32581 + Interview Questions in Mathematics Page 160 InterviewSolution

7951.	From the given triangles, which of the following is true?
Answer» From the given triangles, which of the following is true?

Discussion

7952.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2+5x-a2+a-6=0 [CBSE 2015]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x^{2} + 5 x - (a^{2} + a - 6) = 0$ [CBSE 2015]

Discussion

7953.	If 3 tan θ=3 sin θ, find the value of sin2θ − cos2θ.
Answer» If $\sqrt{3} \tan θ = 3 \sin θ$ , find the value of sin²θ − cos²θ.

Discussion

7954.	In the given figure ∠ABC=40∘, then angle ∠BEA is equal to?
Answer» In the given figure $∠ A B C = 40^{\circ}$ , then angle $∠ B E A$ is equal to?

Discussion

7955.	Question 3 (i) Express 0.¯6 in the form pq, where p and q are integers and q≠0.
Answer» Question 3 (i) Express $0. ¯ 6$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Discussion

7956.	Prove that Cosec(2/7) + cosec (3/7)=cosec (/7)
Answer» Prove that Cosec(2/7) + cosec (3/7)=cosec (/7)

Discussion

7957.	If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =(a) −3(b) 7(c) 2(d) −2
Answer» If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a = (a) −3 (b) 7 (c) 2 (d) −2

Discussion

7958.	A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Answer» A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

Discussion

7959.	The theorem which describes "Two angles and the included side of two triangles are congruent" is:
Answer» The theorem which describes "Two angles and the included side of two triangles are congruent" is:

Discussion

7960.	The distance of the point P(−6, 8) from the origin is [CBSE 2013C](a) 8 (b) 27 (c) 6 (d) 10
Answer» The distance of the point P(−6, 8) from the origin is [CBSE 2013C] (a) 8 (b) $2 \sqrt{7}$ (c) 6 (d) 10

Discussion

7961.	Question 4 (xii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xii) √2,√8,√18,√32……
Answer» Question 4 (xii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xii) $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32} \dots \dots$

Discussion

7962.	The angles of a pentagon are in the ratio 5:4:5:7:6 ; find each angle of the pentagon.
Answer» The angles of a pentagon are in the ratio $5 : 4 : 5 : 7 : 6$ ; find each angle of the pentagon.

Discussion

7963.	Given that 2x – y + z = 240. If z = 2y, y = 2x, then x = ?
Answer» Given that 2x – y + z = 240. If z = 2y, y = 2x, then x = ?

Discussion

7964.	If cos θ=23, then 2 sec2 θ + 2 tan2 θ − 7 is equal to(a) 1(b) 0(c) 3(d) 4
Answer» If $\cos θ = \frac{2}{3}$ , then 2 sec² θ + 2 tan² θ − 7 is equal to (a) 1 (b) 0 (c) 3 (d) 4

Discussion

7965.	A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is(i) divisible by 2 or 3,(ii) a prime number.
Answer» A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) divisible by 2 or 3, (ii) a prime number.

Discussion

7966.	9. From a point 2m above a lake the angle of elevation of a cloud is 30^° and the angle of depression of its reflection is 45^° . The height of cloud is
Answer» 9. From a point 2m above a lake the angle of elevation of a cloud is 30^° and the angle of depression of its reflection is 45^° . The height of cloud is

Discussion

7967.	The difference between the second and first term of a sequence defined by tn=n^3/4n+1 is
Answer» The difference between the second and first term of a sequence defined by tn=n^3/4n+1 is

Discussion

7968.	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

7969.	If [1,p/3] is the mid point of the line segment joining the points [2,0) And [1,2/9] then show that the line 5x+3y+2=0 passes through the point (-1,3p) If 2 positive integers p and q are written as p=a cube b cube And q =a cube b . A and b are prime numbers then verify lcm (p,q) *HCF (p,q)=pq
Answer» If [1,p/3] is the mid point of the line segment joining the points [2,0) And [1,2/9] then show that the line 5x+3y+2=0 passes through the point (-1,3p) If 2 positive integers p and q are written as p=a cube b cube And q =a cube b . A and b are prime numbers then verify lcm (p,q) *HCF (p,q)=pq

7969.

