32581 + Interview Questions in Mathematics

1.	If the point (5,0),(0−2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?
Answer» If the point $(5, 0), (0 - 2)$ and $(3, 6)$ lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?

Discussion

2.	O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. What is the measure of ∠ROQ?
Answer» O is the centre of the circle as shown in the figure, $∠ O R P = 35^{\circ}$ and the distance between P and Q through 'O' is 4 cm. What is the measure of $∠ R O Q$ ?

Discussion

3.	Find the roots of the quadratic equation 3x2 – 5x + 2 = 0 using the quadratic formula.
Answer» Find the roots of the quadratic equation 3 $x^{2}$ – 5x + 2 = 0 using the quadratic formula.

Discussion

4.	The centre and radius of the circle 2x2+2y2−x=0 are
Answer» The centre and radius of the circle $2 x^{2} + 2 y^{2} - x = 0$ are

Discussion

5.	Which of the following statements is / are correct statements? 1. Centroid of a triangle is the point of concurrency of medians. 2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle. 3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle. 4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side. 5. A triangle can have only one excentre.
Answer» Which of the following statements is / are correct statements? 1. Centroid of a triangle is the point of concurrency of medians. 2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle. 3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle. 4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side. 5. A triangle can have only one excentre.

Discussion

6.	The sum of two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
Answer» The sum of two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

Discussion

7.	In the given triangle , which of the following is true ?
Answer» In the given triangle , which of the following is true ?

7.

In the given triangle , which of the following is true ?

Answer»

In the given triangle , which of the following is true ?

Discussion

8.	A ladder is placed in such a way that its foot is at a distance of 15 m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.
Answer» A ladder is placed in such a way that its foot is at a distance of 15 m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.

Discussion

9.	Consider the following AP: 1, a, b, c, 9. Find the common difference.
Answer» Consider the following AP: 1, a, b, c, 9. Find the common difference.

Discussion

10.	In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B. If DB = 1 cm and AB = 3 cm, then ∠CDB = _____
Answer» In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B. If DB = 1 cm and AB = 3 cm, then $∠ C D B$ = _____

10.

In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B. If DB = 1 cm and AB = 3 cm, then ∠CDB = _____

Answer»

In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B.

If DB = 1 cm and AB = 3 cm, then $∠ C D B$ = _____

Discussion

11.	Nazima is doing fly-fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away from her and 2.4 m from the point directly under the tip of the rod. Assuming that the string (from the tip of her rod to the fly) is taut, how much string does she have out (see the adjoining figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Answer» Nazima is doing fly-fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away from her and 2.4 m from the point directly under the tip of the rod. Assuming that the string (from the tip of her rod to the fly) is taut, how much string does she have out (see the adjoining figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

11.

Nazima is doing fly-fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away from her and 2.4 m from the point directly under the tip of the rod. Assuming that the string (from the tip of her rod to the fly) is taut, how much string does she have out (see the adjoining figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Answer»

Nazima is doing fly-fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away from her and 2.4 m from the point directly under the tip of the rod. Assuming that the string (from the tip of her rod to the fly) is taut, how much string does she have out (see the adjoining figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Discussion

12.	Manu invested ₹45,000 in 15% ₹ 100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8,400. The number of shares he still holds and the dividend due to him on these remaining shares are respectively _____.
Answer» Manu invested ₹45,000 in 15% ₹ 100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8,400. The number of shares he still holds and the dividend due to him on these remaining shares are respectively _____.

Discussion

13.	Inner radius of a hollow iron sphere is 9 cm. If Iron is 1 cm thick, find the volume of iron used to make the ball.
Answer» Inner radius of a hollow iron sphere is 9 cm. If Iron is 1 cm thick, find the volume of iron used to make the ball.

Discussion

14.	Question 2 (i) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
Answer» Question 2 (i) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Discussion

15.	The values of x and y in the given figure are respectively ___.
Answer» The values of x and y in the given figure are respectively ___.

