24740 + Interview Questions in Mathematics

1.	Two circles touch each other internally and their centres are O and O′ as shown. The sum of their areas is 180 π sq. cm. and the distance between their centres is 6 cm. What is the diameter of the larger circle?
Answer» Two circles touch each other internally and their centres are $O$ and $O^{'}$ as shown. The sum of their areas is $180 π$ sq. cm. and the distance between their centres is $6 c m .$ What is the diameter of the larger circle?

Discussion

2.	Which of the following numbers is fourth power of a natural number?6765201676520667652076765209
Answer» Which of the following numbers is fourth power of a natural number? 6765201 6765206 6765207 6765209

Discussion

3.	Find the area of shaded portion.
Answer» Find the area of shaded portion.

Discussion

4.	Consider an acute angled ΔABC. D is any point on the side BC such that ar(△ABD)ar(△ADC) = 23. How would you proceed to construct this line segment AD?
Answer» Consider an acute angled ΔABC. D is any point on the side BC such that $\frac{a r (△ A B D)}{a r (△ A D C)}$ = $\frac{2}{3}$ . How would you proceed to construct this line segment AD?

Discussion

5.	Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP.OQ + OR.OS = OR.OP + OQ.OS = OQ.OR + OP.OS Then the triangle PQR has S as its
Answer» Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP.OQ + OR.OS = OR.OP + OQ.OS = OQ.OR + OP.OS Then the triangle PQR has S as its

Discussion

6.	A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. [Take π=227]
Answer» A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. $[T a k e π = \frac{22}{7}]$

Discussion

7.	In the following figure, S is any point on the side QR of Δ PQR. Prove that PQ + QR + RP > 2 PS.
Answer» In the following figure, S is any point on the side QR of Δ PQR. Prove that PQ + QR + RP > 2 PS.

Discussion

8.	The number of books in different shelves of a library are as follows: 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25, 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23, 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21. Prepare a cumulative frequency distribution table using 45-49 as the last class interval.
Answer» The number of books in different shelves of a library are as follows: 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25, 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23, 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21. Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

8.

The number of books in different shelves of a library are as follows: 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25, 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23, 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21. Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

Answer»

The number of books in different shelves of a library are as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45,

16, 20 19, 24, 27, 30, 32, 34, 35, 42,

27, 28, 19, 34, 38, 39, 42, 29, 24, 27,

22, 29, 31, 19, 27, 25, 28, 23, 24, 32,

34, 18, 27, 25, 37, 31, 24, 23, 43, 32,

28, 31, 24, 23, 26, 36, 32, 29, 28, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

Discussion

9.	In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then find the length of EB.
Answer» In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then find the length of EB.

9.

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then find the length of EB.

Answer»

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then find the length of EB.

Discussion

10.	Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Answer» Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Discussion

11.	Visualize 2.665 on the number line, using successive magnification.
Answer» Visualize $2.665$ on the number line, using successive magnification.

Discussion

12.	The graph of linear equation in two variables always represents
Answer» The graph of linear equation in two variables always represents

Discussion

13.	Only 60% and 50% of eligible voters of town A and B respectively, cast their vote in the election. The total number of votes cast were 1200.Which of the following linear equations represents this scenario accurately?(Assume number of eligible voters in town A to be x and in town B to be y)
Answer» Only 60% and 50% of eligible voters of town A and B respectively, cast their vote in the election. The total number of votes cast were $1200.$ Which of the following linear equations represents this scenario accurately? (Assume number of eligible voters in town A to be $x$ and in town B to be $y$ )

Discussion

14.	If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is
Answer» If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 $c m^{3},$ then the length of the shortest edge is

Discussion

15.	In the given figure, if ∠x=∠y and AB = CB, then AE is _____.
Answer» In the given figure, if $∠ x = ∠ y$ and AB = CB, then AE is _____.

Discussion

16.	The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?
Answer» The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

16.