If [1,p/3] is the mid point of the line segment joining the points [2,0) And [1,2/9] then show that the line 5x+3y+2=0 passes through the point (-1,3p) If 2 positive integers p and q are written as p=a cube b cube And q =a cube b . A and b are prime numbers then verify lcm (p,q) *HCF (p,q)=pq

Answer»

If [1,p/3] is the mid point of the line segment joining the points [2,0)

And [1,2/9] then show that the line 5x+3y+2=0 passes through the point (-1,3p)

If 2 positive integers p and q are written as p=a cube b cube

And q =a cube b . A and b are prime numbers then verify lcm (p,q)

*HCF (p,q)=pq

Discussion

7970.	if vectors A=cosWt i +sinWt j and B =cos Wt/2 i + sin Wt/2 j are functions of time then the values of t at which they are orthogonal to each other is
Answer» if vectors A=cosWt i +sinWt j and B =cos Wt/2 i + sin Wt/2 j are functions of time then the values of t at which they are orthogonal to each other is

Discussion

7971.	For waht value/s of p, the quadratic equation 3x2−px+4=0 has real and equal roots?
Answer» For waht value/s of p, the quadratic equation $3 x^{2} - p x + 4 = 0$ has real and equal roots?

Discussion

7972.	Check whether the following congruence are true and false(1) 9 ≡ 23 (mod 12)(2) 15 ≡ 29 (mod 7)(3) 175 ≡ 5 (mod 17)(4) 21 ≡ − 8 (mod 6)
Answer» Check whether the following congruence are true and false (1) 9 ≡ 23 (mod 12) (2) 15 ≡ 29 (mod 7) (3) 175 ≡ 5 (mod 17) (4) 21 ≡ − 8 (mod 6)

7972.

Check whether the following congruence are true and false(1) 9 ≡ 23 (mod 12)(2) 15 ≡ 29 (mod 7)(3) 175 ≡ 5 (mod 17)(4) 21 ≡ − 8 (mod 6)

Answer»

Check whether the following congruence are true and false

(1) 9 ≡ 23 (mod 12)

(2) 15 ≡ 29 (mod 7)

(3) 175 ≡ 5 (mod 17)

(4) 21 ≡ − 8 (mod 6)

Discussion

7973.	In the given figure, OA and OB are opposite rays:(i) If x = 25°, what is the value of y?(ii) If y = 35°, what is the value of x?
Answer» In the given figure, OA and OB are opposite rays: (i) If x = 25°, what is the value of y? (ii) If y = 35°, what is the value of x?

Discussion

7974.	37. Prove that the normal chord to a parabola at the point whose ordinate os equal to its abscissa subtends a right angle at the focus.
Answer» 37. Prove that the normal chord to a parabola at the point whose ordinate os equal to its abscissa subtends a right angle at the focus.

Discussion

7975.	The number of ways in which 48 can be expressed as a product of it primes is (not considering the order in which these primes occur) _____.
Answer» The number of ways in which 48 can be expressed as a product of it primes is (not considering the order in which these primes occur) _____.

Discussion

7976.	The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is(a) 6 cm(b) 8 cm(c) 4 cm(d) 7 cm
Answer» The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is (a) 6 cm (b) 8 cm (c) 4 cm (d) 7 cm

Discussion

7977.	If α & β be the zeroes of 2x2−9x+4 then 1α+1β =
Answer» If $α & β$ be the zeroes of $2 x^{2} - 9 x + 4$ then $\frac{1}{α} + \frac{1}{β}$ =

Discussion

7978.	A trader bought an article for Rs. x and sold it for Rs. 52, thereby making a profit of (x - 10) percent on his outlay. Calculate the cost price.
Answer» A trader bought an article for Rs. x and sold it for Rs. 52, thereby making a profit of (x - 10) percent on his outlay. Calculate the cost price.

Discussion

7979.	Question 118 There are four containers that are arranged in the ascending order of their heights. If the of the smallest container given in figure is expressed as 725x=10.5 cm Then, find the height of the largest container.
Answer» Question 118 There are four containers that are arranged in the ascending order of their heights. If the of the smallest container given in figure is expressed as $\frac{7}{25} x = 10.5$ cm Then, find the height of the largest container.

