32581 + Interview Questions in Mathematics Page 29 InterviewSolution

1401.	Out of all the two digit numbers, what is the probability of the number not being a perfect square?
Answer» Out of all the two digit numbers, what is the probability of the number not being a perfect square?

Discussion

1402.	Find the sum of(i) the first 15 multiples of 8(ii) the first 40 positive integers divisible by (a) 3 (b) 5 (c) 6.(iii) all 3 − digit natural numbers which are divisible by 13.(iv) all 3 − digit natural numbers, which are multiples of 11.(v) all 2 − digit natural numbers divisible by 4.(vi) first 8 multiples of 3.
Answer» Find the sum of (i) the first 15 multiples of 8 (ii) the first 40 positive integers divisible by (a) 3 (b) 5 (c) 6. (iii) all 3 − digit natural numbers which are divisible by 13. (iv) all 3 − digit natural numbers, which are multiples of 11. (v) all 2 − digit natural numbers divisible by 4. (vi) first 8 multiples of 3.

Discussion

1403.	Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.
Answer» Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.

Discussion

1404.	The slant hieght o the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm Find the curved surface of the frustum.
Answer» The slant hieght o the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm Find the curved surface of the frustum.

Discussion

1405.	the angles of depression of the top and bottom of a building 50 meter high as observed from top of a tower are 30^° and 60^°, respectively. find the height of the tower and also the dis†an ce between the building and the tower
Answer» the angles of depression of the top and bottom of a building 50 meter high as observed from top of a tower are 30^° and 60^°, respectively. find the height of the tower and also the dis†an ce between the building and the tower

Discussion

1406.	Solve each of the following quadratic equations: 4x−3=52x+3,x≠0,−32
Answer» Solve each of the following quadratic equations: $\frac{4}{x} - 3 = \frac{5}{2 x + 3}, x \neq 0, \frac{- 3}{2}$

Discussion

1407.	In figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT=60∘,, find ∠PRQ.
Answer» In figure, PQ is a chord of a circle with centre O and PT is a tangent. If $∠ Q P T = 60^{\circ},$ , find $∠ P R Q$ .

Discussion

1408.	Write two rational numbers between √2 and √7
Answer» Write two rational numbers between √2 and √7

Discussion

1409.	Two persons are ′a′ metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer who looks at the top of their head , finds the angular elevations to be complementary, then the height of the shorter person in metres is :
Answer» Two persons are $^{'} a^{'}$ metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer who looks at the top of their head , finds the angular elevations to be complementary, then the height of the shorter person in metres is :

Discussion

1410.	A polynomial of degree ___ is called quadratic polynomial
Answer» A polynomial of degree ___ is called quadratic polynomial

Discussion

1411.	34 What is azumuthal quantam no.?explain it in brief.
Answer» 34 What is azumuthal quantam no.?explain it in brief.

Discussion

1412.	Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Answer» Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

Discussion

1413.	The product of two consecutive odd numbers is 675. If the smaller odd number is x, then the representation of the given condition in the form of quadratic equation is ____________.
Answer» The product of two consecutive odd numbers is 675. If the smaller odd number is $x$ , then the representation of the given condition in the form of quadratic equation is ____________.

Discussion

1414.	If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is(a) 200 m(b) 500 m(c) 30 m(d) 400 m
Answer» If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is (a) 200 m (b) 500 m (c) 30 m (d) 400 m

Discussion

1415.	The cost of 5 pens and 8 pencils is Rs.120,while the cost of 8 pens and 5 pencils is Rs.153.Find the cost of 1 pen and that of 1 pencil.
Answer» The cost of 5 pens and 8 pencils is Rs.120,while the cost of 8 pens and 5 pencils is Rs.153.Find the cost of 1 pen and that of 1 pencil.

Discussion

1416.	If a + c = b, then a zero of the polynomial ax2 + bx + c, is _________.
Answer» If a + c = b, then a zero of the polynomial ax² + bx + c, is _________.

Discussion

1417.	Question 4 Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms?Why?
Answer» Question 4 Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their $10^{t h}$ terms is the same as the difference between their $21^{s t}$ terms, which is the same as the difference between any two corresponding terms?Why?

Discussion

1418.	How many red cards are present in a deck of cards?
Answer» How many red cards are present in a deck of cards?

Discussion

1419.	If the roots of the equations ax2+2bx+c=0 and bx2-2acx+b=0 are simultaneously real then prove that b2=ac.
Answer» If the roots of the equations $a x^{2} + 2 b x + c = 0$ and $b x^{2} - 2 \sqrt{a c} x + b = 0$ are simultaneously real then prove that $b^{2} = a c$ .

