32581 + Interview Questions in Mathematics Page 25 InterviewSolution

1201.	A card is picked up from a deck of 52 playing cards.(i) What is the sample space of the experiment?(ii) What is the event that the chosen card is a black faced card?
Answer» A card is picked up from a deck of 52 playing cards. (i) What is the sample space of the experiment? (ii) What is the event that the chosen card is a black faced card?

Discussion

1202.	A coin is tossed 100 times with following frequency.Head: 25, Tail: 75. (i) Find the probability of getting a tail?(ii) Find the probability of getting a Head?
Answer» A coin is tossed 100 times with following frequency. Head: 25, Tail: 75. (i) Find the probability of getting a tail? (ii) Find the probability of getting a Head?

Discussion

1203.	QR is a tangent at Q to a circle whose centre is P.PR \vert\vert AQ, where AQ is a chord through A, the endpoint of the diameter AB. Prove that BR is tangentat B.
Answer» QR is a tangent at Q to a circle whose centre is P.PR \vert\vert AQ, where AQ is a chord through A, the endpoint of the diameter AB. Prove that BR is tangentat B.

Discussion

1204.	Using factor theorem, show that g(x) is a factor of p(x), whenpx=22x2+5x+2, gx=x+2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 2 \sqrt{2} x^{2} + 5 x + \sqrt{2}, g (x) = x + \sqrt{2}$

Discussion

1205.	PQRS is a cyclic quadrilateral whose diagonals intersect at A. If ∠SQR=80∘ and ∠QPR=30∘, then find ∠SRQ.
Answer» PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $∠ S Q R = 80^{\circ}$ and $∠ Q P R = 30^{\circ},$ then find $∠ S R Q .$

Discussion

1206.	If A=[2340−1−2] , B=[0−2−73−15] and C=[1−1020−6] Find a matrix X sucn that C+X=A+B
Answer» If $A = [\begin{matrix} 2 & 3 & 4 0 & - 1 & - 2 \end{matrix}], B = [\begin{matrix} 0 & - 2 & - 7 3 & - 1 & 5 \end{matrix}] and C = [\begin{matrix} 1 & - 1 & 0 2 & 0 & - 6 \end{matrix}]$ Find a matrix X sucn that C+X=A+B

Discussion

1207.	Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. [CBSE 2014]
Answer» Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. [CBSE 2014]

Discussion

1208.	14. if a+2b+c=4 then max(ab+bc+ca) is (1) 2 (2) 4 (3) 6 (4) 8
Answer» 14. if a+2b+c=4 then max(ab+bc+ca) is (1) 2 (2) 4 (3) 6 (4) 8

Discussion

1209.	Find the probability of getting the sum of two numbers, less than 3 or more than 11, when a pair of distinct dice is thrown together. [CBSE 2017]
Answer» Find the probability of getting the sum of two numbers, less than 3 or more than 11, when a pair of distinct dice is thrown together. [CBSE 2017]

Discussion

1210.	Rationalize and simplify the expression: 1√2+√3+1√2−√5+2√5−√3
Answer» Rationalize and simplify the expression: $\frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{2} - \sqrt{5}} + \frac{2}{\sqrt{5} - \sqrt{3}}$

Discussion

1211.	The value of sec2(tan-12) + cosec2 (cot-1 3) is ____________________.
Answer» The value of sec²(tan^-12) + cosec² (cot^-1 3) is ____________________.

Discussion

1212.	Let A(−1,1),B(3,4) and C(2,0) be given three points. A line y=mx,m>0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ΔABC and ΔPQC respectively, such that A1=3A2, then the value of m is equal to :
Answer» Let $A (- 1, 1), B (3, 4)$ and $C (2, 0)$ be given three points. A line $y = m x, m > 0,$ intersects lines $A C$ and $B C$ at point $P$ and $Q$ respectively. Let $A_{1}$ and $A_{2}$ be the areas of $Δ A B C$ and $Δ P Q C$ respectively, such that $A_{1} = 3 A_{2},$ then the value of $m$ is equal to :

Discussion

1213.	A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Answer» A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $14 m m$ and the diameter of the capsule is $5 m m$ . Find its surface area.

Discussion

1214.	What is the value of 8.0 km in inches? (1 m = 1.094 yards & 1 yrd = 36 inches)
Answer» What is the value of 8.0 km in inches? (1 m = 1.094 yards & 1 yrd = 36 inches)

1214.

What is the value of 8.0 km in inches? (1 m = 1.094 yards & 1 yrd = 36 inches)

Answer»

What is the value of 8.0 km in inches?

