Advertising Suspense A/c 10,000 7,94,000 7,94,000 Terms of C's admission are as follows:(i) C contributes proportionate capital and 60% of his share of goodwill in cash.(ii) Goodwill is to be valued at 2 years' purchase of super profit of last three completed years. Profits for the years ended 31st March were:2017 − ₹ 4,80,000; 2018 − ₹ 9,30,000; 2019 − ₹ 13,80,000.The normal profit is ₹ 5,30,000 with same amount of capital invested in similar industry.(iii) Land and Building was found undervalued by ₹ 1,00,000.(iv) Stock was found overvalued by ₹ 31,000.(v) Provision for Doubtful Debts is to be made equal to 5% of the debtors.(vi) Claim on account of Workmen Compensation is ₹ 11,000.Prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet.

Answer» A and B are partners sharing profits in the ratio of 3 : 2. They admit C as a new partner from 1st April, 2019. They have decided to share future profits in the ratio of 4 : 3 : 3. The Balance Sheet as at 31st March, 2019 is given below:


Liabilities		₹	Assets		₹
A's Capital	1,76,000		Goodwill		34,000
B's Capital	2,54,000	4,30,000	Land and Building		60,000
Workmen Compensation Reserve		20,000	Investment (Market value ₹ 45,000)		50,000
Investments Fluctuation Reserve		10,000	Debtors	1,00,000
Employee's Provident Fund		34,000	Less: Provision for Doubtful Debts	10,000	90,000
C's Loan		3,00,000	Stock		3,00,000
			Bank Balance		2,50,000
			Advertising Suspense A/c		10,000



		7,94,000			7,94,000

Terms of C's admission are as follows:

(i) C contributes proportionate capital and 60% of his share of goodwill in cash.

(ii) Goodwill is to be valued at 2 years' purchase of super profit of last three completed years. Profits for the years ended 31st March were:

2017 − ₹ 4,80,000; 2018 − ₹ 9,30,000; 2019 − ₹ 13,80,000.

The normal profit is ₹ 5,30,000 with same amount of capital invested in similar industry.

(iii) Land and Building was found undervalued by ₹ 1,00,000.

(iv) Stock was found overvalued by ₹ 31,000.

(v) Provision for Doubtful Debts is to be made equal to 5% of the debtors.

(vi) Claim on account of Workmen Compensation is ₹ 11,000.

Prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet.

Discussion

3855.	Question 12If P(9a-2,-b) divides line segment joining A(3a+1,-3) and B(8a,5) in the ratio 3:1, then find the values of a and b.
Answer» Question 12 If P(9a-2,-b) divides line segment joining A(3a+1,-3) and B(8a,5) in the ratio 3:1, then find the values of a and b.

Discussion

3856.	Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.
Answer» Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.

Discussion

3857.	Find the number of terms of the AP −12, −9, −6, ..., 21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained. [CBSE 2013]
Answer» Find the number of terms of the AP −12, −9, −6, ..., 21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained. [CBSE 2013]

Discussion

3858.	A bomber want to destroy a bridge.Two bombs are sufficient to destroy it .If four are dropped,what is the probability that it is destroyed, if the chance of a bomb hitting the target is 0.4
Answer» A bomber want to destroy a bridge.Two bombs are sufficient to destroy it .If four are dropped,what is the probability that it is destroyed, if the chance of a bomb hitting the target is 0.4

Discussion

3859.	A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone. [4 MARKS]
Answer» A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone. [4 MARKS]

Discussion

3860.	The cost (in ₹) of painting a conical tent of radius 3.5 m and slant height 7 m at a rate of ₹ 10/m2 is770
Answer» The cost (in ₹) of painting a conical tent of radius 3.5 m and slant height 7 m at a rate of $₹ 10 / m^{2}$ is 770

Discussion

3861.	The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.
Answer» The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.

Discussion

3862.	The corresponding sides of two triangles △ABC and △PQR are in the ratio 4:23.If ∠B=60∘ and ∠A=40∘, find the measure of ∠R.
Answer» $The corresponding sides of two triangles △ A B C and △ P Q R are in the ratio 4:23.$ $If ∠ B = 60^{\circ} and ∠ A = 40^{\circ}, find the measure of ∠ R .$

Discussion

3863.	If (a, a^2) falls inside the angle made by the linear equations y=x/2, x>0 and y=3x ,x>0, then 'a' belongs to
Answer» If (a, a^2) falls inside the angle made by the linear equations y=x/2, x>0 and y=3x ,x>0, then 'a' belongs to

Discussion

3864.	ntSurface area of a cube changing at the rate of 5m/sec sq. find the rate of change of body diagonal when the side length is 1m.n
Answer» ntSurface area of a cube changing at the rate of 5m/sec sq. find the rate of change of body diagonal when the side length is 1m.n

Discussion

3865.

