32581 + Interview Questions in Mathematics Page 181 InterviewSolution

9001.	The roots of the equation x2 + x - (p +1) = 0, where p is a constant are
Answer» The roots of the equation $x^{2}$ + x - (p +1) = 0, where p is a constant are

Discussion

9002.	Question 2In a triangle ABC, E is the mid-point of the median AD.Show that ar(ΔBED)=14ar(ΔABC)
Answer» Question 2 In a triangle ABC, E is the mid-point of the median AD. Show that ar $(Δ B E D) = \frac{1}{4} a r (Δ A B C)$

Discussion

9003.	A, B and C who are presently sharing profits and losses in the ratio of 5 : 3 : 2 decide to share future profits and losses in the ratio of 2 : 3 : 5. Give the journal entry to distribute 'Investments Fluctuation Reserve' of ₹ 20,000 at the time of change in profit-sharing ratio, when investment (market value ₹ 95,000) appears in the books at ₹ 1,00,000.
Answer» A, B and C who are presently sharing profits and losses in the ratio of 5 : 3 : 2 decide to share future profits and losses in the ratio of 2 : 3 : 5. Give the journal entry to distribute 'Investments Fluctuation Reserve' of ₹ 20,000 at the time of change in profit-sharing ratio, when investment (market value ₹ 95,000) appears in the books at ₹ 1,00,000.

Discussion

9004.	If the sum of a number and its square is 6/25 , then the number is [1] 1/8 [2] 1/4 [3] 1/5 [4] 1/16
Answer» If the sum of a number and its square is 6/25 , then the number is [1] 1/8 [2] 1/4 [3] 1/5 [4] 1/16

Discussion

9005.	Question 1 (iii) For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?
Answer» Question 1 (iii) For what value(s) of $λ$ , does the pair of linear equations $λ x + y = λ^{2} a n d x + λ y = 1$ have a unique solution?

Discussion

9006.	Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is(Use π=3.14)
Answer» Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is(Use $π = 3.14$ )

Discussion

9007.	The first and last term of an A.P are 5 and 45 respectively. If the sum of all the terms is 400, find the common difference.
Answer» The first and last term of an A.P are $5$ and $45$ respectively. If the sum of all the terms is $400,$ find the common difference.

Discussion

9008.	When a whole number a is divided by a non-zero whole number b, then there exists whole numbers q and rsuch that a = bq + r, where r = ......... or r < .............
Answer» When a whole number a is divided by a non-zero whole number b, then there exists whole numbers q and r such that a = bq + r, where r = ......... or r < .............

Discussion

9009.

Following are the bearing of a closed triangular traverse LineFBBBAB S46∘30′EN46∘30′WBCS50∘10′WN50∘45′ECAN10∘30′ES11∘05′WThe correct value of included angle B is

Answer»

Following are the bearing of a closed triangular traverse

Line	FB	BB
AB	$S 46^{\circ} 30^{'} E$	$N 46^{\circ} 30^{'} W$
BC	$S 50^{\circ} 10^{'} W$	$N 50^{\circ} 45^{'} E$
CA	$N 10^{\circ} 30^{'} E$	$S 11^{\circ} 05^{'} W$

The correct value of included angle B is

Discussion

9010.	The nth term of an A.P., the sum of whose n terms is Sn, is(a) Sn + Sn−1(b) Sn − Sn−1(c) Sn + Sn+1(d) Sn − Sn+1
Answer» The nth term of an A.P., the sum of whose n terms is S_n, is (a) S_n + S_n−1 (b) S_n− S_n−1 (c) S_n + S_n+1 (d) S_n − S_n+1

Discussion

9011.	Question 5 Classify the following as linear, quadriatic and cubic polynomials: (i) x2+x (ii) x−x3 (iii) y+y2+4 (iv) 1 + x (v) 3t (vi) r2 (viii)7x3
Answer» Question 5 Classify the following as linear, quadriatic and cubic polynomials: (i) $x^{2} + x$ (ii) $x - x^{3}$ (iii) $y + y^{2} + 4$ (iv) 1 + x (v) 3t (vi) $r^{2}$ (viii) $7 x^{3}$

Discussion

9012.	Find the quadratic polynomial whose zeroes are 6+√33 and 6−√33 .
Answer» Find the quadratic polynomial whose zeroes are $\frac{6 + \sqrt{3}}{3} and \frac{6 - \sqrt{3}}{3} .$

Discussion

9013.	Write down the sequence of natural number ending in 1 or 6 and describe it in two ither ways
Answer» Write down the sequence of natural number ending in 1 or 6 and describe it in two ither ways

Discussion

9014.	Through any given set of four distinct points P, Q, R, S it is possible to draw at most ___circle(s).
Answer» Through any given set of four distinct points P, Q, R, S it is possible to draw at most ___circle(s).