Discussion

16.	The relation between x, y and z where x = 81, y = 4 and z = 3 written in the exponential form is :
Answer» The relation between x, y and z where x = 81, y = 4 and z = 3 written in the exponential form is :

Discussion

17.	The perimeter and area of the rectangle whose 12 cm long diagonal makes an angle of 30∘ with one of its longer sides will be equal to
Answer» The perimeter and area of the rectangle whose 12 cm long diagonal makes an angle of $30^{\circ}$ with one of its longer sides will be equal to

Discussion

18.	The scale factors means__ of sides of triangles.
Answer» The scale factors means__ of sides of triangles.

Discussion

19.	Solve for x: 2x2+6√3x−60=0
Answer» Solve for x: $2 x^{2} + 6 \sqrt{3} x - 60 = 0$

Discussion

20.	The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.
Answer» The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.

Discussion

21.	The probability of drawing neither a king nor a spade from a pack of 52 cards is.
Answer» The probability of drawing neither a king nor a spade from a pack of 52 cards is.

Discussion

22.	Two vertices of △ABC are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are (a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)
Answer» Two vertices of $△ A B C$ are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are (a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

22.

Two vertices of △ABC are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are (a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

Answer»

Two vertices of $△ A B C$ are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are

(a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

Discussion

23.	Solve for the roots of the quadratic equation x2−5x+6=0
Answer» Solve for the roots of the quadratic equation $x^{2} - 5 x + 6 = 0$

Discussion

24.	Prove that: tanA+tanBcotA+cotB=tan A tan B
Answer» Prove that: $\frac{t a n A + t a n B}{c o t A + c o t B} = t a n A t a n B$

24.

Prove that: tanA+tanBcotA+cotB=tan A tan B

Answer»

Prove that:

$\frac{t a n A + t a n B}{c o t A + c o t B} = t a n A t a n B$

Discussion

25.	A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.
Answer» A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.

Discussion

26.	In an AP, it is given that S5+S7=167 and S10=235, then find the AP, where Sn denotes the sum of its first n terms.
Answer» In an AP, it is given that $S_{5} + S_{7} = 167 a n d S_{10} = 235,$ then find the AP, where $S_{n}$ denotes the sum of its first n terms.

Discussion

27.	If the replacement set is the set of natural numbers, find the solution set for the given linear Inequations 9x + 4 < 67 ?
Answer» If the replacement set is the set of natural numbers, find the solution set for the given linear Inequations 9x + 4 < 67 ?

Discussion

28.	The curve drawn by taking upper limits along x-axis and cumulative frequency along y-axis is :
Answer» The curve drawn by taking upper limits along x-axis and cumulative frequency along y-axis is :

Discussion

29.	2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.
Answer» 2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.

Discussion

30.	An integer is chosen at random between 1 and 100. Find the probability that it is 1)divisible by 8 2) not divisible by 8
Answer» An integer is chosen at random between 1 and 100. Find the probability that it is 1)divisible by 8 2) not divisible by 8

30.

An integer is chosen at random between 1 and 100. Find the probability that it is 1)divisible by 8 2) not divisible by 8

Answer»

An integer is chosen at random between 1 and 100. Find the probability that it is

1)divisible by 8

2) not divisible by 8

Discussion

31.	Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract? [4 MARKS]
Answer» Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract? [4 MARKS]

Discussion

32.	The roots of the equation ax2 + bx + c =0 will be reciprocal of each other if (a) a=b (b) c=a (c) b=c (d) b=0
Answer» The roots of the equation ax2 + bx + c =0 will be reciprocal of each other if (a) a=b (b) c=a (c) b=c (d) b=0

Discussion

33.	In factorization of quadratic equation why we have not taken 6×1 instead of 3×2?
Answer» In factorization of quadratic equation why we have not taken $6 \times 1$ instead of $3 \times 2$ ?