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data: Class interval 5−10 10−15 15−20 20−25 25−30 30−35 35−40 Frequency 2 12 2 4 3 4 3

Answer»

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data:

Class interval	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	12	2	4	3	4	3

Discussion

3866.	The enrolment in a school during six consecutive years was as follows:1555, 1670, 1750, 2013, 2540, 2820. Find the mean enrolment of the school for this period.
Answer» The enrolment in a school during six consecutive years was as follows: 1555, 1670, 1750, 2013, 2540, 2820. Find the mean enrolment of the school for this period.

Discussion

3867.	In ΔABC and ΔDEF, if ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are ________ but not ________.
Answer» In ΔABC and ΔDEF, if ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are ________ but not ________.

Discussion

3868.	A rectangular sheet of paper 40 cm ⨯ 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is [CBSE 2014](a) 3.5(b) 7(c) 807(d) 5
Answer» A rectangular sheet of paper 40 cm ⨯ 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is [CBSE 2014] (a) 3.5 (b) 7 (c) $\frac{80}{7}$ (d) 5

Discussion

3869.	The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.
Answer» The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

Discussion

3870.	For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x’. The quadratic equation representing the situation is:
Answer» For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x’. The quadratic equation representing the situation is:

Discussion

3871.	Find the value of x in the given figure if ∠AOB=70∘ and AB=CD.
Answer» Find the value of $x$ in the given figure if $∠ A O B = 70^{\circ}$ and $A B = C D .$

Discussion

3872.	A box contains paper slips with numbers written on them −4 odd and 5 even. Two more paper slips, one with an odd number and another with an even number are put in. Does the probability of getting an odd number increase of decrease? What about the probability of getting an even number?
Answer» A box contains paper slips with numbers written on them −4 odd and 5 even. Two more paper slips, one with an odd number and another with an even number are put in. Does the probability of getting an odd number increase of decrease? What about the probability of getting an even number?

Discussion

3873.	In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them: The ratio of ∠BOC and ∠POQ is ___
Answer» In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them: The ratio of $∠ B O C$ and $∠ P O Q$ is ___

3873.

In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them: The ratio of ∠BOC and ∠POQ is ___

Answer»

In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them:

The ratio of $∠ B O C$ and $∠ P O Q$ is ___

Discussion

3874.	Let p be a prime number. If p divides a2 then _________, where a is a positive integer.
Answer» Let p be a prime number. If p divides $a^{2}$ then _________, where a is a positive integer.

Discussion

3875.	A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45o. The height of the tower will be
Answer» A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45^o. The height of the tower will be

Discussion

3876.	A hemispherical bowl of internal radius 9 cm is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles are needed to empty the bowl ?
Answer» A hemispherical bowl of internal radius 9 cm is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles are needed to empty the bowl ?

Discussion

3877.	tan(2A)=cot(A-180) then find value of A
Answer» tan(2A)=cot(A-180) then find value of A

Discussion

3878.

Write the following transactions in the Cash Book of Premium Stores, Kolkata (Proprietor Amrit Kumar): 2018 ₹ Jan 1 Commenced business with cash 50,000 Jan 2 Opened Bank Account and deposited cash in bank 20,000 Purchased goods in cash of ₹5,000 plus CGST and SGST 6% each 5,000 Jan 4 Paid wages 500 Jan 6 Cash sales of ₹2,000 plus CGST and SGST 6% each 2,000 Purchased goods for ₹10,000 plus CGST and SGST 6% each for cash Jan 10 Sold goods of ₹ 4,000 plus CGST and SGST 6% each and payment received by cheque which is deposited in Bank, allowed cash discount of ₹400 Received from Amit 5,900 Allowed him discount 100 Jan 15 Paid to Bhaskar 2,800 Received discount 200 Jan 18 Purchased goods from Kanchan, Delhi of ₹10,000 plus IGST 12% Jan 20 Goods were destroyed during transportation, Transport Company settled the claim for ₹10,000 in full Jan 27 Received cheque from the transport company 10,000 Jan 28 Withdrew for office use 5,000

Answer» Write the following transactions in the Cash Book of Premium Stores, Kolkata (Proprietor Amrit Kumar):