The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

Answer»

The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

Discussion

17.	X and Y are partners. X's capital is Rs 10,000, Y's capital is Rs 6,000. Interest is payable at 6% p.a. Y is entitled to a salary of Rs 300 per month. Profits for current year before charging any interest and salary to Mr. Y is Rs 8,000. Divide the profit between X and Y.
Answer» X and Y are partners. X's capital is Rs 10,000, Y's capital is Rs 6,000. Interest is payable at 6% p.a. Y is entitled to a salary of Rs 300 per month. Profits for current year before charging any interest and salary to Mr. Y is Rs 8,000. Divide the profit between X and Y.

Discussion

18.	in the graph \log Kc is on y axis and 1/T in x axis.the angle which the line makes with -ve direction of x axis is 45deg. y intercept is 10. find enthalpy
Answer» in the graph \log Kc is on y axis and 1/T in x axis.the angle which the line makes with -ve direction of x axis is 45deg. y intercept is 10. find enthalpy

Discussion

19.	The side BC of a Δ ABC is bisected at D; O is any point in AD. BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that O is the mid-point of OX. Prove that AO : AX = AF : AB and show that FE ∥ BC.
Answer» The side BC of a $Δ$ ABC is bisected at D; O is any point in AD. BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that O is the mid-point of OX. Prove that AO : AX = AF : AB and show that FE $∥$ BC.

Discussion

20.	In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to
Answer» In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to

Discussion

21.	Factorise - 1. a(b-c)x^2+b(c-a)x+c(a-b) 2.a^2(b-c)+b^2(c-a)+c^2(a-b)3.(x+1)(x+3)(x+5)(x+7)+15 4. x^2+x-(a+1)(a+2)5.x^2-y^2-6xa+2ya+8a^2 6.2a^2b^2+2b^2c^2+2c^2a^2 -a^4-b^4-c^4 7.2a^2+2a-3ab-b +b^28.2a^3-a^3b-b^3
Answer» Factorise - 1. a(b-c)x^2+b(c-a)x+c(a-b) 2.a^2(b-c)+b^2(c-a)+c^2(a-b) 3.(x+1)(x+3)(x+5)(x+7)+15 4. x^2+x-(a+1)(a+2) 5.x^2-y^2-6xa+2ya+8a^2 6.2a^2b^2+2b^2c^2+2c^2a^2 -a^4-b^4-c^4 7.2a^2+2a-3ab-b +b^2 8.2a^3-a^3b-b^3

Discussion

22.	If a=9-2√6and b=57/a ,find value of a²+b²
Answer» If a=9-2√6and b=57/a ,find value of a²+b²

Discussion

23.	12 elephants in an elephant camp consumed 240 kg of jaggery everyday. If 3 more elephants were brought to the camp, how much more jaggery would be needed to feed them?
Answer» 12 elephants in an elephant camp consumed 240 kg of jaggery everyday. If 3 more elephants were brought to the camp, how much more jaggery would be needed to feed them?

Discussion

24.	Question 2 The equation 2x + 5y = 7 has a unique solution, if x and y are: A) Natural numbers B) Positive real numbers C) Real numbers D) Rational numbers
Answer» Question 2 The equation 2x + 5y = 7 has a unique solution, if x and y are: A) Natural numbers B) Positive real numbers C) Real numbers D) Rational numbers

Discussion

25.	Question 7Find the value of the polynomial 3x3–4x2+7x–5, when x = 3 and also when x = -3.
Answer» Question 7 Find the value of the polynomial $3 x^{3} - 4 x^{2} + 7 x - 5$ , when x = 3 and also when x = -3.

Discussion

26.	A number is 27 more than the number obtained by reversing it's digits.if it's ones place is x and tens digit y.Write a linear linear equation representing the above statement
Answer» A number is 27 more than the number obtained by reversing it's digits.if it's ones place is x and tens digit y.Write a linear linear equation representing the above statement

Discussion

27.	Question 12 (iv)ABCD is a trapezium in which AB \|\| CD and AD =BC (see the given figure). Show that Diagonal AC=diagonal BD.
Answer» Question 12 (iv) ABCD is a trapezium in which AB \|\| CD and AD =BC (see the given figure). Show that Diagonal AC=diagonal BD.