Discussion

34.	It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Answer» It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Discussion

35.	Question 6 A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data. Number of cars0−1010−2020−3030−4040−5050−6060−7070−80Frequency71413122011158
Answer» Question 6 A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data. $\begin{matrix} Number of cars & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 Frequency & 7 & 14 & 13 & 12 & 20 & 11 & 15 & 8 \end{matrix}$

Discussion

36.	A person buys 240 shares at nominal value of Rs 40 each, which he sells out at Rs 47 each. Find his profit and profit percent.
Answer» A person buys 240 shares at nominal value of Rs 40 each, which he sells out at Rs 47 each. Find his profit and profit percent.

Discussion

37.	Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs 8,088 from the bank after 3years, find the value of his monthly instalment.
Answer» Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs 8,088 from the bank after 3years, find the value of his monthly instalment.

Discussion

38.	Class marks of a distribution are 26, 31, 36, 41, 46, 51, 61, 66, 71. The lower and upper class limits of the first class interval are
Answer» Class marks of a distribution are 26, 31, 36, 41, 46, 51, 61, 66, 71. The lower and upper class limits of the first class interval are

Discussion

39.	Question 3 Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=cd. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Answer» Question 3 Recall, $π$ is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, $π = \frac{c}{d}$ . This seems to contradict the fact that $π$ is irrational. How will you resolve this contradiction?

Discussion

40.	Question 4 (i) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.
Answer» Question 4 (i) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.

Discussion

41.	Which of the following is the correct representation of the inequation: 3x≤9,x is a natural number.
Answer» Which of the following is the correct representation of the inequation: $3 x \leq 9, x is a natural number.$

Discussion

42.	the HCF of 65 and 117 is of the expression in the form 65m-117 find the value of m also find the lcm of 65 and 117 using prime factorisation method.
Answer» the HCF of 65 and 117 is of the expression in the form 65m-117 find the value of m also find the lcm of 65 and 117 using prime factorisation method.

Discussion

43.	Question 8 If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give the reason for your answer.
Answer» Question 8 If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give the reason for your answer.

Discussion

44.	Question 5 (viii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (viii) (sinA+cosecA)2+(cosA+secA)2=7+tan2A+cot2A
Answer» Question 5 (viii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (viii) $(s i n A + c o s e c A)^{2} + (c o s A + s e c A)^{2} = 7 + t a n^{2} A + c o t^{2} A$

Discussion

45.	In the given figure, DE \|\| BC and AD : DB = 5 : 4, then area of ΔDOEarea of ΔDCE is
Answer» In the given figure, DE \|\| BC and AD : DB = 5 : 4, then $\frac{a r e a o f Δ D O E}{a r e a o f Δ D C E}$ is

Discussion

46.	In △ PQR , ∠ Q = 90∘. If cot ~P = √3 then, find sin P + cos Rtan R.
Answer» In $△$ PQR , $∠$ Q = $90^{\circ}$ . If cot ~P = $\sqrt{3}$ then, find $\frac{s i n P + c o s R}{t a n R}$ .

Discussion

47.	Question 87 A shopkeeper was selling all his items at 25% discount. During the off-season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?
Answer» Question 87 A shopkeeper was selling all his items at 25% discount. During the off-season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?

47.

Question 87 A shopkeeper was selling all his items at 25% discount. During the off-season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?

Answer»

Question 87

A shopkeeper was selling all his items at 25% discount. During the off-season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?

Discussion

48.	Pavan gave a number, 98429758, to Akash and asked him to find the difference between the numbers 2 and 7 in the based on place value. The difference will be ___.
Answer» Pavan gave a number, 98429758, to Akash and asked him to find the difference between the numbers 2 and 7 in the based on place value. The difference will be ___.

Discussion

49.	Why is 1 neither prime nor composite? Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?
Answer» Why is 1 neither prime nor composite? Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?

49.

Why is 1 neither prime nor composite? Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?

Answer»

Why is 1 neither prime nor composite?

Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?