7979.

Question 118 There are four containers that are arranged in the ascending order of their heights. If the of the smallest container given in figure is expressed as 725x=10.5 cm Then, find the height of the largest container.

Answer»

Question 118

There are four containers that are arranged in the ascending order of their heights. If the of the smallest container given in figure is expressed as $\frac{7}{25} x = 10.5$ cm Then, find the height of the largest container.

Discussion

7980.	Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case:(i) fx=2x3+x2-5x+2; 12, 1, -2(ii) g(x) = x3 − 4x2 + 5x − 2; 2, 1, 1
Answer» Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case: (i) $f (x) = 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2$ (ii) g(x) = x³ − 4x² + 5x − 2; 2, 1, 1

Discussion

7981.	22. The mean of 25 observation is 39.If the mean of the first 13 observation is 32 and the mean of last 13 observation is 52,then find the 13th observation
Answer» 22. The mean of 25 observation is 39.If the mean of the first 13 observation is 32 and the mean of last 13 observation is 52,then find the 13th observation

Discussion

7982.	We want to make a paper pyramid with base a square of side 10 centimetres and height 12 centimetres. What should be the lengths of the sides of the triangles?
Answer» We want to make a paper pyramid with base a square of side 10 centimetres and height 12 centimetres. What should be the lengths of the sides of the triangles?

Discussion

7983.	Four friends named Ravi, Suresh, Rani, Geetha put their names in a box. A name is picked at random. What is the probability of getting a boy's name
Answer» Four friends named Ravi, Suresh, Rani, Geetha put their names in a box. A name is picked at random. What is the probability of getting a boy's name

Discussion

7984.	The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.
Answer» The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.

Discussion

7985.	With the vertices of △ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.
Answer» With the vertices of $△$ ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

Discussion

7986.	In a combat between A,B and C , A tries to hit B and C , and B and C try to hit A. Probability of A , B and C hitting targets are 2/3 , 1/2 and 1/3 respectively. If A is hit , find the probability that B hits A and C does not.
Answer» In a combat between A,B and C , A tries to hit B and C , and B and C try to hit A. Probability of A , B and C hitting targets are 2/3 , 1/2 and 1/3 respectively. If A is hit , find the probability that B hits A and C does not.

Discussion

7987.	1. Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers, but no even numbers
Answer» 1. Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers, but no even numbers

Discussion

7988.	If α and β are the zeros of the polynomial f(x) = x2 + px + q, then a polynomial having 1αand 1β is its zero is(a) x2 + qx + p(b) x2 − px + q(c) qx2 + px + 1(d) px2 + qx + 1
Answer» If α and β are the zeros of the polynomial f(x) = x² + px + q, then a polynomial having $\frac{1}{α} and \frac{1}{β}$ is its zero is (a) x² + qx + p (b) x² − px + q (c) qx² + px + 1 (d) px² + qx + 1

Discussion

7989.	A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the metal sheet used, if it costs ₹ 5 per 100 cm2. (Take π = 3·14)
Answer» A container made up of a metal sheet is in the form of a frustum of a cone of height 16 $c m$ with radii of its lower and upper ends as 8 $c m$ and 20 $c m$ respectively. Find the cost of the metal sheet used, if it costs ₹ 5 per 100 $c m^{2}$ . (Take $π$ = 3·14)

Discussion

7990.	Identify the incorrect set of the following.
Answer» Identify the incorrect set of the following.

7990.

Identify the incorrect set of the following.

Answer»

Identify the incorrect set of the following.

Discussion

7991.	13. If the adjoining figure O is the centre of the circle chord CD is parallel to the diameter AB. If angle ABC=25^° ,calculate angle CED
Answer» 13. If the adjoining figure O is the centre of the circle chord CD is parallel to the diameter AB. If angle ABC=25^° ,calculate angle CED

Discussion

7992.	21. What is mean or average , mode , median
Answer» 21. What is mean or average , mode , median

Discussion

7993.	Find out the value.96sin65°sin35°sin80° ÷ (sin20°+2sin80°cos30°)
Answer» Find out the value. 96sin65°sin35°sin80° ÷ (sin20°+2sin80°cos30°)

Discussion

7994.	The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?
Answer» The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?