Discussion

9015.	The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is: (a) 8000 (b) 1600 (c) 320 (d) 1605
Answer» The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is: (a) 8000 (b) 1600 (c) 320 (d) 1605

9015.

The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is: (a) 8000 (b) 1600 (c) 320 (d) 1605

Answer»

The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is:

(a) 8000 (b) 1600 (c) 320 (d) 1605

Discussion

9016.	Question 7 (i)If cot θ=78, evaluate:(i) (1+sin θ)(1−sin θ)(1+cos θ)(1−cos θ)
Answer» Question 7 (i) If $c o t θ = \frac{7}{8}$ , evaluate: (i) $\frac{(1 + s i n θ) (1 - s i n θ)}{(1 + c o s θ) (1 - c o s θ)}$

Discussion

9017.	tan 55cot 55 × sin 30 = A Find the value of 2A.
Answer» $\frac{t a n 55}{c o t 55}$ $\times$ sin 30 = A Find the value of 2A.

9017.

tan 55cot 55 × sin 30 = A Find the value of 2A.

Answer»

$\frac{t a n 55}{c o t 55}$ $\times$ sin 30 = A

Find the value of 2A.

Discussion

9018.	Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:(i) 2x + 3y = 12,x − y = 1(ii) 3x + 2y − 4 = 0,2x − 3y − 7 = 0(iii) 3x + 2y − 11 = 02x − 3y + 10 = 0
Answer» Solve the following system of linear equation graphically and shade the region between the two lines and x-axis: (i) 2x + 3y = 12, x − y = 1 (ii) 3x + 2y − 4 = 0, 2x − 3y − 7 = 0 (iii) 3x + 2y − 11 = 0 2x − 3y + 10 = 0

Discussion

9019.	Through the mid -point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL. [4 MARKS]
Answer» Through the mid -point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL. [4 MARKS]

Discussion

9020.	A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.
Answer» A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

Discussion

9021.	The final marks in mathematics of 30 students are as follows:53, 61, 48, 60, 78, 68, 55, 100, 67, 90,75, 88, 77, 37, 84, 58, 60, 48, 62, 56,44, 58, 52, 64, 98, 59, 70, 39, 50, 60.(i) Arrange these marks in ascending order, 30 to 39 one group,40 to 49 second group etc.Now answer the following:(ii) What is the highest score?(iii) What is the lowest score?(iv) What is the range?(v) If 40 is the passmark, how many have failed?(vi) How many have scored 75 or more?(vii) Which observations between 50 and 60 have not actually appeared?(viii) How many have scored less than 50?
Answer» The final marks in mathematics of 30 students are as follows: 53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60. (i) Arrange these marks in ascending order, 30 to 39 one group,40 to 49 second group etc. Now answer the following: (ii) What is the highest score? (iii) What is the lowest score? (iv) What is the range? (v) If 40 is the passmark, how many have failed? (vi) How many have scored 75 or more? (vii) Which observations between 50 and 60 have not actually appeared? (viii) How many have scored less than 50?

Discussion

9022.	Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its54th term?
Answer» Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its $54^{t h}$ term?

Discussion

9023.	Consider any simple triangle. Construct another triangle similar to the first triangle with their sides equal to 34 of the corresponding sides of the initial triangle.
Answer» Consider any simple triangle. Construct another triangle similar to the first triangle with their sides equal to $\frac{3}{4}$ of the corresponding sides of the initial triangle.

Discussion

9024.	The equation of y-axis in space is(a) x = 0, z = 0 (b) x = 0, y = 0 (c) y = 0, z = 0 (d) y = 0
Answer» The equation of y-axis in space is (a) x = 0, z = 0 (b) x = 0, y = 0 (c) y = 0, z = 0 (d) y = 0

Discussion

9025.	tan (A+B) = m , tan (A-B) = n , then cot2B=?
Answer» tan (A+B) = m , tan (A-B) = n , then cot2B=?

Discussion

9026.	The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are(a) (3, 0)(b) (0, 2)(c) (2, 3)(d) (3, 2)
Answer» The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are (a) (3, 0) (b) (0, 2) (c) (2, 3) (d) (3, 2)

Discussion

9027.	The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find : (i) the equation of AB; (ii) the co-ordinates of the point where the line AB intersects the y-axis.
Answer» The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find : (i) the equation of AB; (ii) the co-ordinates of the point where the line AB intersects the y-axis.