Discussion

1420.	Are every twin prime also co primes
Answer» Are every twin prime also co primes

Discussion

1421.	On a horizontal plane there is vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.
Answer» On a horizontal plane there is vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.

Discussion

1422.	If the point of intersection of a less than and more than ogive is (15,20), then the value of median is
Answer» If the point of intersection of a less than and more than ogive is (15,20), then the value of median is

Discussion

1423.	If α and β are zeroes of polynomial x2 + x + 1, then the polynomial whose zeroes are (α + β) and αβ is
Answer» If α and β are zeroes of polynomial x2 + x + 1, then the polynomial whose zeroes are (α + β) and αβ is

Discussion

1424.	In the given figure, PQ \|\| AB and PR \|\| BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.
Answer» In the given figure, PQ \|\| AB and PR \|\| BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.

Discussion

1425.	If x = –9 is a root of x372x276x = 0, then other two roots are ___________.
Answer» If x = –9 is a root of $\|\begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix}\| = 0,$ then other two roots are ___________.

Discussion

1426.	If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 k = 0$ has real equal roots, then values of $k$ are

Discussion

1427.	2.If the points (k, 2-2k), (-k+1, 2k) and (-4-k, 6-2k) are collinear, then k=1(b)2(a) 1(d)2(c)
Answer» 2.If the points (k, 2-2k), (-k+1, 2k) and (-4-k, 6-2k) are collinear, then k=1(b)2(a) 1(d)2(c)

Discussion

1428.	Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠ BAF. If ∠BAE = 60°, then find the value of ∠BAC.
Answer» Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠ BAF. If ∠BAE = 60°, then find the value of ∠BAC.

Discussion

1429.	If the ratio of the sum of the first m and n terms of an AP is m2:n2 . Show that the ratio of it's mth and n th terms is (2m-1):(2n-1)
Answer» If the ratio of the sum of the first m and n terms of an AP is m²:n². Show that the ratio of it's m^th and n ^thterms is (2m-1):(2n-1)

Discussion

1430.	What is the angle between the two vectors shown in the figure?
Answer» What is the angle between the two vectors shown in the figure?

Discussion

1431.	△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 cm2, then area of △EFB is equal to
Answer» $△ A B C$ is an isosceles triangle in which AB = AC = 13 cm. If area of $△ A D C$ is $169 c m^{2}$ , then area of $△ E F B$ is equal to

1431.

△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 cm2, then area of △EFB is equal to

Answer»

$△ A B C$ is an isosceles triangle in which AB = AC = 13 cm. If area of $△ A D C$ is $169 c m^{2}$ , then area of $△ E F B$ is equal to

Discussion

1432.	Question 5Construct the following and give justification :A rhombus whose diagonals are 4cm and 6cm in lengths.
Answer» Question 5 Construct the following and give justification : A rhombus whose diagonals are 4cm and 6cm in lengths.

Discussion

1433.	Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: 2x−3y=12,x+3y=6.
Answer» Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: $2 x - 3 y = 12, x + 3 y = 6.$

Discussion

1434.	Which of the following is a pair of co-primes ? (a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)
Answer» Which of the following is a pair of co-primes ? (a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)

1434.

Which of the following is a pair of co-primes ? (a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)

Answer»

Which of the following is a pair of co-primes ?

(a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)

Discussion

1435.	How many pairs of positive integers x,y exist such that HCF(x,y)+LCM(x,y)=91?
Answer» How many pairs of positive integers $x, y$ exist such that $HCF (x, y) + LCM (x, y) = 91$ ?

Discussion

1436.	Question 5Classify the following as linear, quadriatic and cubic polynomials:(i) x2+x(ii) x−x3(iii) y+y2+4(iv) 1 + x(v) 3t(vi) r2(viii)7x3
Answer» Question 5 Classify the following as linear, quadriatic and cubic polynomials: (i) $x^{2} + x$ (ii) $x - x^{3}$ (iii) $y + y^{2} + 4$ (iv) 1 + x (v) 3t (vi) $r^{2}$ (viii) $7 x^{3}$

Discussion

1437.	1. Two flag posts of height 33m and 22m are on the opposite sides of a road of width 48 m. Ends of a rope are tied to the top of each flag post and rope is passing through a hook placed on the road. Find the minimum length of rope required (in meters)
Answer» 1. Two flag posts of height 33m and 22m are on the opposite sides of a road of width 48 m. Ends of a rope are tied to the top of each flag post and rope is passing through a hook placed on the road. Find the minimum length of rope required (in meters)