Discussion

7995.	Find the slope of line AB.
Answer» Find the slope of line AB.

7995.

Find the slope of line AB.

Answer»

Find the slope of line AB.

Discussion

7996.	Prove each of the following identities:i cot2θ-1sin2θ=-1ii tan2θ-1cos2θ=-1iii cos2θ+11+cot2θ=1
Answer» Prove each of the following identities: $(i) \cot^{2} θ - \frac{1}{\sin^{2} θ} = - 1 (ii) \tan^{2} θ - \frac{1}{\cos^{2} θ} = - 1 (iii) \cos^{2} θ + \frac{1}{(1 + \cot^{2} θ)} = 1$

Discussion

7997.	let a , b, c be three non zero vectors such that no two of them are collinear and (axb)xc = (1/3) \|b\| \|c\| a. if theta is the angle between b and c then sin theta is
Answer» let a , b, c be three non zero vectors such that no two of them are collinear and (axb)xc = (1/3) \|b\| \|c\| a. if theta is the angle between b and c then sin theta is

Discussion

7998.	Question 66 (ii)How many edges does the following solid have?Cylinder
Answer» Question 66 (ii) How many edges does the following solid have? Cylinder

Discussion

7999.	Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge. (round off to nearest whole number)
Answer» Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge. (round off to nearest whole number)

7999.

Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge. (round off to nearest whole number)

Answer»

Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge.
(round off to nearest whole number)

Discussion

8000.	Find the G.P. if(a) T3 : T6 = 1 : 8 and T5 = 64(b) T4 : T8 = 1 : 81 and T6 = 486(c) S10 : S5 = 33 : 1 and T6 = 32(d) S8 : S4 = 97 : 81 and T5 = 16
Answer» Find the G.P. if (a) T₃ : T₆ = 1 : 8 and T₅ = 64 (b) T₄ : T8 = 1 : 81 and T₆ = 486 (c) S₁₀ : S₅ = 33 : 1 and T₆= 32 (d) S₈ : S₄ = 97 : 81 and T₅ = 16

8000.

Find the G.P. if(a) T3 : T6 = 1 : 8 and T5 = 64(b) T4 : T8 = 1 : 81 and T6 = 486(c) S10 : S5 = 33 : 1 and T6 = 32(d) S8 : S4 = 97 : 81 and T5 = 16

Answer»

Find the G.P. if

(a) T₃ : T₆ = 1 : 8 and T₅ = 64

(b) T₄ : T8 = 1 : 81 and T₆ = 486

(c) S₁₀ : S₅ = 33 : 1 and T₆= 32

(d) S₈ : S₄ = 97 : 81 and T₅ = 16

Discussion

Explore topic-wise InterviewSolutions in .

From the given triangles, which of the following is true?

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2+5x-a2+a-6=0 [CBSE 2015]

If 3 tan θ=3 sin θ, find the value of sin2θ − cos2θ.

In the given figure ∠ABC=40∘, then angle ∠BEA is equal to?

Question 3 (i) Express 0.¯6 in the form pq, where p and q are integers and q≠0.

Prove that Cosec(2/7) + cosec (3/7)=cosec (/7)

If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =(a) −3(b) 7(c) 2(d) −2

A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

The theorem which describes "Two angles and the included side of two triangles are congruent" is:

The distance of the point P(−6, 8) from the origin is [CBSE 2013C](a) 8 (b) 27 (c) 6 (d) 10

Question 4 (xii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xii) √2,√8,√18,√32……

The angles of a pentagon are in the ratio 5:4:5:7:6 ; find each angle of the pentagon.

Given that 2x – y + z = 240. If z = 2y, y = 2x, then x = ?

If cos θ=23, then 2 sec2 θ + 2 tan2 θ − 7 is equal to(a) 1(b) 0(c) 3(d) 4

A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is(i) divisible by 2 or 3,(ii) a prime number.