2018		₹
Jan 1	Commenced business with cash	50,000
Jan 2	Opened Bank Account and deposited cash in bank	20,000
	Purchased goods in cash of ₹5,000 plus CGST and SGST 6% each	5,000
Jan 4	Paid wages	500
Jan 6	Cash sales of ₹2,000 plus CGST and SGST 6% each	2,000
	Purchased goods for ₹10,000 plus CGST and SGST 6% each for cash
Jan 10	Sold goods of ₹ 4,000 plus CGST and SGST 6% each and payment received by cheque which is deposited in Bank, allowed cash discount of ₹400
	Received from Amit	5,900
	Allowed him discount	100
Jan 15	Paid to Bhaskar	2,800
	Received discount	200
Jan 18	Purchased goods from Kanchan, Delhi of ₹10,000 plus IGST 12%
Jan 20	Goods were destroyed during transportation, Transport Company settled the claim for ₹10,000 in full
Jan 27	Received cheque from the transport company	10,000
Jan 28	Withdrew for office use	5,000

Discussion

3879.	Find the 19th term of the following A.P.7, 13, 19, 25,....
Answer» Find the 19^th term of the following A.P. 7, 13, 19, 25,....

Discussion

3880.	A says to B" i was four times as old as you were when i was as old as you are" . if the sum of their present ages is 33 find the present ages of A and B
Answer» A says to B" i was four times as old as you were when i was as old as you are" . if the sum of their present ages is 33 find the present ages of A and B

Discussion

3881.	if the point p(4a,2a-1) lies on the graph of the graph of equationx-2y=2,then the number of values of a is/are
Answer» if the point p(4a,2a-1) lies on the graph of the graph of equationx-2y=2,then the number of values of a is/are

Discussion

3882.	Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.
Answer» Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

Discussion

3883.	Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is(a) 15 (b) 45 (c) 130 (d) 59
Answer» Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is (a) $\frac{1}{5}$ (b) $\frac{4}{5}$ (c) $\frac{1}{30}$ (d) $\frac{5}{9}$

Discussion

3884.	A village has a population of 4000, requires 150 litres water per head per day. It has a tank measuring 20 m , 15 m , 6 m. How many days for the water is sufficient enough once the tank is made full.
Answer» A village has a population of 4000, requires 150 litres water per head per day. It has a tank measuring 20 m , 15 m , 6 m. How many days for the water is sufficient enough once the tank is made full.

Discussion

3885.	Prove that (tan θ+cot θ)2=sec2 θ+cosec2 θ [3 MARKS]
Answer» Prove that $(t a n θ + c o t θ)^{2} = s e c^{2} θ + c o s e c^{2} θ$ [3 MARKS]

Discussion

3886.	Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.[Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
Answer» Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]

Discussion

3887.	If x+1x=2 then the positive value of √x+1√x will be
Answer» If $x + \frac{1}{x} = 2$ then the positive value of $\sqrt{x} + \frac{1}{\sqrt{x}}$ will be

Discussion

3888.	In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP=BQ
Answer» In the given figure, centre of two circles is $O$ . Chord $A B$ of bigger circle intersects the smaller circle in points $P$ and $Q$ . Show that $A P = B Q$

Discussion

3889.	Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm. 150178153156162184170176186173153186162159180183165180150156
Answer» Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm. $\begin{matrix} 150 & 178 153 & 156 162 & 184 170 & 176 186 & 173 153 & 186 162 & 159 180 & 183 165 & 180 150 & 156 \end{matrix}$

3889.

Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm. 150178153156162184170176186173153186162159180183165180150156

Answer»

Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm.

$\begin{matrix} 150 & 178 153 & 156 162 & 184 170 & 176 186 & 173 153 & 186 162 & 159 180 & 183 165 & 180 150 & 156 \end{matrix}$

Discussion

3890.	Question 6Describe how the two figures below are alike and how they are different. Which box has larger lateral surface area?
Answer» Question 6 Describe how the two figures below are alike and how they are different. Which box has larger lateral surface area?

Discussion

3891.	If a and b are the zeroes of 2x2 + 5 x + k such that a2+b2+ ab = 21/4, find k
Answer» If a and b are the zeroes of 2x² + 5 x + k such that a²+b²+ ab = 21/4, find k

Discussion

3892.	If sec^-1 (tanx) + cosec^-1 (tanx)= pi/2Then exhaustive range of x is?
Answer» If sec^-1 (tanx) + cosec^-1 (tanx)= pi/2 Then exhaustive range of x is?

Discussion

3893.	Let and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
Answer» Let and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC.