Discussion

1438.	We have a circle with centre O and two radii OA and OB. If the perimeter of minor sector OAB is 55 cm, and the radius of the circle is 7cm, the value of ∠AOB is
Answer» We have a circle with centre O and two radii OA and OB. If the perimeter of minor sector OAB is 55 cm, and the radius of the circle is 7cm, the value of ∠AOB is

Discussion

1439.	If matrix A=[a00b] is square root of [4009], then the number of such possible matrices is (where a,b∈R)
Answer» If matrix $A = [\begin{matrix} a & 0 0 & b \end{matrix}]$ is square root of $[\begin{matrix} 4 & 0 0 & 9 \end{matrix}],$ then the number of such possible matrices is (where $a, b \in R$ )

Discussion

1440.	Find the value of k for which each of the following system of equations have infinitely many solutions :kx+3y=2k+12k+1x+9y=7k+1
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $k x + 3 y = 2 k + 1 2 (k + 1) x + 9 y = 7 k + 1$

Discussion

1441.	The area of a circle whose area and circumference are numerically equal, is(a) 2π sq. units(b) 4 π sq. units(c) 6π sq. units(d) 8π sq. units
Answer» The area of a circle whose area and circumference are numerically equal, is (a) 2 $π$ sq. units (b) 4 $π$ sq. units (c) 6 $π$ sq. units (d) 8 $π$ sq. units

Discussion

1442.	In the given figure, O is the centre of the circle AB is a chord and AT is the tangent at A. If ∠AOB = 100∘ then ∠BAT is equal to [CBSE 2011](a) 40∘(b) 50∘(c) 90∘(d) 100∘
Answer» In the given figure, O is the centre of the circle AB is a chord and AT is the tangent at A. If ∠AOB = 100^∘ then ∠BAT is equal to [CBSE 2011] (a) 40^∘ (b) 50^∘ (c) 90^∘ (d) 100^∘

Discussion

1443.	From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively. Find(i) the horizontal distance between AB and CD,(ii) the height of the lamp post,(iii) the difference between the heights of the building and the lamp post. [CBSE 2009]
Answer» From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively. Find (i) the horizontal distance between AB and CD, (ii) the height of the lamp post, (iii) the difference between the heights of the building and the lamp post. [CBSE 2009]

Discussion

1444.	The sum of square of zeroes of the cubic polynomial x^3 + ax^2 + bx + c is
Answer» The sum of square of zeroes of the cubic polynomial x^3 + ax^2 + bx + c is

Discussion

1445.	Use Euclid’s Division lemma to show that the square of any positive integer is either of the form 3m or (3m+1) for some integer m.
Answer» Use Euclid’s Division lemma to show that the square of any positive integer is either of the form 3m or (3m+1) for some integer m.

Discussion

1446.	A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?
Answer» A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?

Discussion

1447.	Mr. Siddhant opened a recurring deposit account in a bank. He deposited in the installment of ₹ 2500 per month for two years. At the time of maturity he received an amount of ₹ 67,500. Calculate the rate of interest per annum.
Answer» Mr. Siddhant opened a recurring deposit account in a bank. He deposited in the installment of ₹ 2500 per month for two years. At the time of maturity he received an amount of ₹ 67,500. Calculate the rate of interest per annum.

Discussion

1448.	Three cubes of each side 4 cm are joined end to end. Find the total surface area of the resulting cuboid.
Answer» Three cubes of each side 4 cm are joined end to end. Find the total surface area of the resulting cuboid.

Discussion

1449.	12. If f(x) and g(x) are linear polynomial function such that for all x belongs to R fog = gof =I if f(0) = 4 and g(5) = 10 then the value of f(50) is equal to (1) 0 (2) 5 (3) 9 (4) 19
Answer» 12. If f(x) and g(x) are linear polynomial function such that for all x belongs to R fog = gof =I if f(0) = 4 and g(5) = 10 then the value of f(50) is equal to (1) 0 (2) 5 (3) 9 (4) 19

Discussion

1450.	The prime factorisation of a and b area=22×3×5 and b=2×32.What is the LCM of a and b?180
Answer» The prime factorisation of a and b are $a = 2^{2} \times 3 \times 5 and b = 2 \times 3^{2} .$ What is the LCM of a and b? 180

Discussion

Explore topic-wise InterviewSolutions in .

Out of all the two digit numbers, what is the probability of the number not being a perfect square?

Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.

The slant hieght o the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm Find the curved surface of the frustum.

the angles of depression of the top and bottom of a building 50 meter high as observed from top of a tower are 30^° and 60^°, respectively. find the height of the tower and also the dis†an ce between the building and the tower

Solve each of the following quadratic equations: 4x−3=52x+3,x≠0,−32

In figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT=60∘,, find ∠PRQ.

