32581 + Interview Questions in Mathematics Page 273 InterviewSolution

13601.	Prove the identity cos2A/1+sinA+1+sinA/cosA=2secA
Answer» Prove the identity cos2A/1+sinA+1+sinA/cosA=2secA

Discussion

13602.	State the converse of Pythagoras' theorem.
Answer» State the converse of Pythagoras' theorem.

Discussion

13603.	Simplify the following : (i) (2x + 5) (3x - 2) + (x + 2) (2x - 3)
Answer» Simplify the following : (i) (2x + 5) (3x - 2) + (x + 2) (2x - 3)

Discussion

13604.	Question 12 A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.
Answer» Question 12 A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.

Discussion

13605.	ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the area of ∆ANC and ∆ABC.
Answer» ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the area of ∆ANC and ∆ABC.

Discussion

13606.	Solve the following systems of equations graphically:2x + y − 3 = 02x − 3y − 7 = 0
Answer» Solve the following systems of equations graphically: 2x + y − 3 = 0 2x − 3y − 7 = 0

Discussion

13607.	If the distance between the points A(–3, –14) and B(a, –5) is 9 units, then a = __________.
Answer» If the distance between the points A(–3, –14) and B(a, –5) is 9 units, then a = __________.

Discussion

13608.	Find the roots of the following equation applying quadratic formula. 4x2+4√3x+3=0
Answer» Find the roots of the following equation applying quadratic formula. $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

13609.	In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –(1) m(arc PR)(2) m(arc QS)(3) m(arc QSR)
Answer» In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find – (1) m(arc PR) (2) m(arc QS) (3) m(arc QSR)

Discussion

13610.	One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.
Answer» One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.

Discussion

13611.	The circumference of a globe is 88 cm. Calculate the surface area of the globe.
Answer» The circumference of a globe is 88 cm. Calculate the surface area of the globe.

Discussion

13612.	The probability of drawing a number card with an even number on it, from a deck whose face cards and ace have all been removed already, is?
Answer» The probability of drawing a number card with an even number on it, from a deck whose face cards and ace have all been removed already, is?

Discussion

13613.	5. Fixed price in a taxi is ruppes x and charged per km is ruppes y.if Fair for 10km is ruppes 70,then write the given data in the form of a linear equation in two variables. Also represent it graphically.what will the fixed charges ,if charges per km are rupees 5 ?
Answer» 5. Fixed price in a taxi is ruppes x and charged per km is ruppes y.if Fair for 10km is ruppes 70,then write the given data in the form of a linear equation in two variables. Also represent it graphically.what will the fixed charges ,if charges per km are rupees 5 ?

Discussion

13614.	If p=ax.by.cz and q=3x.b4.5z where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?
Answer» If $p = a^{x} . b^{y} . c^{z}$ and $q = 3^{x} . b^{4} {.5}^{z}$ where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

Discussion

13615.	The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g. [Assume π=227]
Answer» The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if $1 c m^{3}$ of wood has a mass of 0.6 g. $[A s s u m e π = \frac{22}{7}]$

Discussion

13616.	Arithmetic mean of two numbers lies ___________ the two numbers.
Answer» Arithmetic mean of two numbers lies ___________ the two numbers.

Discussion

13617.	Question 7Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to (a+c)(b+c−2a)2(b−a)
Answer» Question 7 Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to $\frac{(a + c) (b + c - 2 a)}{2 (b - a)}$

Discussion

13618.	Using prime factorization, find the HCF and LCM of(i) 8, 9, 25(ii) 12, 15, 21(iii) 17, 23, 29(iv) 24, 36, 40(v) 30, 72, 432(vi) 21, 28, 36, 45
Answer» Using prime factorization, find the HCF and LCM of (i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29 (iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45

Discussion

13619.	Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP × CR = DC × PR.
Answer» Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP $\times$ CR = DC $\times$ PR.

13619.

Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP × CR = DC × PR.

Answer»

Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP $\times$ CR = DC $\times$ PR.