Discussion

28.	Find the value of k if (1,3k) lies on kx + 4y = 26
Answer» Find the value of k if (1,3k) lies on kx + 4y = 26

Discussion

29.	Represent 625 as a decimal
Answer» Represent $\frac{6}{25}$ as a decimal

Discussion

30.	prove that it is rational no. or irrational no. under root 7
Answer» prove that it is rational no. or irrational no. under root 7

Discussion

31.	A tank with length, breadth and height of 5, 6 and 3 units respectively is open at the top. Find the cost of anti-microbial coating inside the tank if it is done at Rs. 10 per sq. units.
Answer» A tank with length, breadth and height of 5, 6 and 3 units respectively is open at the top. Find the cost of anti-microbial coating inside the tank if it is done at Rs. 10 per sq. units.

Discussion

32.	In the figure below, O is the centre of the circle and ∠QPR=x∘,∠ORQ=y∘. Which statement is true about x∘ and y∘?
Answer» In the figure below, O is the centre of the circle and $∠ Q P R = x^{\circ}, ∠ O R Q = y^{\circ} .$ Which statement is true about $x^{\circ}$ and $y^{\circ}$ ?

Discussion

33.	2x2_13x+18
Answer» 2x^2_13x+18

Discussion

34.	Find the value of k, if x − 1 is a factor of x2 + x + k.
Answer» Find the value of k, if x − 1 is a factor of x² + x + k.

Discussion

35.	Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB=PD.
Answer» Two equal chords $A B$ and $C D$ of a circle when produced intersect at a point $P .$ Prove that $P B = P D .$

Discussion

36.	What is the meaning of polynomial?
Answer» What is the meaning of polynomial?

Discussion

37.	If ∠BOC=80°and OA bisects ∠BAC, then find the value of ∠ABO in degrees.20
Answer» If $∠ B O C = 80 °$ and OA bisects $∠ B A C$ , then find the value of $∠ A B O$ in degrees. 20

Discussion

38.	Prove that the figure obtained by joining the mid points of the adjacent sides of rectangle is a rhombus.
Answer» Prove that the figure obtained by joining the mid points of the adjacent sides of rectangle is a rhombus.

Discussion

39.	Write the equation of a line parallel to y-axis and passing through the point (-3, -7).
Answer» Write the equation of a line parallel to y-axis and passing through the point (-3, -7).

Discussion

40.	In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:ΔAMC≅ΔBMD
Answer» In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: $Δ A M C ≅ Δ B M D$

Discussion

41.	A metal cuboid of dimensions 49 m, 22 m and 14 m is melted and cast into 7 identical cylinders of radius 7 m. These cylinders are again melted and cast into cubes such that the side of each cube is equal to half of the height of each cylinder. The numbers of cubes thus formed is __________.
Answer» A metal cuboid of dimensions 49 m, 22 m and 14 m is melted and cast into 7 identical cylinders of radius 7 m. These cylinders are again melted and cast into cubes such that the side of each cube is equal to half of the height of each cylinder. The numbers of cubes thus formed is __________.

Discussion

42.	If in triangle ABC, sides opposite to angles A,B,C are a,b and c respectively, then the value of 1+cos(A−B)cosC1+cos(A−C)cosB=
Answer» If in triangle $A B C,$ sides opposite to angles $A, B, C$ are $a, b$ and $c$ respectively, then the value of $\frac{1 + cos (A - B) cos C}{1 + cos (A - C) cos B} =$

Discussion

43.	49. Prove that any line passing through the incentre of a triangle divides the area and perimeter of the triangle in the same ratio.
Answer» 49. Prove that any line passing through the incentre of a triangle divides the area and perimeter of the triangle in the same ratio.

Discussion

44.	Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).
Answer» Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).

Discussion

45.	For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?
Answer» For the given linear equation $y - 3 x + 1 = 0,$ what are the values of $y$ if $x = [3, - 4, 2]$ ?