Discussion

3894.

Enter the following transactions in proper Subsidiary Books, post them into Ledger Accounts, balance the accounts and prepare a Trial Balance : 2017 Jan. 1 Assets : Cash in hand ₹ 20,000; Debtors : Sri Gopal ₹ 15,000, Poonam & Co. ₹ 30,000; Stock ₹ 1,75,000, Machinery ₹ 1,20,000; Furniture ₹ 40,000. Liabilities: Bank Overdraft ₹ 33,000; Creditors : Niranjan Lal ₹ 24,000, Bombay Trading Co. ₹ 16,000. Jan. 2 Purchased from Manohar Lal & Sons goods of the list price of ₹ 20,000 at 10% trade discount. 5 Returned to Manohar Lal & sons goods of the list price of ₹ 2,000. 10 Issued a Cheque to Manohar Lal & Sons in full settlement of their account. 12 Sold to Sri Gopal, goods worth ₹ 25,000. 15 Received Cash ₹ 10,000 and a Cheque for ₹ 8,000 from Sir Gopal. The Cheque was immediately sent to bank. 16 Withdrew for personal use : Cash ₹ 5,000 and goods ₹ 3,000. 17 Accepted a bill for 45 days drawn by Niranjan Lal for the amount due to him. 18 Acceptance received from Poonam & Co. for the amount due from them payable after 30 days. 19 Sold to Raghubir Brothers, goods valued ₹ 16,000. 20 Cash purchases ₹ 15,000. 22 Withdrew from bank fo office use ₹ 10,000. 23 Purchased from Bombay Trading Co., goods valued ₹ 24,000. 24 Sri Gopal returned goods worth ₹ 2,000. 25 Received from Raghubir Brothers ₹ 10,000. 27 Accepted a bill for ₹ 25,000 for 1 month drawn by Bombay Trading Co. 27 Paid Rent by Cheque ₹ 2,800. Received Commission in Cash ₹ 800. 31 Paid salaries ₹ 5,000.

Answer» Enter the following transactions in proper Subsidiary Books, post them into Ledger Accounts, balance the accounts and prepare a Trial Balance :

2017
Jan. 1	Assets :	Cash in hand ₹ 20,000; Debtors : Sri Gopal ₹ 15,000, Poonam & Co. ₹ 30,000; Stock ₹ 1,75,000, Machinery ₹ 1,20,000; Furniture ₹ 40,000.
	Liabilities:	Bank Overdraft ₹ 33,000; Creditors : Niranjan Lal ₹ 24,000, Bombay Trading Co. ₹ 16,000.
Jan. 2		Purchased from Manohar Lal & Sons goods of the list price of ₹ 20,000 at 10% trade discount.
5		Returned to Manohar Lal & sons goods of the list price of ₹ 2,000.
10		Issued a Cheque to Manohar Lal & Sons in full settlement of their account.
12		Sold to Sri Gopal, goods worth ₹ 25,000.
15		Received Cash ₹ 10,000 and a Cheque for ₹ 8,000 from Sir Gopal. The Cheque was immediately sent to bank.
16		Withdrew for personal use : Cash ₹ 5,000 and goods ₹ 3,000.
17		Accepted a bill for 45 days drawn by Niranjan Lal for the amount due to him.
18		Acceptance received from Poonam & Co. for the amount due from them payable after 30 days.
19		Sold to Raghubir Brothers, goods valued ₹ 16,000.
20		Cash purchases ₹ 15,000.
22		Withdrew from bank fo office use ₹ 10,000.
23		Purchased from Bombay Trading Co., goods valued ₹ 24,000.
24		Sri Gopal returned goods worth ₹ 2,000.
25		Received from Raghubir Brothers ₹ 10,000.
27		Accepted a bill for ₹ 25,000 for 1 month drawn by Bombay Trading Co.
27		Paid Rent by Cheque ₹ 2,800.
		Received Commission in Cash ₹ 800.
31		Paid salaries ₹ 5,000.

Discussion

3895.	Solve the following inequation and graph the solution on the number line. −223≤x+13<313;xϵR [4 MARKS]
Answer» Solve the following inequation and graph the solution on the number line. $- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x ϵ R$ [4 MARKS]

Discussion

3896.	A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cm3 (Take π=227) __
Answer» A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest $c m^{3}$ (Take $π = \frac{22}{7}$ ) __

Discussion

3897.	Find the polynomial from the given information.Quotient =x3+2xDivisor =x2+12xRemainder =5
Answer» $Find the polynomial from the given information.$ $Quotient = x^{3} + 2 x$ $Divisor = x^{2} + \frac{1}{2} x$ $Remainder = 5$

Discussion

3898.	A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .
Answer» A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

Discussion

3899.	In the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.
Answer» In the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.