Discussion

13620.	Two particles are projected with same velocity but at angles of projection 35 and 55 . Their horizontal ranges are in the ratio _____
Answer» Two particles are projected with same velocity but at angles of projection 35 and 55 . Their horizontal ranges are in the ratio _____

Discussion

13621.	Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.
Answer» Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

Discussion

13622.	D is a point on side BC of ΔABC, such that AD = AC Show that AB > AD.
Answer» D is a point on side BC of ΔABC, such that AD = AC Show that AB > AD.

Discussion

13623.	When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.
Answer» When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.

Discussion

13624.	In the given figure, points G, D, E, F are concyclic points of a circle with centre C.∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).
Answer» In the given figure, points G, D, E, F are concyclic points of a circle with centre C. ∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).

Discussion

13625.	Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.
Answer» Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.

Discussion

13626.	What is the remainder when 3x2−7x+5 is divided by (x−1) ?
Answer» What is the remainder when $3 x^{2} - 7 x + 5$ is divided by $(x - 1)$ ?

Discussion

13627.	If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5) then find the value of p.
Answer» If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5) then find the value of p.

Discussion

13628.	What will be the reflection of the point (4, 5) about the X-axis, in the fourth quadrant?
Answer» What will be the reflection of the point (4, 5) about the X-axis, in the fourth quadrant?

Discussion

13629.	Which of the following options are equal to cos2A−sin2A ?
Answer» Which of the following options are equal to ${cos}^{2} A - {sin}^{2} A$ ?

Discussion

13630.	Solve the following systems of equations: 5x+1−2y−1=12 10x+1+2y−1=52, where x≠−1 and y≠1
Answer» Solve the following systems of equations: $\frac{5}{x + 1} - \frac{2}{y - 1} = \frac{1}{2}$ $\frac{10}{x + 1} + \frac{2}{y - 1} = \frac{5}{2}$ , where $x \neq - 1 a n d y \neq 1$

13630.

Solve the following systems of equations: 5x+1−2y−1=12 10x+1+2y−1=52, where x≠−1 and y≠1

Answer»

Solve the following systems of equations:

$\frac{5}{x + 1} - \frac{2}{y - 1} = \frac{1}{2}$

$\frac{10}{x + 1} + \frac{2}{y - 1} = \frac{5}{2}$ , where $x \neq - 1 a n d y \neq 1$

Discussion

13631.	A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.
Answer» A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.

Discussion

13632.	The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto
Answer» The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto

Discussion

13633.	What is the length of the chord in the figure below?
Answer» What is the length of the chord in the figure below?

13633.

What is the length of the chord in the figure below?

Answer»

What is the length of the chord in the figure below?

Discussion

13634.	The marks obtained by 40 students in class X of a certain school in a math paper, are presented in the table.The total marks in that exam was 50. Find the mean using direct method.Marks obtainedNumber of students0−10310−20420−301330−401540−505
Answer» The marks obtained by 40 students in class X of a certain school in a math paper, are presented in the table.The total marks in that exam was 50. Find the mean using direct method. $\begin{matrix} Marks obtained & Number of students 0 - 10 & 3 10 - 20 & 4 20 - 30 & 13 30 - 40 & 15 40 - 50 & 5 \end{matrix}$

Discussion

13635.	In the following figure OM=ON and AB=12cm. Find the length of CN.
Answer» In the following figure OM=ON and AB=12cm. Find the length of CN.

Discussion

13636.	Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Arrange the steps in correct sequential order. Step I: After that, a ray BY is drawn parallel to AX making equal acute angle as in the previous step. Step II: AB = 7.6 cm is drawn. Step III: A ray AX making an acute angle with AB is drawn. Step IV: A5 and B8 is joined and it intersected AB at point C diving it in the ratio 5:8. AC : CB = 5 : 8 Step V: Point A1, A2, A3, A4 and A5 is marked on AX and point B1, B2.... to B8 is marked on BY such that AA1 = A1A2 = A2A3=....A4A5 BB1= B1B2 = .... B7B8
Answer» Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Arrange the steps in correct sequential order. Step I: After that, a ray BY is drawn parallel to AX making equal acute angle as in the previous step. Step II: AB = 7.6 cm is drawn. Step III: A ray AX making an acute angle with AB is drawn. Step IV: A5 and B8 is joined and it intersected AB at point C diving it in the ratio 5:8. AC : CB = 5 : 8 Step V: Point A1, A2, A3, A4 and A5 is marked on AX and point B1, B2.... to B8 is marked on BY such that AA1 = A1A2 = A2A3=....A4A5 BB1= B1B2 = .... B7B8

