32581 + Interview Questions in Mathematics Page 16 InterviewSolution

751.	Write the standard form of y = 7x- 4, and find the value of a, b, c.
Answer» Write the standard form of y = 7x- 4, and find the value of a, b, c.

Discussion

752.	Question 4Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.Number of heart beats per minute65−6868−7171−7474−7777−8080−8383−86Number of women2438742
Answer» Question 4 Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method. $\begin{matrix} Number of heart beats per minute & 65 - 68 & 68 - 71 & 71 - 74 & 74 - 77 & 77 - 80 & 80 - 83 & 83 - 86 Number of women & 2 & 4 & 3 & 8 & 7 & 4 & 2 \end{matrix}$

752.

Question 4Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.Number of heart beats per minute65−6868−7171−7474−7777−8080−8383−86Number of women2438742

Answer»

Question 4

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

$\begin{matrix} Number of heart beats per minute & 65 - 68 & 68 - 71 & 71 - 74 & 74 - 77 & 77 - 80 & 80 - 83 & 83 - 86 Number of women & 2 & 4 & 3 & 8 & 7 & 4 & 2 \end{matrix}$

Discussion

753.	Solve each of the following systems of equations by the method of cross-multiplication :bax+aby=a2+b2x+y=2ab
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $\frac{b}{a} x + \frac{a}{b} y = a^{2} + b^{2} x + y = 2 a b$

Discussion

754.	If mth term of an AP is 1n and nth term is 1m then find the sum of its first mn terms.
Answer» If $m^{t h}$ term of an AP is $\frac{1}{n}$ and $n^{t h}$ term is $\frac{1}{m}$ then find the sum of its first $m n$ terms.

Discussion

755.	As observed from the top of a light house, 100 m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30∘ to 60∘. Find the distance travelled by the ship during the period of observation. (Use √3=1.73)
Answer» As observed from the top of a light house, 100 m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from $30^{\circ}$ to $60^{\circ}$ . Find the distance travelled by the ship during the period of observation. (Use $\sqrt{3} = 1.73$ )

Discussion

756.	Find the values of x, which satisfy the inequation: 2≤ 12−2x3≤ 116 , x ϵ N.
Answer» Find the values of x, which satisfy the inequation: $2 \leq \frac{1}{2} - \frac{2 x}{3} \leq \frac{11}{6}$ , x $ϵ$ N.

756.

Find the values of x, which satisfy the inequation: 2≤ 12−2x3≤ 116 , x ϵ N.

Answer»

Find the values of x, which satisfy the inequation:

$2 \leq \frac{1}{2} - \frac{2 x}{3} \leq \frac{11}{6}$ , x $ϵ$ N.

Discussion

757.	What is retardation
Answer» What is retardation

Discussion

758.	Changes in the pattern of tastes and preferences of the consumers will affect the levels of
Answer» Changes in the pattern of tastes and preferences of the consumers will affect the levels of

Discussion

759.	In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 50∘ then what is the measure of ∠OAB is [CBSE 2015]
Answer» In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 50^∘ then what is the measure of ∠OAB is [CBSE 2015]

Discussion

760.	The radius and height of a right cone are in the ratio 3:4. Then the ratio of total surface area to curved surface of the cone is
Answer» The radius and height of a right cone are in the ratio $3 : 4.$ Then the ratio of total surface area to curved surface of the cone is

Discussion

761.	If (a−b)2,(a2+b2) are the first two terms of an AP, then which of the following will be the next term?
Answer» If $(a - b)^{2}, (a^{2} + b^{2})$ are the first two terms of an AP, then which of the following will be the next term?

Discussion

762.	What is corollary?
Answer» What is corollary?

Discussion

763.	The sum of the numerator and the denominator of a fraction is 8. If 3 is added to both the numerator and the denominator, the fraction becomes 34. Find the fraction.
Answer» The sum of the numerator and the denominator of a fraction is 8. If 3 is added to both the numerator and the denominator, the fraction becomes $\frac{3}{4}$ . Find the fraction.

Discussion

764.	Match the APs to their nth terms.
Answer» Match the APs to their $n^{th}$ terms.

Discussion

765.	A triangle of maximum area inscribed in a circle of radius r1) is a right angled triangle2) is an equilatoral triangle3) is an isoscles triangle4) does not exist
Answer» A triangle of maximum area inscribed in a circle of radius r 1) is a right angled triangle 2) is an equilatoral triangle 3) is an isoscles triangle 4) does not exist

Discussion

766.	Using cardboard construct the following polyhedral:(i) A square based prism (ii) Square based pyramid (iii) Hexagonal based pyramid.
Answer» Using cardboard construct the following polyhedral: (i) A square based prism (ii) Square based pyramid (iii) Hexagonal based pyramid.

766.