9027.

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find : (i) the equation of AB; (ii) the co-ordinates of the point where the line AB intersects the y-axis.

Answer»

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :

(i) the equation of AB;

(ii) the co-ordinates of the point where the line AB intersects the y-axis.

Discussion

9028.	A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
Answer» A die is rolled. Let $E$ be the event “die shows $4$ ” and $F$ be the event “die shows even number”. Are $E and F$ mutually exclusive?

Discussion

9029.	Question 3 If tan2A=cot(A−18∘), where 2A is an acute angle, find the value of A.
Answer» Question 3 If $t a n 2 A = c o t (A - 18^{\circ})$ , where 2A is an acute angle, find the value of A.

Discussion

9030.	Midee Ltd. invited applications for issuing 27,000 shares of ₹ 100 each payable as follows: ₹ 50—per share on application; ₹ 10—per share on allotment; and Balance—on First and Final call.Applications were received for 40,000 shares. Full allotment was made to the applicants of 7,000 shares. The remaining applicants were allotted 20,000 shares on pro rata basis. Excess money received on applications was adjusted towards allotment and call.Asha, holding 600 shares was belonged to the category of applicants to whom full allotment was made ,paid the call money at the time of allotment . Ankur, who belonged to the category of applicants to whom shares were allotted on pro rata basis did not pay anything after application on his 200 shares . Ankur's shares were forfeited after the First and Final call. These shares were later reissued at ₹ 105 per share as fully paid-up.Pass necessary journal entries in the books of Midee Ltd . for the above transactions, by opening Calls-in-Arrears and Calls-in-Advance Accounts wherever necessary.
Answer» Midee Ltd. invited applications for issuing 27,000 shares of ₹ 100 each payable as follows: ₹ 50 $—$ per share on application; ₹ 10 $—$ per share on allotment; and Balance $—$ on First and Final call. Applications were received for 40,000 shares. Full allotment was made to the applicants of 7,000 shares. The remaining applicants were allotted 20,000 shares on pro rata basis. Excess money received on applications was adjusted towards allotment and call. Asha, holding 600 shares was belonged to the category of applicants to whom full allotment was made ,paid the call money at the time of allotment . Ankur, who belonged to the category of applicants to whom shares were allotted on pro rata basis did not pay anything after application on his 200 shares . Ankur's shares were forfeited after the First and Final call. These shares were later reissued at ₹ 105 per share as fully paid-up. Pass necessary journal entries in the books of Midee Ltd . for the above transactions, by opening Calls-in-Arrears and Calls-in-Advance Accounts wherever necessary.

Discussion

9031.	The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.
Answer» The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

Discussion

9032.	Using Euclid's Division lemma, show that the cubeof any positive integer is of the form 9m, 9m +1or 9m +8
Answer» Using Euclid's Division lemma, show that the cubeof any positive integer is of the form 9m, 9m +1or 9m +8

Discussion

9033.	Question 12Circumference of two circles are equal. Is it necessary that their areas be equal? Why?
Answer» Question 12 Circumference of two circles are equal. Is it necessary that their areas be equal? Why?

Discussion

9034.	Question 3Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using a similarity criterion for two triangles, show that AOOC=OBOD.
Answer» Question 3 Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using a similarity criterion for two triangles, show that $\frac{A O}{O C} = \frac{O B}{O D}$ .

Discussion

9035.	A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?(i) that the sum of the two numbers that turn up is 7?(ii) of obtaining a total of 6?(iii) of obtaining a total of 10?(iv) of obtaining the same number on both dice?(v) of obtaining a total more than 9?(vi) that the sum of the two numbers appearing on the top of the dice is 13?(vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12?(viii) that the product of numbers appearing on the top of the dice is less than 9. [CBSE 2014](ix) that the difference of the numbers appearing on the top of two dice is 2. [CBSE 2014](x) that the numbers obtained have a product less then 16.
Answer» A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability? (i) that the sum of the two numbers that turn up is 7? (ii) of obtaining a total of 6? (iii) of obtaining a total of 10? (iv) of obtaining the same number on both dice? (v) of obtaining a total more than 9? (vi) that the sum of the two numbers appearing on the top of the dice is 13? (vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12? (viii) that the product of numbers appearing on the top of the dice is less than 9. [CBSE 2014] (ix) that the difference of the numbers appearing on the top of two dice is 2. [CBSE 2014] (x) that the numbers obtained have a product less then 16.