Discussion

13637.	Which term of the A.P. 3, 15, 27, 39, ... will be 120 more than its 21st term?
Answer» Which term of the A.P. 3, 15, 27, 39, ... will be 120 more than its 21^st term?

Discussion

13638.	By actual division find the quotient and remainder when 3x raised to power 4-rx raised to power 3-3x-1 is divided by X+1
Answer» By actual division find the quotient and remainder when 3x raised to power 4-rx raised to power 3-3x-1 is divided by X+1

Discussion

13639.	Prove that positive or negative irrational number is always an irrational number
Answer» Prove that positive or negative irrational number is always an irrational number

Discussion

13640.	ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]
Answer» ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]

13640.

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]

Answer»

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]

Discussion

13641.	Tan theta+ sec theta =7 then Tan theta - sec theta=?
Answer» Tan theta+ sec theta =7 then Tan theta - sec theta=?

Discussion

13642.	The decimal expansion of 141120 will terminate after how many places?
Answer» The decimal expansion of $\frac{141}{120}$ will terminate after how many places?

Discussion

13643.	Question 1Let ΔABC∼ΔDEF and their areas be, respectively, 64cm2 and 121cm2. If EF = 15.4 cm, find BC.
Answer» Question 1 Let $Δ A B C \sim Δ D E F$ and their areas be, respectively, $64 c m^{2}$ and $121 c m^{2}$ . If EF = 15.4 cm, find BC.

Discussion

13644.	how a irrational number can be cons†an t in a polynomial as it is non terminating and non repeating
Answer» how a irrational number can be cons†an t in a polynomial as it is non terminating and non repeating

Discussion

13645.

The following table shows the marks scored by 140 students in an examination of a certain paper. Marks: 0−10 10−20 20−30 30−40 40−50 Number of students: 20 24 40 36 20 Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Answer» The following table shows the marks scored by 140 students in an examination of a certain paper.

Marks:	0−10	10−20	20−30	30−40	40−50
Number of students:	20	24	40	36	20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Discussion

13646.	from a circular canvas of diameter 56m a sector of 270^° was cut out and a conical tent was formed by joining the straight ends of this piece. find the radius and height of ten
Answer» from a circular canvas of diameter 56m a sector of 270^° was cut out and a conical tent was formed by joining the straight ends of this piece. find the radius and height of ten

Discussion

13647.	Describe the locus for questions 1 to 13 given below: The locus of vertices of all isosceles triangles having a common base.
Answer» Describe the locus for questions 1 to 13 given below: The locus of vertices of all isosceles triangles having a common base.

13647.

Describe the locus for questions 1 to 13 given below: The locus of vertices of all isosceles triangles having a common base.

Answer»

Describe the locus for questions 1 to 13 given below:

The locus of vertices of all isosceles triangles having a common base.

Discussion

13648.	Question 172 ABCD is a parallelogram. Find the values of x, y and z.
Answer» Question 172 ABCD is a parallelogram. Find the values of x, y and z.

Discussion

13649.	Question 5 A metallic right circular cone 20 cm high and whose vertical angle is 60∘ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 116 cm, find the length of the wire.
Answer» Question 5 A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.

Discussion

13650.

A manufacturing company sells a T.V. to a trader A for Rs 18000. Trader A sells it to trader B at a profit of Rs 750 and trader B sells it to a consumer at a profit of Rs 900. If the rate of sales tax (under VAT) is 10% find i) the amount of tax received by the Government ii) the amount paid by the consumer for the T.V.