(1 m = 1.094 yards & 1 yrd = 36 inches)

Discussion

1215.	Which one of the following measures is determined only after the construction of cumulative frequency distribution?(a) Mean(b) Median(c) Mode(d) None of these
Answer» Which one of the following measures is determined only after the construction of cumulative frequency distribution? (a) Mean (b) Median (c) Mode (d) None of these

Discussion

1216.	If px=x3-5x2+4x-3 and gx=x-2, show that p(x) is not a multiple of g(x).
Answer» If $p (x) = x^{3} - 5 x^{2} + 4 x - 3 and g (x) = x - 2$ , show that p(x) is not a multiple of g(x).

Discussion

1217.	If a ∆ ABC, AD is the bisector of ∠A, meeting side BC at D.(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm. find AB.(vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.
Answer» If a ∆ ABC, AD is the bisector of ∠A, meeting side BC at D. (i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC. (ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC. (iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD. (iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC. (v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm. find AB. (vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC. (vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC. (viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

Discussion

1218.	{ On dividing }6x^3+11x^2-39x-45 by a polynomial }g(x) , the quotient is }6x+5 and the }}{ remainder is }-38x+40, find }g(x) .
Answer» { On dividing }6x^3+11x^2-39x-45 by a polynomial }g(x) , the quotient is }6x+5 and the }}{ remainder is }-38x+40, find }g(x) .

Discussion

1219.	Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: 238
Answer» Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: $\frac{23}{8}$

Discussion

1220.	Which of the following is a factor of x2−6x−16?
Answer» Which of the following is a factor of $x^{2} - 6 x - 16$ ?

Discussion

1221.	6n cannot end with digit 5 for _______ value of n.
Answer» 6ⁿ cannot end with digit 5 for _______ value of n.

Discussion

1222.	Question 39 Fill in the blanks to make the statement true. 11×(−5)=−( ___ × ___ ) = ___
Answer» Question 39 Fill in the blanks to make the statement true. $11 \times (- 5) = -$ ( ___ $\times$ ___ ) = ___

1222.

Question 39 Fill in the blanks to make the statement true. 11×(−5)=−( _ × _ ) = ___

Answer»

Question 39

Fill in the blanks to make the statement true.

$11 \times (- 5) = -$ ( ___ $\times$ ___ ) = ___

Discussion

1223.	If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.
Answer» If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.

Discussion

1224.	The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life−time(in days)Less than 50Less than 100Less than 150Less than 200Less than 250Less than 300Number of bulbs721527991100 From this table,construct the frequency distribution table.
Answer» The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. $\begin{matrix} L i f e - t i m e (i n d a y s) & L e s s t h a n 50 & L e s s t h a n 100 & L e s s t h a n 150 & L e s s t h a n 200 & L e s s t h a n 250 & L e s s t h a n 300 N u m b e r o f b u l b s & 7 & 21 & 52 & 79 & 91 & 100 \end{matrix}$ From this table,construct the frequency distribution table.

1224.

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life−time(in days)Less than 50Less than 100Less than 150Less than 200Less than 250Less than 300Number of bulbs721527991100 From this table,construct the frequency distribution table.

Answer»

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

$\begin{matrix} L i f e - t i m e (i n d a y s) & L e s s t h a n 50 & L e s s t h a n 100 & L e s s t h a n 150 & L e s s t h a n 200 & L e s s t h a n 250 & L e s s t h a n 300 N u m b e r o f b u l b s & 7 & 21 & 52 & 79 & 91 & 100 \end{matrix}$

From this table,construct the frequency distribution table.

Discussion

1225.	Mark the correct alternative in each of the following:In a family of 3 children, the probability of having at least one boy is(a) 78 (b) 18 (c) 58 (d) 34 [CBSE 2014]
Answer» Mark the correct alternative in each of the following: In a family of 3 children, the probability of having at least one boy is (a) $\frac{7}{8}$ (b) $\frac{1}{8}$ (c) $\frac{5}{8}$ (d) $\frac{3}{4}$ [CBSE 2014]

Discussion

1226.	Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 34 times the corresponding sides of the first triangle.
Answer» Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of the first triangle.

Discussion

1227.	Cos theta+sin theta =√2cos theta show thatcos theta-sin theta =√2sin theta
Answer» Cos theta+sin theta =√2cos theta show thatcos theta-sin theta =√2sin theta

Discussion

1228.	The following table gives the distribution of the life time of 400 neon lamps:Lite time:(in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048Find the median life.
Answer» The following table gives the distribution of the life time of 400 neon lamps: $\begin{matrix} Lite time : (in hours) & Number of lamps 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$ Find the median life.

Discussion

1229.	Solve each of the following quadratic equations:4x-3=52x+3, x≠0, -32 [CBSE 2014]
Answer» Solve each of the following quadratic equations: $\frac{4}{x} - 3 = \frac{5}{2 x + 3}, x \neq 0, - \frac{3}{2}$ [CBSE 2014]

Discussion

1230.	What is the value of sin 180
Answer» What is the value of sin 180

Discussion

1231.	Which of the following debts is incurred for meeting the balance of payment deficits?
Answer» Which of the following debts is incurred for meeting the balance of payment deficits?