Discussion

9036.	The largest possible number with which when 60 and 98 are divided , leaves remainder 3 in each case ...??
Answer» The largest possible number with which when 60 and 98 are divided , leaves remainder 3 in each case ...??

Discussion

9037.	Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.
Answer» Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.

Discussion

9038.	A cardboard rectangle is cut out and the midpoint of one side is joined to the other ends to make a triangle. If you randomly put a dot in the rectangle, what is the probability that it would be within the triangle?
Answer» A cardboard rectangle is cut out and the midpoint of one side is joined to the other ends to make a triangle. If you randomly put a dot in the rectangle, what is the probability that it would be within the triangle?

Discussion

9039.	In an office, the working hours are from 10.30 AM to 5.30 PM. In between, 30 minutes are spent on lunch. Find the ratio of office hours to the time spent for lunch.
Answer» In an office, the working hours are from 10.30 AM to 5.30 PM. In between, 30 minutes are spent on lunch. Find the ratio of office hours to the time spent for lunch.

Discussion

9040.	2 is(a) a rational number(b) an irrational number(c) a terminating decimal(d) a nonterminating repeating decimal
Answer» $\sqrt{2}$ is (a) a rational number (b) an irrational number (c) a terminating decimal (d) a nonterminating repeating decimal

Discussion

9041.	Which of the following is(are) correct for ∫dx√2−6x−9x2=Asin−1(f(x))+C(where A is a fixed constant and C is integration constant)
Answer» Which of the following is(are) correct for $\int \frac{d x}{\sqrt{2 - 6 x - 9 x^{2}}} = A {sin}^{- 1} (f (x)) + C$ (where $A$ is a fixed constant and $C$ is integration constant)

Discussion

9042.	Find the value of k for which each of the following system of equations have no solution :2x-ky+3=03x+2y-1=0
Answer» Find the value of k for which each of the following system of equations have no solution : $2 x - k y + 3 = 0 3 x + 2 y - 1 = 0$

Discussion

9043.	Examine whether the following numbers are rational or irrational.(i) 3+3(ii) 7-2(iii) 53×253(iv) 7×343(v) 13117(vi) 8×2
Answer» Examine whether the following numbers are rational or irrational. (i) $3 + \sqrt{3}$ (ii) $\sqrt{7} - 2$ (iii) $\sqrt[3]{5} \times \sqrt[3]{25}$ (iv) $\sqrt{7} \times \sqrt{343}$ (v) $\sqrt{\frac{13}{117}}$ (vi) $\sqrt{8} \times \sqrt{2}$

Discussion

9044.	Find the value of x and y if:(x+y, x-y) = (12, 2)
Answer» Find the value of x and y if: (x+y, x-y) = (12, 2)

Discussion

9045.	Find the mean of the given data. Class intervalFrequency0−1007100−20011200−30015300−4009400−5008
Answer» Find the mean of the given data. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 0 - 100 & 7 100 - 200 & 11 200 - 300 & 15 300 - 400 & 9 400 - 500 & 8 \end{matrix}$

Discussion

9046.	In the following figure, DE\|\|AC and DF\|\|AE. Prove that BFFE=BEEC .
Answer» In the following figure, DE\|\|AC and DF\|\|AE. Prove that $\frac{B F}{F E} = \frac{B E}{E C}$ .

Discussion

9047.	Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter.How long would it take to fill a conical vessel whose diamter at the base is 40cm and depth 24cm?
Answer» Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter.How long would it take to fill a conical vessel whose diamter at the base is 40cm and depth 24cm?

Discussion

9048.	A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in cm2) if the height of the conical part is 12 cm. ___
Answer» A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in $c m^{2}$ ) if the height of the conical part is 12 cm. ___

Discussion

9049.	Question 11Prove that the parallelogram circumscribing a circle is a rhombus.
Answer» Question 11 Prove that the parallelogram circumscribing a circle is a rhombus.

Discussion

9050.	There is a group of people, some of them are creative, some are caring and theremaining 15 are optimistic. The number of caring people is twice the number ofcreative people. If the sum of one fourth of the square of creative people along withall the caring and optimistic ones is equal to square of the number of creative people,find(i) the total number of people in the group.(ii) how many people in the group are creative?
Answer» There is a group of people, some of them are creative, some are caring and the remaining 15 are optimistic. The number of caring people is twice the number of creative people. If the sum of one fourth of the square of creative people along with all the caring and optimistic ones is equal to square of the number of creative people, find (i) the total number of people in the group. (ii) how many people in the group are creative?

Discussion

Explore topic-wise InterviewSolutions in .

