24740 + Interview Questions in Mathematics Page 221 InterviewSolution

11001.	23. The length of chord of the parabola y=4X which passes through the vertex and makes 30^° angle with x-axis
Answer» 23. The length of chord of the parabola y=4X which passes through the vertex and makes 30^° angle with x-axis

Discussion

11002.	If A=⎡⎢⎣02bcab−ca−bc⎤⎥⎦ is orthogonal, then \|abc\| is equal to
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 2 b & c a & b & - c a & - b & c \end{matrix} ⎤ ⎥ ⎦$ is orthogonal, then $\| a b c \|$ is equal to

Discussion

11003.	State whether 10.064 is rational or irrational no. Represent it in p/q form.
Answer» State whether 10.064 is rational or irrational no. Represent it in p/q form.

Discussion

11004.	Show how √5can be represented on the number line
Answer» Show how √5can be represented on the number line

Discussion

11005.	Mirror image of point (1, 2) with respect to the y-axis is ______.
Answer» Mirror image of point (1, 2) with respect to the y-axis is ______.

Discussion

11006.	Draw an angle of 40°.Copy its supplementary angle.
Answer» Draw an angle of 40°. Copy its supplementary angle.

Discussion

11007.	Jasmine has a bag of sweets. It has 3 yellow sweets, 5 green sweets, 7 red sweets, 4 purple sweets and 1 black sweet. If Jasmine takes out one sweet whose probability is 14, then what colour sweet has she taken out ?
Answer» Jasmine has a bag of sweets. It has 3 yellow sweets, 5 green sweets, 7 red sweets, 4 purple sweets and 1 black sweet. If Jasmine takes out one sweet whose probability is $\frac{1}{4}$ , then what colour sweet has she taken out ?

Discussion

11008.	For the equations 2x+3y=13 and 5x−4y=−2 where x≠0 & y≠0, the value of
Answer» For the equations $\frac{2}{x} + \frac{3}{y} = 13$ and $\frac{5}{x} - \frac{4}{y} = - 2$ where $x \neq 0 & y \neq 0$ , the value of

Discussion

11009.	Factorise1 – 27a3
Answer» Factorise 1 – 27a³

Discussion

11010.	Express 0.75 as a rational number.
Answer» Express 0.75 as a rational number.

Discussion

11011.	Question 10 Rationalize the denominator of the following (i)23√3(ii)√40√3(iii)3+√24√2(iv)16√41−5(v)2+√32−√3(vi)√6√2+√3(vii)√3+√2√3−√2 (viii)3√5+√3√5−√3 (ix)4√3+5√2√48+√18 Thinking process For rationalizing the denominator multiplying numerator by the conjugate of the denominator term and simplify it to get the result.
Answer» Question 10 Rationalize the denominator of the following $(i) \frac{2}{3 \sqrt{3}} (i i) \frac{\sqrt{40}}{\sqrt{3}} (i i i) \frac{3 + \sqrt{2}}{4 \sqrt{2}} (i v) \frac{16}{\sqrt{41 - 5}} (v) \frac{2 + \sqrt{3}}{2 - \sqrt{3}} (v i) \frac{\sqrt{6}}{\sqrt{2} + \sqrt{3}} (v i i) \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ $(v i i i) \frac{3 \sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ $(i x) \frac{4 \sqrt{3} + 5 \sqrt{2}}{\sqrt{48} + \sqrt{18}}$ Thinking process For rationalizing the denominator multiplying numerator by the conjugate of the denominator term and simplify it to get the result.

Discussion

11012.	.The sum of the first 2011 terms of a G.P. is 200. The sum of the first 4022 terms of the same series is 380.Find the sum of the first 6033 terms of the series
Answer» .The sum of the first 2011 terms of a G.P. is 200. The sum of the first 4022 terms of the same series is 380.Find the sum of the first 6033 terms of the series

Discussion

11013.	The diameter of a road roller is 60 cm and it is 140 cm long. It levelled an area of 79,200 cm2. How many turns did the road roller take to level the said area?
Answer» The diameter of a road roller is 60 cm and it is 140 cm long. It levelled an area of $79, 200 c m^{2}$ . How many turns did the road roller take to level the said area?

Discussion

11014.	What did the Professor mean by "intelligent reading"?
Answer» What did the Professor mean by "intelligent reading"?

Discussion

11015.	For any three sets A,B & C;A∪(B∪C)=
Answer» For any three sets $A, B & C; A \cup (B \cup C) =$

Discussion

11016.	A solid cylinder is melted and cast into a cone of same radius.The heights of the cone and cylinder are in the ratio
Answer» A solid cylinder is melted and cast into a cone of same radius.The heights of the cone and cylinder are in the ratio

Discussion

11017.	int_(0)^(1) 1/sqrt(2-x-x^2)dx
Answer» int_(0)^(1) 1/sqrt(2-x-x^2)dx

Discussion

11018.	Find the values of a and b if 5+2√37+4√3=a+b√3
Answer» Find the values of $a$ and $b$ if $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

11018.