Discussion

46.	Question 9 Simplify the following (i)√45−3√20+4√5(ii)√248+√549(iii)4√12×7√6(iv)4√28+3√7+3√7(v)3√3+2√27+7√3(vi)(√3−√2)2(vii)4√81−83√216+155√32+√225(viii)3√8+1√2(ix)2√33−√36
Answer» Question 9 Simplify the following $(i) \sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} (i i) \frac{\sqrt{24}}{8} + \frac{\sqrt{54}}{9} (i i i) 4 \sqrt{12} \times 7 \sqrt{6} (i v) 4 \sqrt{28} + 3 \sqrt{7} + \sqrt[3]{7} (v) 3 \sqrt{3} + 2 \sqrt{27} + \frac{7}{\sqrt{3}} (v i) (\sqrt{3} - \sqrt{2})^{2} (v i i) \sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225} (v i i i) \frac{3}{\sqrt{8}} + \frac{1}{\sqrt{2}} (i x) \frac{2 \sqrt{3}}{3} - \frac{\sqrt{3}}{6}$

Discussion

47.	A locker can be opened by dialing a fixed three-digit code (between 000 and 999). A stranger, who does not know the code, tries to open the locker by dialing three digits at random. If p is the probability that the stranger succeeds at the kth trial, then the value of 1000p is
Answer» A locker can be opened by dialing a fixed three-digit code (between $000$ and $999$ ). A stranger, who does not know the code, tries to open the locker by dialing three digits at random. If $p$ is the probability that the stranger succeeds at the $k t h$ trial, then the value of $1000 p$ is

Discussion

48.	Solve: 3x−1×52y−3=225
Answer» Solve: $3^{x - 1} \times 5^{2 y - 3} = 225$

Discussion

49.	Simplify each of the following:(i) 175 × 175 + 2 × 175 × 25 + 25 × 25(ii) 322 × 322 − 2 × 322 × 22 + 22 × 22(iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × × 0.24(iv) 7.83 ×7.83-1.17×1.176.66
Answer» Simplify each of the following: (i) 175 × 175 + 2 × 175 × 25 + 25 × 25 (ii) 322 × 322 − 2 × 322 × 22 + 22 × 22 (iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × × 0.24 (iv) $\frac{7.83 \times 7.83 - 1.17 \times 1.17}{6.66}$

Discussion

50.	Using Euclid's division lemma, find the HCF of 1848, 3058 and 1331.
Answer» Using Euclid's division lemma, find the HCF of 1848, 3058 and 1331.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two circles touch each other internally and their centres are O and O′ as shown. The sum of their areas is 180 π sq. cm. and the distance between their centres is 6 cm. What is the diameter of the larger circle?

Which of the following numbers is fourth power of a natural number?6765201676520667652076765209

Find the area of shaded portion.

Consider an acute angled ΔABC. D is any point on the side BC such that ar(△ABD)ar(△ADC) = 23. How would you proceed to construct this line segment AD?

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP.OQ + OR.OS = OR.OP + OQ.OS = OQ.OR + OP.OS Then the triangle PQR has S as its

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. [Take π=227]

In the following figure, S is any point on the side QR of Δ PQR. Prove that PQ + QR + RP > 2 PS.

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then find the length of EB.

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

Visualize 2.665 on the number line, using successive magnification.

The graph of linear equation in two variables always represents

Only 60% and 50% of eligible voters of town A and B respectively, cast their vote in the election. The total number of votes cast were 1200.Which of the following linear equations represents this scenario accurately?(Assume number of eligible voters in town A to be x and in town B to be y)

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is

In the given figure, if ∠x=∠y and AB = CB, then AE is _____.