Using cardboard construct the following polyhedral:(i) A square based prism (ii) Square based pyramid (iii) Hexagonal based pyramid.

Answer»

Using cardboard construct the following polyhedral:

(i) A square based prism (ii) Square based pyramid (iii) Hexagonal based pyramid.

Discussion

767.	Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and displacement covered by him if all the distances in the figure are in kilometers?Ans - _
Answer» Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and displacement covered by him if all the distances in the figure are in kilometers? Ans - _

Discussion

768.	If a and b are the zeroes of the quadratic polynomial x2 - 6x + a, find the value of 'a'. If 3a + 2b = 20
Answer» If a and b are the zeroes of the quadratic polynomial x²- 6x + a, find the value of 'a'. If 3a + 2b = 20

Discussion

769.	A dealer gets a scooty from Maharashtra at ₹60000. He sells it in Gujarat at a profit of 20%. If the GST rate is 12 %, Find the selling price in Gujarat including GST.
Answer» A dealer gets a scooty from Maharashtra at ₹60000. He sells it in Gujarat at a profit of 20%. If the GST rate is 12 %, Find the selling price in Gujarat including GST.

Discussion

770.	Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?
Answer» Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?

Discussion

771.	a) Find the ratio in which the point P (-1, a) divides the joining of points A(-5, 4) and B (3, -2). Hence, find a. b) The line joining the points A(4, -5) and B (4, 5) is divided by the point P, such that AP: PB = 2 : 3. Find the coordinates of point P. [6 MARKS]
Answer» a) Find the ratio in which the point P (-1, a) divides the joining of points A(-5, 4) and B (3, -2). Hence, find a. b) The line joining the points A(4, -5) and B (4, 5) is divided by the point P, such that AP: PB = 2 : 3. Find the coordinates of point P. [6 MARKS]

Discussion

772.	In which one of the following subsets , cos2A + sin2A = 1 is valid
Answer» In which one of the following subsets , $c o s^{2} A$ + $s i n^{2} A$ = 1 is valid

Discussion

773.	What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm? [CBSE 2012]
Answer» What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm? [CBSE 2012]

Discussion

774.	Find the number of complex roots for a 12th degree polynomial f(x) if there is no positive and negative real roots but f(0) = 0. __
Answer» Find the number of complex roots for a 12^th degree polynomial f(x) if there is no positive and negative real roots but f(0) = 0. __

Discussion

775.	x2=y+z;y2=x+z;z2=x+y 1(x+1)+1(y+1)+1(z+1)
Answer» $x^{2} = y + z; y^{2} = x + z; z^{2} = x + y$ $\frac{1}{(x + 1)} + \frac{1}{(y + 1)} + \frac{1}{(z + 1)}$

Discussion

776.	Prove that the points (a, b), (a1, b1) and (a −a1, b −b1) are collinear if ab1 = a1b.
Answer» Prove that the points (a, b), (a₁, b₁) and (a −a₁, b −b₁) are collinear if ab₁ = a₁b.

Discussion

777.	State the condition for one solution, infinite solutions and no solution for a pair of linear equations.
Answer» State the condition for one solution, infinite solutions and no solution for a pair of linear equations.

Discussion

778.	The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms,then its fourth term will be
Answer» The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms,then its fourth term will be

Discussion

779.	The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, then find its volume.
Answer» The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, then find its volume.

Discussion

780.	The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be 45∘ and 30∘. What is the distance between the two objects? (Take √3=1.732)
Answer» The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be $45^{\circ} and 30^{\circ}$ . What is the distance between the two objects? (Take $\sqrt{3} = 1.732$ )

Discussion

781.	Find the value of ‘’ if ( – 2) is a factor of 3 + 22 – + 10. Hence check if ( + 5) is also a factor.
Answer» Find the value of ‘’ if ( – 2) is a factor of ³ + 2² – + 10. Hence check if ( + 5) is also a factor.

Discussion

782.	If △ABC ∼ △DEF such that 2AB = DE and BC = 6 cm, find EF
Answer» If △ABC ∼ △DEF such that 2AB = DE and BC = 6 cm, find EF

Discussion

783.	Sahil deposited Rs. 90 per month in a cumulative (recurring) deposit account for six years. The amount payable to him on maturity if the rate of interest is 8 % will be equal to ___.
Answer» Sahil deposited Rs. 90 per month in a cumulative (recurring) deposit account for six years. The amount payable to him on maturity if the rate of interest is 8 % will be equal to ___.

Discussion

784.	Question 2 (ii) Give two different examples of pair of (ii) Non-similar figures
Answer» Question 2 (ii) Give two different examples of pair of (ii) Non-similar figures

Discussion

785.	A line through the point P(2,3) meets the line x-2y+7=0 and x+3y-3 =0 at points A and B respectively. If P divides AB externally in the ratio 3:2 find the equation of line AB .
Answer» A line through the point P(2,3) meets the line x-2y+7=0 and x+3y-3 =0 at points A and B respectively. If P divides AB externally in the ratio 3:2 find the equation of line AB .