Find the values of a and b if 5+2√37+4√3=a+b√3

Answer»

Find the values of $a$ and $b$

if $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

Discussion

11019.	What is the value of b if,(3,1) is a solution for the equation: 6x+by=25 ?
Answer» What is the value of b if, $(3, 1)$ is a solution for the equation: $6 x + b y = 25$ ?

Discussion

11020.	Question 2A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. The acute angle between the diagonals is(a) 55∘(b) 50∘(c) 40∘(d) 25∘
Answer» Question 2 A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$ . The acute angle between the diagonals is (a) $55^{\circ}$ (b) $50^{\circ}$ (c) $40^{\circ}$ (d) $25^{\circ}$

Discussion

11021.	Classify the following as linear, quadratic and cubic polynomials:(i)4x3+2x+6 (ii)x+5(iii)9x3 (iv)2x2+2x+7
Answer» Classify the following as linear, quadratic and cubic polynomials: $(i) 4 x^{3} + 2 x + 6$ $(i i) x + 5$ $(i i i) 9 x^{3}$ $(i v) 2 x^{2} + 2 x + 7$

Discussion

11022.	If the angles of a triangle are 30°, 30° and 120°, then the triangle is ___.
Answer» If the angles of a triangle are 30°, 30° and 120°, then the triangle is ___.

Discussion

11023.	Steps for the construction of a 30° angle.Choose the correct order.1: Draw a ray OA.2: With B as centre and the same radius as before, draw another arc to cut the previous arc at C.3: Draw the bisector OE of ∠AOD.4: Join OC and produce it to D.5: With O as centre and any suitable radius draw an arc above OA cutting it at a point B.
Answer» Steps for the construction of a 30° angle. Choose the correct order. 1: Draw a ray OA. 2: With B as centre and the same radius as before, draw another arc to cut the previous arc at C. 3: Draw the bisector OE of ∠AOD. 4: Join OC and produce it to D. 5: With O as centre and any suitable radius draw an arc above OA cutting it at a point B.

Discussion

11024.	What is the difference between else and elif construct of if statement?
Answer» What is the difference between else and elif construct of if statement?

Discussion

11025.	Explain polynomial in one variable x of degree n
Answer» Explain polynomial in one variable x of degree n

Discussion

11026.	OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD
Answer» OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD

Discussion

11027.	Find the area of the shaded region.
Answer» Find the area of the shaded region.

Discussion

11028.	9. The numerator of a rational number is 17 more than its denominator. The numerator of its absolute is 7 more than its denominator. Find the rational number.
Answer» 9. The numerator of a rational number is 17 more than its denominator. The numerator of its absolute is 7 more than its denominator. Find the rational number.

Discussion

11029.	Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg):4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Answer» Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00 Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Discussion

11030.	Computethe following:(i) (ii) (iii) (v)
Answer» Compute the following: (i) (ii) (iii) (v)

11030.

Computethe following:(i) (ii) (iii) (v)

Answer»

Compute
the following:

(i) (ii)

(iii)

(v)

Discussion

11031.	Question 7A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
Answer» Question 7 A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Discussion

11032.	Question 4 Construct the following and give justification : An equilateral triangle, if its altitude is 3.2cm.
Answer» Question 4 Construct the following and give justification : An equilateral triangle, if its altitude is 3.2cm.

Discussion

11033.	Using factor theorem, show that g(x) is a factor of p(x), when p(x)=3x3+x2−20x+12,g(x)=3x−2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2$

Discussion

11034.	If the radius and height of a cylinder are increased by 10% and decreased by 5% respectively, then what will be the percentage change in volume? [4 MARKS]
Answer» If the radius and height of a cylinder are increased by $10 %$ and decreased by $5 %$ respectively, then what will be the percentage change in volume? [4 MARKS]

Discussion

11035.	factorise 5-15(x+y)2
Answer» factorise 5-15(x+y)²

11035.

factorise 5-15(x+y)2

Answer»

factorise

5-15(x+y)²

Discussion

11036.	Question 11 (iii)In ΔABC and ΔDEF ,AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that AD \|\| CF and AD = CF.
Answer» Question 11 (iii) In $Δ A B C a n d Δ D E F$ ,AB=DE, AB \|\| DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that AD \|\| CF and AD = CF.