The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

X and Y are partners. X's capital is Rs 10,000, Y's capital is Rs 6,000. Interest is payable at 6% p.a. Y is entitled to a salary of Rs 300 per month. Profits for current year before charging any interest and salary to Mr. Y is Rs 8,000. Divide the profit between X and Y.

in the graph \log Kc is on y axis and 1/T in x axis.the angle which the line makes with -ve direction of x axis is 45deg. y intercept is 10. find enthalpy

The side BC of a Δ ABC is bisected at D; O is any point in AD. BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that O is the mid-point of OX. Prove that AO : AX = AF : AB and show that FE ∥ BC.

In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to

Factorise - 1. a(b-c)x^2+b(c-a)x+c(a-b) 2.a^2(b-c)+b^2(c-a)+c^2(a-b)3.(x+1)(x+3)(x+5)(x+7)+15 4. x^2+x-(a+1)(a+2)5.x^2-y^2-6xa+2ya+8a^2 6.2a^2b^2+2b^2c^2+2c^2a^2 -a^4-b^4-c^4 7.2a^2+2a-3ab-b +b^28.2a^3-a^3b-b^3

If a=9-2√6and b=57/a ,find value of a²+b²

12 elephants in an elephant camp consumed 240 kg of jaggery everyday. If 3 more elephants were brought to the camp, how much more jaggery would be needed to feed them?

Question 2 The equation 2x + 5y = 7 has a unique solution, if x and y are: A) Natural numbers B) Positive real numbers C) Real numbers D) Rational numbers

Question 7Find the value of the polynomial 3x3–4x2+7x–5, when x = 3 and also when x = -3.

A number is 27 more than the number obtained by reversing it's digits.if it's ones place is x and tens digit y.Write a linear linear equation representing the above statement

Question 12 (iv)ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that Diagonal AC=diagonal BD.

Find the value of k if (1,3k) lies on kx + 4y = 26

Represent 625 as a decimal

prove that it is rational no. or irrational no. under root 7

A tank with length, breadth and height of 5, 6 and 3 units respectively is open at the top. Find the cost of anti-microbial coating inside the tank if it is done at Rs. 10 per sq. units.

In the figure below, O is the centre of the circle and ∠QPR=x∘,∠ORQ=y∘. Which statement is true about x∘ and y∘?

2x2_13x+18

Find the value of k, if x − 1 is a factor of x2 + x + k.

Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB=PD.

What is the meaning of polynomial?

If ∠BOC=80°and OA bisects ∠BAC, then find the value of ∠ABO in degrees.20

Prove that the figure obtained by joining the mid points of the adjacent sides of rectangle is a rhombus.

Write the equation of a line parallel to y-axis and passing through the point (-3, -7).

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:ΔAMC≅ΔBMD

A metal cuboid of dimensions 49 m, 22 m and 14 m is melted and cast into 7 identical cylinders of radius 7 m. These cylinders are again melted and cast into cubes such that the side of each cube is equal to half of the height of each cylinder. The numbers of cubes thus formed is __________.

If in triangle ABC, sides opposite to angles A,B,C are a,b and c respectively, then the value of 1+cos(A−B)cosC1+cos(A−C)cosB=

49. Prove that any line passing through the incentre of a triangle divides the area and perimeter of the triangle in the same ratio.

Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).

For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?

Question 9 Simplify the following (i)√45−3√20+4√5(ii)√248+√549(iii)4√12×7√6(iv)4√28+3√7+3√7(v)3√3+2√27+7√3(vi)(√3−√2)2(vii)4√81−83√216+155√32+√225(viii)3√8+1√2(ix)2√33−√36

A locker can be opened by dialing a fixed three-digit code (between 000 and 999). A stranger, who does not know the code, tries to open the locker by dialing three digits at random. If p is the probability that the stranger succeeds at the kth trial, then the value of 1000p is

Solve: 3x−1×52y−3=225

Simplify each of the following:(i) 175 × 175 + 2 × 175 × 25 + 25 × 25(ii) 322 × 322 − 2 × 322 × 22 + 22 × 22(iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × × 0.24(iv) 7.83 ×7.83-1.17×1.176.66

Using Euclid's division lemma, find the HCF of 1848, 3058 and 1331.