Discussion

786.	The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD=∠BCD=90∘. Then the length of AB is ____.
Answer» The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and $∠ A B D = ∠ B C D = 90^{\circ}$ . Then the length of AB is ____.

786.

The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD=∠BCD=90∘. Then the length of AB is ____.

Answer»

The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and $∠ A B D = ∠ B C D = 90^{\circ}$ . Then the length of AB is ____.

Discussion

787.	Given A=[123231] and B=[3−13−102], then find 2A−B
Answer» Given $A = [\begin{matrix} 1 & 2 & 3 2 & 3 & 1 \end{matrix}]$ and $B = [\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}],$ then find $2 A - B$

Discussion

788.	Write down the decimal expansions of(i) 133125(ii) 178(iii) 151600
Answer» Write down the decimal expansions of (i) $\frac{13}{3125}$ (ii) $\frac{17}{8}$ (iii) $\frac{15}{1600}$

Discussion

789.	In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then –
Answer» In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then –

Discussion

790.	In a deck of 52 cards, there are 4 kings, 4 queens, and 4 jacks, which are known as the face cards. If a card is drawn from the deck, what is the probability of it being a face card?
Answer» In a deck of 52 cards, there are 4 kings, 4 queens, and 4 jacks, which are known as the face cards. If a card is drawn from the deck, what is the probability of it being a face card?

Discussion

791.	The number of different possible orders of matrices having 18 elements and all are identical is:
Answer» The number of different possible orders of matrices having $18$ elements and all are identical is:

Discussion

792.	In the given figure, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°
Answer» In the given figure, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°

Discussion

793.	Determine the nature of the roots of the following quadratic equations:(i) 2x2 − 3x + 5 = 0(ii) 2x2 − 6x + 3 = 0(iii) 35x2-23x+1=0(iv) 3x2-43x+4=0(v) 3x2-26x+2=0
Answer» Determine the nature of the roots of the following quadratic equations: (i) 2x² − 3x + 5 = 0 (ii) 2x² − 6x + 3 = 0 (iii) $\frac{3}{5} x^{2} - \frac{2}{3} x + 1 = 0$ (iv) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$ (v) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$

Discussion

794.	a small block slides down a smooth inclined plane,starting from rest at time t=0.let sn be the distance travelled by the block in the interval t=n-1 to t=n.Then,the ratio sn/sn+1 is:(a)2n-1/2n (b)2n-1/2n+1 (c)2n+1/2n-1 (d)2n/2n-1
Answer» a small block slides down a smooth inclined plane,starting from rest at time t=0.let sn be the distance travelled by the block in the interval t=n-1 to t=n.Then,the ratio sn/sn+1 is: (a)2n-1/2n (b)2n-1/2n+1 (c)2n+1/2n-1 (d)2n/2n-1

Discussion

795.	A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder. ___
Answer» A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder. ___

795.

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder. ___

Answer»

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder.

___

Discussion

796.	AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]
Answer» AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]

796.

AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]

Answer»

AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]

Discussion

797.	In a parallelogram , one angle is 45th of its adjacent angle. Then the angles of the parallelogram are
Answer» In a parallelogram , one angle is $\frac{4}{5}$ ^th of its adjacent angle. Then the angles of the parallelogram are

Discussion

798.	If a and d are the first term and the common difference of an AP, Sn denotes the sum of n terms of an AP. If Sn=Pn+Qn2, what are a and d in terms of P and Q?
Answer» If $a$ and $d$ are the first term and the common difference of an AP, $S_{n}$ denotes the sum of $n$ terms of an AP. If $S_{n} = P n + Q n^{2}$ , what are $a$ and $d$ in terms of $P$ and $Q$ ?

Discussion

799.	On the basis of graph, the pair of linear equation gives _______________solution(s).
Answer» On the basis of graph, the pair of linear equation gives _______________solution(s).

799.

On the basis of graph, the pair of linear equation gives _______________solution(s).

Answer»

On the basis of graph, the pair of linear equation gives _______________solution(s).

Discussion

800.	The sum of four consecutive numbers in A.P. is 32 and the ration of the product of the first and last terms to the product of two middle terms is 7:15. Find the number.
Answer» The sum of four consecutive numbers in A.P. is 32 and the ration of the product of the first and last terms to the product of two middle terms is 7:15. Find the number.

Discussion

Explore topic-wise InterviewSolutions in .

Write the standard form of y = 7x- 4, and find the value of a, b, c.