Discussion

1232.	In a ∆ABC, ∠A = 90°, AB = 5 cm and AC = 12 cm. If AD ⊥ BC, then AD =(a) 132cm(b) 6013cm(c) 1360cm(d) 21513cm
Answer» In a ∆ABC, ∠A = 90°, AB = 5 cm and AC = 12 cm. If AD ⊥ BC, then AD = (a) $\frac{13}{2} cm$ (b) $\frac{60}{13} cm$ (c) $\frac{13}{60} cm$ (d) $\frac{2 \sqrt{15}}{13} cm$

Discussion

1233.	Two different dice are thrown together. Find the probability that (i) the sum of the numbers appeared is less than 7. (ii) the product of the numbers appeared is less than 18.
Answer» Two different dice are thrown together. Find the probability that (i) the sum of the numbers appeared is less than 7. (ii) the product of the numbers appeared is less than 18.

Discussion

1234.	In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?
Answer» In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?

Discussion

1235.	Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?
Answer» Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?

1235.

Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?

Answer»

Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?

Discussion

1236.	If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of ΔAPQ.
Answer» If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of $Δ A P Q .$

1236.

If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of ΔAPQ.

Answer»

If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of $Δ A P Q .$

Discussion

1237.	Factorise each of the following: 8a3 + b3 + 12a2b + 6ab2
Answer» Factorise each of the following: 8 $a^{3}$ + $b^{3}$ + 12 $a^{2}$ b + 6a $b^{2}$

Discussion

1238.	The volume of the cone is 83 cu ft and its base area is 712 sq ft.The height of the right circular cone is ft.
Answer» The volume of the cone is $\frac{8}{3}$ cu ft and its base area is $7 \frac{1}{2}$ sq ft. The height of the right circular cone is ft.

Discussion

1239.	What must be added to 2x4 – 5x3 + 2x2 – x – 3 so that the result is exactly divisible by (x – 2)?
Answer» What must be added to 2x⁴– 5x³+ 2x² – x – 3 so that the result is exactly divisible by (x – 2)?

Discussion

1240.	The class-mark of the class 130-150 is ___________.
Answer» The class-mark of the class 130-150 is ___________.

Discussion

1241.	y=2x+4 and are parallel lines.
Answer» $y = 2 x + 4$ and are parallel lines.

Discussion

1242.	Find the volume of the largest cylinder that can be inscribed in a sphere of radius 'r' cm.
Answer» Find the volume of the largest cylinder that can be inscribed in a sphere of radius 'r' cm.

Discussion

1243.	Sketch the graph of y= \vert1+e^{\vert x\vert}-e^{-x
Answer» Sketch the graph of y= \vert1+e^{\vert x\vert}-e^{-x

Discussion

1244.	6. If alpha and beta are the zeroes of the quadratic polynomial xsquare - x-2 , find the polynomial whose zeroes are (1+2alpha) and (1+2beta).
Answer» 6. If alpha and beta are the zeroes of the quadratic polynomial xsquare - x-2 , find the polynomial whose zeroes are (1+2alpha) and (1+2beta).

Discussion

1245.	Which of the following in not a quadratic equation:
Answer» Which of the following in not a quadratic equation:

Discussion

1246.	Euclid's division lemma state that for any two positive integera a and b there exist unique integer q and r such that a=bq+r Write the condition in which r must statisfy a=bq+r
Answer» Euclid's division lemma state that for any two positive integera a and b there exist unique integer q and r such that a=bq+r Write the condition in which r must statisfy a=bq+r

Discussion

1247.	Find the mean marks per student, using Step Deviation method method: Marks51525354555Number of students12182720176
Answer» Find the mean marks per student, using Step Deviation method method: $\begin{matrix} Marks & 5 & 15 & 25 & 35 & 45 & 55 Number of students & 12 & 18 & 27 & 20 & 17 & 6 \end{matrix}$

Discussion

1248.	Solve the following systems of equations:3x-y+711+2=102y+x+117=10
Answer» Solve the following systems of equations: $3 x - \frac{y + 7}{11} + 2 = 10 2 y + \frac{x + 11}{7} = 10$

Discussion

1249.	Write the pair of linear equations which has the unique solutions x=2,y=-3. How many such pairs can you write?
Answer» Write the pair of linear equations which has the unique solutions x=2,y=-3. How many such pairs can you write?

Discussion

1250.	ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.
Answer» ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.

1250.

ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.

Answer»

ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.

Discussion

Explore topic-wise InterviewSolutions in .

A card is picked up from a deck of 52 playing cards.(i) What is the sample space of the experiment?(ii) What is the event that the chosen card is a black faced card?