Discussion

3900.	Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is(i) not divisible by 3,(ii) a prime number greater than 7,(iii) not a perfect square number.
Answer» Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) not divisible by 3, (ii) a prime number greater than 7, (iii) not a perfect square number.

Discussion

Explore topic-wise InterviewSolutions in .

If 2 and -2 are two zeros of the polynomial (x4+x3−34x2−4x+120), find all the zeros of the given polynomial.

Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

Question 12If P(9a-2,-b) divides line segment joining A(3a+1,-3) and B(8a,5) in the ratio 3:1, then find the values of a and b.

Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.

Find the number of terms of the AP −12, −9, −6, ..., 21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained. [CBSE 2013]

A bomber want to destroy a bridge.Two bombs are sufficient to destroy it .If four are dropped,what is the probability that it is destroyed, if the chance of a bomb hitting the target is 0.4

The cost (in ₹) of painting a conical tent of radius 3.5 m and slant height 7 m at a rate of ₹ 10/m2 is770

The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.

The corresponding sides of two triangles △ABC and △PQR are in the ratio 4:23.If ∠B=60∘ and ∠A=40∘, find the measure of ∠R.

If (a, a^2) falls inside the angle made by the linear equations y=x/2, x>0 and y=3x ,x>0, then 'a' belongs to

ntSurface area of a cube changing at the rate of 5m/sec sq. find the rate of change of body diagonal when the side length is 1m.n

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data: Class interval 5−10 10−15 15−20 20−25 25−30 30−35 35−40 Frequency 2 12 2 4 3 4 3

The enrolment in a school during six consecutive years was as follows:1555, 1670, 1750, 2013, 2540, 2820. Find the mean enrolment of the school for this period.

In ΔABC and ΔDEF, if ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are ________ but not ________.

A rectangular sheet of paper 40 cm ⨯ 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is [CBSE 2014](a) 3.5(b) 7(c) 807(d) 5

The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x’. The quadratic equation representing the situation is:

Find the value of x in the given figure if ∠AOB=70∘ and AB=CD.

A box contains paper slips with numbers written on them −4 odd and 5 even. Two more paper slips, one with an odd number and another with an even number are put in. Does the probability of getting an odd number increase of decrease? What about the probability of getting an even number?

In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them: The ratio of ∠BOC and ∠POQ is ___

Let p be a prime number. If p divides a2 then _________, where a is a positive integer.

A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45o. The height of the tower will be

A hemispherical bowl of internal radius 9 cm is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles are needed to empty the bowl ?

tan(2A)=cot(A-180) then find value of A

Find the 19th term of the following A.P.7, 13, 19, 25,....

A says to B" i was four times as old as you were when i was as old as you are" . if the sum of their present ages is 33 find the present ages of A and B

if the point p(4a,2a-1) lies on the graph of the graph of equationx-2y=2,then the number of values of a is/are

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is(a) 15 (b) 45 (c) 130 (d) 59

A village has a population of 4000, requires 150 litres water per head per day. It has a tank measuring 20 m , 15 m , 6 m. How many days for the water is sufficient enough once the tank is made full.

Prove that (tan θ+cot θ)2=sec2 θ+cosec2 θ [3 MARKS]

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.[Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]

If x+1x=2 then the positive value of √x+1√x will be

In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP=BQ

Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm. 150178153156162184170176186173153186162159180183165180150156

Question 6Describe how the two figures below are alike and how they are different. Which box has larger lateral surface area?

If a and b are the zeroes of 2x2 + 5 x + k such that a​​​​​​2+b​​​​​​2+ ab = 21/4, find k

If sec^-1 (tanx) + cosec^-1 (tanx)= pi/2Then exhaustive range of x is?

Let and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.

Solve the following inequation and graph the solution on the number line. −223≤x+13&lt;313;xϵR [4 MARKS]

Find the polynomial from the given information.Quotient =x3+2xDivisor =x2+12xRemainder =5

A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

In the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is(i) not divisible by 3,(ii) a prime number greater than 7,(iii) not a perfect square number.

In ΔABC and ΔDEF, if ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are but not .

If a and b are the zeroes of 2x2 + 5 x + k such that a2+b2+ ab = 21/4, find k

Solve the following inequation and graph the solution on the number line. −223≤x+13<313;xϵR [4 MARKS]