Solve each of the following systems of equations by the method of cross-multiplication :bax+aby=a2+b2x+y=2ab

If mth term of an AP is 1n and nth term is 1m then find the sum of its first mn terms.

As observed from the top of a light house, 100 m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30∘ to 60∘. Find the distance travelled by the ship during the period of observation. (Use √3=1.73)

Find the values of x, which satisfy the inequation: 2≤ 12−2x3≤ 116 , x ϵ N.

What is retardation

Changes in the pattern of tastes and preferences of the consumers will affect the levels of

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 50∘ then what is the measure of ∠OAB is [CBSE 2015]

The radius and height of a right cone are in the ratio 3:4. Then the ratio of total surface area to curved surface of the cone is

If (a−b)2,(a2+b2) are the first two terms of an AP, then which of the following will be the next term?

What is corollary?

The sum of the numerator and the denominator of a fraction is 8. If 3 is added to both the numerator and the denominator, the fraction becomes 34. Find the fraction.

Match the APs to their nth terms.

A triangle of maximum area inscribed in a circle of radius r1) is a right angled triangle2) is an equilatoral triangle3) is an isoscles triangle4) does not exist

Using cardboard construct the following polyhedral:(i) A square based prism (ii) Square based pyramid (iii) Hexagonal based pyramid.

Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and displacement covered by him if all the distances in the figure are in kilometers?Ans - _

If a and b are the zeroes of the quadratic polynomial x2 - 6x + a, find the value of 'a'. If 3a + 2b = 20

A dealer gets a scooty from Maharashtra at ₹60000. He sells it in Gujarat at a profit of 20%. If the GST rate is 12 %, Find the selling price in Gujarat including GST.

Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?

a) Find the ratio in which the point P (-1, a) divides the joining of points A(-5, 4) and B (3, -2). Hence, find a. b) The line joining the points A(4, -5) and B (4, 5) is divided by the point P, such that AP: PB = 2 : 3. Find the coordinates of point P. [6 MARKS]

In which one of the following subsets , cos2A + sin2A = 1 is valid

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm? [CBSE 2012]

Find the number of complex roots for a 12th degree polynomial f(x) if there is no positive and negative real roots but f(0) = 0. __

x2=y+z;y2=x+z;z2=x+y 1(x+1)+1(y+1)+1(z+1)

Prove that the points (a, b), (a1, b1) and (a −a1, b −b1) are collinear if ab1 = a1b.

State the condition for one solution, infinite solutions and no solution for a pair of linear equations.

The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms,then its fourth term will be

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, then find its volume.

The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be 45∘ and 30∘. What is the distance between the two objects? (Take √3=1.732)

Find the value of ‘’ if ( – 2) is a factor of 3 + 22 – + 10. Hence check if ( + 5) is also a factor.

If △ABC ∼ △DEF such that 2AB = DE and BC = 6 cm, find EF

Sahil deposited Rs. 90 per month in a cumulative (recurring) deposit account for six years. The amount payable to him on maturity if the rate of interest is 8 % will be equal to ___.

Question 2 (ii) Give two different examples of pair of (ii) Non-similar figures

A line through the point P(2,3) meets the line x-2y+7=0 and x+3y-3 =0 at points A and B respectively. If P divides AB externally in the ratio 3:2 find the equation of line AB .

The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD=∠BCD=90∘. Then the length of AB is ____.

Given A=[123231] and B=[3−13−102], then find 2A−B

Write down the decimal expansions of(i) 133125(ii) 178(iii) 151600

In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then –

In a deck of 52 cards, there are 4 kings, 4 queens, and 4 jacks, which are known as the face cards. If a card is drawn from the deck, what is the probability of it being a face card?

The number of different possible orders of matrices having 18 elements and all are identical is:

In the given figure, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°

Determine the nature of the roots of the following quadratic equations:(i) 2x2 − 3x + 5 = 0(ii) 2x2 − 6x + 3 = 0(iii) 35x2-23x+1=0(iv) 3x2-43x+4=0(v) 3x2-26x+2=0

a small block slides down a smooth inclined plane,starting from rest at time t=0.let sn be the distance travelled by the block in the interval t=n-1 to t=n.Then,the ratio sn/sn+1 is:(a)2n-1/2n (b)2n-1/2n+1 (c)2n+1/2n-1 (d)2n/2n-1

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder. ___

AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED. [3 MARKS]

In a parallelogram , one angle is 45th of its adjacent angle. Then the angles of the parallelogram are

If a and d are the first term and the common difference of an AP, Sn denotes the sum of n terms of an AP. If Sn=Pn+Qn2, what are a and d in terms of P and Q?

On the basis of graph, the pair of linear equation gives _______________solution(s).

The sum of four consecutive numbers in A.P. is 32 and the ration of the product of the first and last terms to the product of two middle terms is 7:15. Find the number.