Discussion

50.	The mean of a set of observation is ¯¯¯x. If each observation is divided by α [α≠0], and then is increased by 10, then the mean of the new set is:
Answer» The mean of a set of observation is $¯ ¯ ¯ x$ . If each observation is divided by $α [α \neq 0$ ], and then is increased by 10, then the mean of the new set is:

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the point (5,0),(0−2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?

O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. What is the measure of ∠ROQ?

Find the roots of the quadratic equation 3x2 – 5x + 2 = 0 using the quadratic formula.

The centre and radius of the circle 2x2+2y2−x=0 are

The sum of two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

In the given triangle , which of the following is true ?

A ladder is placed in such a way that its foot is at a distance of 15 m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.

Consider the following AP: 1, a, b, c, 9. Find the common difference.

In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B. If DB = 1 cm and AB = 3 cm, then ∠CDB = _____

Manu invested ₹45,000 in 15% ₹ 100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8,400. The number of shares he still holds and the dividend due to him on these remaining shares are respectively _____.

Inner radius of a hollow iron sphere is 9 cm. If Iron is 1 cm thick, find the volume of iron used to make the ball.

Question 2 (i) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

The values of x and y in the given figure are respectively ___.

The relation between x, y and z where x = 81, y = 4 and z = 3 written in the exponential form is :

The perimeter and area of the rectangle whose 12 cm long diagonal makes an angle of 30∘ with one of its longer sides will be equal to

The scale factors means__ of sides of triangles.

Solve for x: 2x2+6√3x−60=0

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.

The probability of drawing neither a king nor a spade from a pack of 52 cards is.

Two vertices of △ABC are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are (a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

Solve for the roots of the quadratic equation x2−5x+6=0

Prove that: tanA+tanBcotA+cotB=tan A tan B

A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.

In an AP, it is given that S5+S7=167 and S10=235, then find the AP, where Sn denotes the sum of its first n terms.

If the replacement set is the set of natural numbers, find the solution set for the given linear Inequations 9x + 4 &lt; 67 ?

The curve drawn by taking upper limits along x-axis and cumulative frequency along y-axis is :

2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.

An integer is chosen at random between 1 and 100. Find the probability that it is 1)divisible by 8 2) not divisible by 8

Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract? [4 MARKS]

The roots of the equation ax2 + bx + c =0 will be reciprocal of each other if (a) a=b (b) c=a (c) b=c (d) b=0

In factorization of quadratic equation why we have not taken 6×1 instead of 3×2?

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Question 6 A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data. Number of cars0−1010−2020−3030−4040−5050−6060−7070−80Frequency71413122011158

A person buys 240 shares at nominal value of Rs 40 each, which he sells out at Rs 47 each. Find his profit and profit percent.

Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs 8,088 from the bank after 3years, find the value of his monthly instalment.

Class marks of a distribution are 26, 31, 36, 41, 46, 51, 61, 66, 71. The lower and upper class limits of the first class interval are

Question 3 Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=cd. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Which of the following is the correct representation of the inequation: 3x≤9,x is a natural number.

the HCF of 65 and 117 is of the expression in the form 65m-117 find the value of m also find the lcm of 65 and 117 using prime factorisation method.

Question 8 If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give the reason for your answer.

Question 5 (viii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (viii) (sinA+cosecA)2+(cosA+secA)2=7+tan2A+cot2A

In the given figure, DE || BC and AD : DB = 5 : 4, then area of ΔDOEarea of ΔDCE is

In △ PQR , ∠ Q = 90∘. If cot ~P = √3 then, find sin P + cos Rtan R.

Question 87 A shopkeeper was selling all his items at 25% discount. During the off-season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1200, how much did she pay for it?

Pavan gave a number, 98429758, to Akash and asked him to find the difference between the numbers 2 and 7 in the based on place value. The difference will be ___.

Why is 1 neither prime nor composite? Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?

The mean of a set of observation is ¯¯¯x. If each observation is divided by α [α≠0], and then is increased by 10, then the mean of the new set is:

If the replacement set is the set of natural numbers, find the solution set for the given linear Inequations 9x + 4 < 67 ?