A coin is tossed 100 times with following frequency.Head: 25, Tail: 75. (i) Find the probability of getting a tail?(ii) Find the probability of getting a Head?

QR is a tangent at Q to a circle whose centre is P.PR \vert\vert AQ, where AQ is a chord through A, the endpoint of the diameter AB. Prove that BR is tangentat B.

Using factor theorem, show that g(x) is a factor of p(x), whenpx=22x2+5x+2, gx=x+2

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If ∠SQR=80∘ and ∠QPR=30∘, then find ∠SRQ.

If A=[2340−1−2] , B=[0−2−73−15] and C=[1−1020−6] Find a matrix X sucn that C+X=A+B

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. [CBSE 2014]

14. if a+2b+c=4 then max(ab+bc+ca) is (1) 2 (2) 4 (3) 6 (4) 8

Find the probability of getting the sum of two numbers, less than 3 or more than 11, when a pair of distinct dice is thrown together. [CBSE 2017]

Rationalize and simplify the expression: 1√2+√3+1√2−√5+2√5−√3

The value of sec2(tan-12) + cosec2 (cot-1 3) is ____________________.

Let A(−1,1),B(3,4) and C(2,0) be given three points. A line y=mx,m&gt;0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ΔABC and ΔPQC respectively, such that A1=3A2, then the value of m is equal to :

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

What is the value of 8.0 km in inches? (1 m = 1.094 yards &amp; 1 yrd = 36 inches)

Which one of the following measures is determined only after the construction of cumulative frequency distribution?(a) Mean(b) Median(c) Mode(d) None of these

If px=x3-5x2+4x-3 and gx=x-2, show that p(x) is not a multiple of g(x).

{ On dividing }6x^3+11x^2-39x-45 by a polynomial }g(x) , the quotient is }6x+5 and the }}{ remainder is }-38x+40, find }g(x) .

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: 238

Which of the following is a factor of x2−6x−16?

6n cannot end with digit 5 for _______ value of n.

Question 39 Fill in the blanks to make the statement true. 11×(−5)=−( ___ × ___ ) = ___

If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life−time(in days)Less than 50Less than 100Less than 150Less than 200Less than 250Less than 300Number of bulbs721527991100 From this table,construct the frequency distribution table.

Mark the correct alternative in each of the following:In a family of 3 children, the probability of having at least one boy is(a) 78 (b) 18 (c) 58 (d) 34 [CBSE 2014]

Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 34 times the corresponding sides of the first triangle.

Cos theta+sin theta =√2cos theta show thatcos theta-sin theta =√2sin theta

The following table gives the distribution of the life time of 400 neon lamps:Lite time:(in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048Find the median life.

Solve each of the following quadratic equations:4x-3=52x+3, x≠0, -32 [CBSE 2014]

What is the value of sin 180

Which of the following debts is incurred for meeting the balance of payment deficits?

In a ∆ABC, ∠A = 90°, AB = 5 cm and AC = 12 cm. If AD ⊥ BC, then AD =(a) 132cm(b) 6013cm(c) 1360cm(d) 21513cm

Two different dice are thrown together. Find the probability that (i) the sum of the numbers appeared is less than 7. (ii) the product of the numbers appeared is less than 18.

In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?

Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?

If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of ΔAPQ.

Factorise each of the following: 8a3 + b3 + 12a2b + 6ab2

The volume of the cone is 83 cu ft and its base area is 712 sq ft.The height of the right circular cone is ft.

What must be added to 2x4 – 5x3 + 2x2 – x – 3 so that the result is exactly divisible by (x – 2)?

The class-mark of the class 130-150 is ___________.

y=2x+4 and are parallel lines.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius 'r' cm.

Sketch the graph of y= \vert1+e^{\vert x\vert}-e^{-x

6. If alpha and beta are the zeroes of the quadratic polynomial xsquare - x-2 , find the polynomial whose zeroes are (1+2alpha) and (1+2beta).

Which of the following in not a quadratic equation:

Euclid's division lemma state that for any two positive integera a and b there exist unique integer q and r such that a=bq+r Write the condition in which r must statisfy a=bq+r

Find the mean marks per student, using Step Deviation method method: Marks51525354555Number of students12182720176

Solve the following systems of equations:3x-y+711+2=102y+x+117=10

Write the pair of linear equations which has the unique solutions x=2,y=-3. How many such pairs can you write?

ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.

Let A(−1,1),B(3,4) and C(2,0) be given three points. A line y=mx,m>0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ΔABC and ΔPQC respectively, such that A1=3A2, then the value of m is equal to :

What is the value of 8.0 km in inches? (1 m = 1.094 yards & 1 yrd = 36 inches)

Question 39 Fill in the blanks to make the statement true. 11×(−5)=−( _ × _ ) = ___