The roots of the equation x2 + x - (p +1) = 0, where p is a constant are

Question 2In a triangle ABC, E is the mid-point of the median AD.Show that ar(ΔBED)=14ar(ΔABC)

If the sum of a number and its square is 6/25 , then the number is [1] 1/8 [2] 1/4 [3] 1/5 [4] 1/16

Question 1 (iii) For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is(Use π=3.14)

The first and last term of an A.P are 5 and 45 respectively. If the sum of all the terms is 400, find the common difference.

When a whole number a is divided by a non-zero whole number b, then there exists whole numbers q and rsuch that a = bq + r, where r = ......... or r < .............

Following are the bearing of a closed triangular traverse LineFBBBAB S46∘30′EN46∘30′WBCS50∘10′WN50∘45′ECAN10∘30′ES11∘05′WThe correct value of included angle B is

The nth term of an A.P., the sum of whose n terms is Sn, is(a) Sn + Sn−1(b) Sn − Sn−1(c) Sn + Sn+1(d) Sn − Sn+1

Question 5 Classify the following as linear, quadriatic and cubic polynomials: (i) x2+x (ii) x−x3 (iii) y+y2+4 (iv) 1 + x (v) 3t (vi) r2 (viii)7x3

Find the quadratic polynomial whose zeroes are 6+√33 and 6−√33 .

Write down the sequence of natural number ending in 1 or 6 and describe it in two ither ways

Through any given set of four distinct points P, Q, R, S it is possible to draw at most ___circle(s).

The product of two numbers is 1600 and their HCF is 5. The LCM of the numbers is: (a) 8000 (b) 1600 (c) 320 (d) 1605

Question 7 (i)If cot θ=78, evaluate:(i) (1+sin θ)(1−sin θ)(1+cos θ)(1−cos θ)

tan 55cot 55 × sin 30 = A Find the value of 2A.

Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:(i) 2x + 3y = 12,x − y = 1(ii) 3x + 2y − 4 = 0,2x − 3y − 7 = 0(iii) 3x + 2y − 11 = 02x − 3y + 10 = 0

Through the mid -point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL. [4 MARKS]

A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its54th term?

Consider any simple triangle. Construct another triangle similar to the first triangle with their sides equal to 34 of the corresponding sides of the initial triangle.

The equation of y-axis in space is​(a) x = 0, z = 0 (b) x = 0, y = 0 (c) y = 0, z = 0 (d) y = 0

tan (A+B) = m , tan (A-B) = n , then cot2B=?

The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are(a) (3, 0)(b) (0, 2)(c) (2, 3)(d) (3, 2)

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find : (i) the equation of AB; (ii) the co-ordinates of the point where the line AB intersects the y-axis.

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

Question 3 If tan2A=cot(A−18∘), where 2A is an acute angle, find the value of A.

The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

Using Euclid's Division lemma, show that the cubeof any positive integer is of the form 9m, 9m +1or 9m +8

Question 12Circumference of two circles are equal. Is it necessary that their areas be equal? Why?

Question 3Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that AOOC=OBOD.

The largest possible number with which when 60 and 98 are divided , leaves remainder 3 in each case ...??

Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.

A cardboard rectangle is cut out and the midpoint of one side is joined to the other ends to make a triangle. If you randomly put a dot in the rectangle, what is the probability that it would be within the triangle?

In an office, the working hours are from 10.30 AM to 5.30 PM. In between, 30 minutes are spent on lunch. Find the ratio of office hours to the time spent for lunch.

2 is(a) a rational number(b) an irrational number(c) a terminating decimal(d) a nonterminating repeating decimal

Which of the following is(are) correct for ∫dx√2−6x−9x2=Asin−1(f(x))+C(where A is a fixed constant and C is integration constant)

Find the value of k for which each of the following system of equations have no solution :2x-ky+3=03x+2y-1=0

Examine whether the following numbers are rational or irrational.(i) 3+3(ii) 7-2(iii) 53×253(iv) 7×343(v) 13117(vi) 8×2

Find the value of x and y if:(x+y, x-y) = (12, 2)

Find the mean of the given data. Class intervalFrequency0−1007100−20011200−30015300−4009400−5008

In the following figure, DE||AC and DF||AE. Prove that BFFE=BEEC .

Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter.How long would it take to fill a conical vessel whose diamter at the base is 40cm and depth 24cm?

Question 11Prove that the parallelogram circumscribing a circle is a rhombus.

The equation of y-axis in space is(a) x = 0, z = 0 (b) x = 0, y = 0 (c) y = 0, z = 0 (d) y = 0