Write two rational numbers between √2 and √7

Two persons are ′a′ metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer who looks at the top of their head , finds the angular elevations to be complementary, then the height of the shorter person in metres is :

A polynomial of degree ___ is called quadratic polynomial

34 What is azumuthal quantam no.?explain it in brief.

Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

The product of two consecutive odd numbers is 675. If the smaller odd number is x, then the representation of the given condition in the form of quadratic equation is ____________.

If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is(a) 200 m(b) 500 m(c) 30 m(d) 400 m

The cost of 5 pens and 8 pencils is Rs.120,while the cost of 8 pens and 5 pencils is Rs.153.Find the cost of 1 pen and that of 1 pencil.

If a + c = b, then a zero of the polynomial ax2 + bx + c, is _________.

Question 4 Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms?Why?

How many red cards are present in a deck of cards?

If the roots of the equations ax2+2bx+c=0 and bx2-2acx+b=0 are simultaneously real then prove that b2=ac.

Are every twin prime also co primes

On a horizontal plane there is vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.

If the point of intersection of a less than and more than ogive is (15,20), then the value of median is

If α and β are zeroes of polynomial x2 + x + 1, then the polynomial whose zeroes are (α + β) and αβ is

In the given figure, PQ || AB and PR || BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.

If x = –9 is a root of x372x276x = 0, then other two roots are ___________.

If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are

2.If the points (k, 2-2k), (-k+1, 2k) and (-4-k, 6-2k) are collinear, then k=1(b)2(a) 1(d)2(c)

Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠ BAF. If ∠BAE = 60°, then find the value of ∠BAC.

If the ratio of the sum of the first m and n terms of an AP is m2:n​​​​​​2 ​​​​​​. Show that the ratio of it's m​​​​​​th and n th terms is (2m-1):(2n-1)

What is the angle between the two vectors shown in the figure?

△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 cm2, then area of △EFB is equal to

Question 5Construct the following and give justification :​​​​​​​​​​​​​​A rhombus whose diagonals are 4cm and 6cm in lengths.

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis: 2x−3y=12,x+3y=6.

Which of the following is a pair of co-primes ? (a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)

How many pairs of positive integers x,y exist such that HCF(x,y)+LCM(x,y)=91?

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

1. Two flag posts of height 33m and 22m are on the opposite sides of a road of width 48 m. Ends of a rope are tied to the top of each flag post and rope is passing through a hook placed on the road. Find the minimum length of rope required (in meters)

We have a circle with centre O and two radii OA and OB. If the perimeter of minor sector OAB is 55 cm, and the radius of the circle is 7cm, the value of ∠AOB is

If matrix A=[a00b] is square root of [4009], then the number of such possible matrices is (where a,b∈R)

Find the value of k for which each of the following system of equations have infinitely many solutions :kx+3y=2k+12k+1x+9y=7k+1

The area of a circle whose area and circumference are numerically equal, is(a) 2π sq. units(b) 4 π sq. units(c) 6π sq. units(d) 8π sq. units

In the given figure, O is the centre of the circle AB is a chord and AT is the tangent at A. If ∠AOB = 100∘ then ∠BAT is equal to [CBSE 2011](a) 40∘(b) 50∘(c) 90∘(d) 100∘

The sum of square of zeroes of the cubic polynomial x^3 + ax^2 + bx + c is

Use Euclid’s Division lemma to show that the square of any positive integer is either of the form 3m or (3m+1) for some integer m.

A hemispherical tank full of water is emptied by a pipe at the rate of 0.0005 litres/second. How much time will it take to empty two thirds of the tank, if it is 6 m in diameter?

Mr. Siddhant opened a recurring deposit account in a bank. He deposited in the installment of ₹ 2500 per month for two years. At the time of maturity he received an amount of ₹ 67,500. Calculate the rate of interest per annum.

Three cubes of each side 4 cm are joined end to end. Find the total surface area of the resulting cuboid.

12. If f(x) and g(x) are linear polynomial function such that for all x belongs to R fog = gof =I if f(0) = 4 and g(5) = 10 then the value of f(50) is equal to (1) 0 (2) 5 (3) 9 (4) 19

The prime factorisation of a and b area=22×3×5 and b=2×32.What is the LCM of a and b?180

If the ratio of the sum of the first m and n terms of an AP is m2:n2 . Show that the ratio of it's mth and n th terms is (2m-1):(2n-1)

Question 5Construct the following and give justification :A rhombus whose diagonals are 4cm and 6cm in lengths.