9. From a point 2m above a lake the angle of elevation of a cloud is 30^° and the angle of depression of its reflection is 45^° . The height of cloud is

The difference between the second and first term of a sequence defined by tn=n^3/4n+1 is

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.

If [1,p/3] is the mid point of the line segment joining the points [2,0) And [1,2/9] then show that the line 5x+3y+2=0 passes through the point (-1,3p) If 2 positive integers p and q are written as p=a cube b cube And q =a cube b . A and b are prime numbers then verify lcm (p,q) *HCF (p,q)=pq

if vectors A=cosWt i +sinWt j and B =cos Wt/2 i + sin Wt/2 j are functions of time then the values of t at which they are orthogonal to each other is

For waht value/s of p, the quadratic equation 3x2−px+4=0 has real and equal roots?

Check whether the following congruence are true and false(1) 9 ≡ 23 (mod 12)(2) 15 ≡ 29 (mod 7)(3) 175 ≡ 5 (mod 17)(4) 21 ≡ − 8 (mod 6)

In the given figure, OA and OB are opposite rays:(i) If x = 25°, what is the value of y?(ii) If y = 35°, what is the value of x?

37. Prove that the normal chord to a parabola at the point whose ordinate os equal to its abscissa subtends a right angle at the focus.

The number of ways in which 48 can be expressed as a product of it primes is (not considering the order in which these primes occur) _____.

The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is(a) 6 cm(b) 8 cm(c) 4 cm(d) 7 cm

If α &amp; β be the zeroes of 2x2−9x+4 then 1α+1β =

A trader bought an article for Rs. x and sold it for Rs. 52, thereby making a profit of (x - 10) percent on his outlay. Calculate the cost price.

Question 118 There are four containers that are arranged in the ascending order of their heights. If the of the smallest container given in figure is expressed as 725x=10.5 cm Then, find the height of the largest container.

Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case:(i) fx=2x3+x2-5x+2; 12, 1, -2(ii) g(x) = x3 − 4x2 + 5x − 2; 2, 1, 1

22. The mean of 25 observation is 39.If the mean of the first 13 observation is 32 and the mean of last 13 observation is 52,then find the 13th observation

We want to make a paper pyramid with base a square of side 10 centimetres and height 12 centimetres. What should be the lengths of the sides of the triangles?

Four friends named Ravi, Suresh, Rani, Geetha put their names in a box. A name is picked at random. What is the probability of getting a boy's name

The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.

With the vertices of △ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

In a combat between A,B and C , A tries to hit B and C , and B and C try to hit A. Probability of A , B and C hitting targets are 2/3 , 1/2 and 1/3 respectively. If A is hit , find the probability that B hits A and C does not.

1. Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers, but no even numbers

If α and β are the zeros of the polynomial f(x) = x2 + px + q, then a polynomial having 1αand 1β is its zero is(a) x2 + qx + p(b) x2 − px + q(c) qx2 + px + 1(d) px2 + qx + 1

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the metal sheet used, if it costs ₹ 5 per 100 cm2. (Take π = 3·14)

Identify the incorrect set of the following.

13. If the adjoining figure O is the centre of the circle chord CD is parallel to the diameter AB. If angle ABC=25^° ,calculate angle CED

21. What is mean or average , mode , median

Find out the value.96sin65°sin35°sin80° ÷ (sin20°+2sin80°cos30°)

The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?

Find the slope of line AB.

Prove each of the following identities:i cot2θ-1sin2θ=-1ii tan2θ-1cos2θ=-1iii cos2θ+11+cot2θ=1

let a , b, c be three non zero vectors such that no two of them are collinear and (axb)xc = (1/3) |b| |c| a. if theta is the angle between b and c then sin theta is

Question 66 (ii)How many edges does the following solid have?Cylinder

Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge. (round off to nearest whole number)

Find the G.P. if(a) T3 : T6 = 1 : 8 and T5 = 64(b) T4 : T8 = 1 : 81 and T6 = 486(c) S10 : S5 = 33 : 1 and T6 = 32(d) S8 : S4 = 97 : 81 and T5 = 16

If α & β be the zeroes of 2x2−9x+4 then 1α+1β =