Answer»

A manufacturing company sells a T.V. to a trader A for Rs 18000. Trader A sells it to trader B at a profit of Rs 750 and trader B sells it to a consumer at a profit of Rs 900. If the rate of sales tax (under VAT) is 10% find

i) the amount of tax received by the Government

ii) the amount paid by the consumer for the T.V.

Discussion

Explore topic-wise InterviewSolutions in .

Prove the identity cos2A/1+sinA+1+sinA/cosA=2secA

State the converse of Pythagoras' theorem.

Simplify the following : (i) (2x + 5) (3x - 2) + (x + 2) (2x - 3)

Question 12 A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.

ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the area of ∆ANC and ∆ABC.

Solve the following systems of equations graphically:2x + y − 3 = 02x − 3y − 7 = 0

If the distance between the points A(–3, –14) and B(a, –5) is 9 units, then a = __________.

Find the roots of the following equation applying quadratic formula. 4x2+4√3x+3=0

In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –(1) m(arc PR)(2) m(arc QS)(3) m(arc QSR)

One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.

The circumference of a globe is 88 cm. Calculate the surface area of the globe.

The probability of drawing a number card with an even number on it, from a deck whose face cards and ace have all been removed already, is?

5. Fixed price in a taxi is ruppes x and charged per km is ruppes y.if Fair for 10km is ruppes 70,then write the given data in the form of a linear equation in two variables. Also represent it graphically.what will the fixed charges ,if charges per km are rupees 5 ?

If p=ax.by.cz and q=3x.b4.5z where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g. [Assume π=227]

Arithmetic mean of two numbers lies ___________ the two numbers.

Question 7Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to (a+c)(b+c−2a)2(b−a)

Using prime factorization, find the HCF and LCM of(i) 8, 9, 25(ii) 12, 15, 21(iii) 17, 23, 29(iv) 24, 36, 40(v) 30, 72, 432(vi) 21, 28, 36, 45

Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP × CR = DC × PR.

Two particles are projected with same velocity but at angles of projection 35 and 55 . Their horizontal ranges are in the ratio _____

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

D is a point on side BC of ΔABC, such that AD = AC Show that AB > AD.

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.

In the given figure, points G, D, E, F are concyclic points of a circle with centre C.∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.

What is the remainder when 3x2−7x+5 is divided by (x−1) ?

If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5) then find the value of p.

What will be the reflection of the point (4, 5) about the X-axis, in the fourth quadrant?

Which of the following options are equal to cos2A−sin2A ?

Solve the following systems of equations: 5x+1−2y−1=12 10x+1+2y−1=52, where x≠−1 and y≠1

The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto

What is the length of the chord in the figure below?

The marks obtained by 40 students in class X of a certain school in a math paper, are presented in the table.The total marks in that exam was 50. Find the mean using direct method.Marks obtainedNumber of students0−10310−20420−301330−401540−505

In the following figure OM=ON and AB=12cm. Find the length of CN.

Which term of the A.P. 3, 15, 27, 39, ... will be 120 more than its 21st term?

By actual division find the quotient and remainder when 3x raised to power 4-rx raised to power 3-3x-1 is divided by X+1

Prove that positive or negative irrational number is always an irrational number

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]​

Tan theta+ sec theta =7 then Tan theta - sec theta=?

The decimal expansion of 141120 will terminate after how many places?

Question 1Let ΔABC∼ΔDEF and their areas be, respectively, 64cm2 and 121cm2. If EF = 15.4 cm, find BC.

how a irrational number can be cons†an t in a polynomial as it is non terminating and non repeating

The following table shows the marks scored by 140 students in an examination of a certain paper. Marks: 0−10 10−20 20−30 30−40 40−50 Number of students: 20 24 40 36 20 Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

from a circular canvas of diameter 56m a sector of 270^° was cut out and a conical tent was formed by joining the straight ends of this piece. find the radius and height of ten

Describe the locus for questions 1 to 13 given below: The locus of vertices of all isosceles triangles having a common base.

Question 172 ABCD is a parallelogram. Find the values of x, y and z.

Question 5 A metallic right circular cone 20 cm high and whose vertical angle is 60∘ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 116 cm, find the length of the wire.

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]