Discussion

11037.	f(x)=√x²-25+1/√84-x²
Answer» f(x)=√x²-25+1/√84-x²

Discussion

11038.	Prove that ar(ΔAPB)=ar(ΔACQ)
Answer» Prove that $a r (Δ A P B) = a r (Δ A C Q)$

Discussion

11039.	The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___.
Answer» The table below shows the sale of shirts of various sizes in a week. $\begin{matrix} S h i r t s i z e & 38 & 39 & 40 & 41 & 42 N u m b e r s o l d & 60 & 73 & 89 & 90 & 23 \end{matrix}$ The size which is demanded the most is ___.

11039.

The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___.

Answer»

The table below shows the sale of shirts of various sizes in a week.

$\begin{matrix} S h i r t s i z e & 38 & 39 & 40 & 41 & 42 N u m b e r s o l d & 60 & 73 & 89 & 90 & 23 \end{matrix}$

The size which is demanded the most is

___.

Discussion

11040.	I have 14 apples with me, out of which 27 of them were spoilt. From the remaining good ones, I sold a few of them and was left with 15 of the fresh apples. I gave half of the remaining apples to my friend. Find the total number of apples which are left with me.
Answer» I have 14 apples with me, out of which $\frac{2}{7}$ of them were spoilt. From the remaining good ones, I sold a few of them and was left with $\frac{1}{5}$ of the fresh apples. I gave half of the remaining apples to my friend. Find the total number of apples which are left with me.

Discussion

11041.	Using a protractor, draw an angle of measure 72°. With this angle as given, draw angles of measure 36° and 54°.
Answer» Using a protractor, draw an angle of measure 72°. With this angle as given, draw angles of measure 36° and 54°.

Discussion

11042.

Fill in the blanks KE (J) m (kg) v (m/s) ___ 28 15 2000 10 _ 9520 ___ 4

Answer»

Fill in the blanks

KE (J)	m (kg)	v (m/s)
_____	28	15
2000	10	_____
9520	_____	4

Discussion

11043.	In a parallelogram ABCD diagonals AC and BD intersects at O and AC =12.8 cm and BD=7.6 cm, then the measure of OC and OD respectively equal to
Answer» In a parallelogram ABCD diagonals AC and BD intersects at O and AC =12.8 cm and BD=7.6 cm, then the measure of OC and OD respectively equal to

Discussion

11044.	Solve : 3power x power 2 :3power x=9:1
Answer» Solve : 3power x power 2 :3power x=9:1

Discussion

11045.	Question: 4Which of the following is an equation ?(a) x + 1(b) x - 1(c) x - 1 = 0(d) x + 1 > 0
Answer» Question: 4 Which of the following is an equation ? (a) x + 1 (b) x - 1 (c) x - 1 = 0 (d) x + 1 > 0

11045.

Question: 4Which of the following is an equation ?(a) x + 1(b) x - 1(c) x - 1 = 0(d) x + 1 > 0

Answer»

Question: 4

Which of the following is an equation ?

(a) x + 1

(b) x - 1

(c) x - 1 = 0

(d) x + 1 > 0

Discussion

11046.	Which of the following numbers is a rational number between 14 and 35 ?
Answer» Which of the following numbers is a rational number between $\frac{1}{4}$ and $\frac{3}{5}$ ?

Discussion

11047.	A solid cuboid of iron with dimensions 53cm\ast40cm\ast15cm is melted and recasted into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the lenght of pipe?
Answer» A solid cuboid of iron with dimensions 53cm\ast40cm\ast15cm is melted and recasted into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the lenght of pipe?

Discussion

11048.	A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.
Answer» A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

Discussion

11049.	A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.
Answer» A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.

Discussion

11050.	ntABCD is a rhombus in which angle A = 60 degree. Find the ratio AC : BD.n
Answer» ntABCD is a rhombus in which angle A = 60 degree. Find the ratio AC : BD.n

Discussion

Explore topic-wise InterviewSolutions in .

23. The length of chord of the parabola y=4X which passes through the vertex and makes 30^° angle with x-axis

If A=⎡⎢⎣02bcab−ca−bc⎤⎥⎦ is orthogonal, then |abc| is equal to

State whether 10.064 is rational or irrational no. Represent it in p/q form.

Show how √5can be represented on the number line

Mirror image of point (1, 2) with respect to the y-axis is ______.

Draw an angle of 40°.Copy its supplementary angle.

Jasmine has a bag of sweets. It has 3 yellow sweets, 5 green sweets, 7 red sweets, 4 purple sweets and 1 black sweet. If Jasmine takes out one sweet whose probability is 14, then what colour sweet has she taken out ?

For the equations 2x+3y=13 and 5x−4y=−2 where x≠0 &amp; y≠0, the value of

Factorise1 – 27a3

Express 0.75 as a rational number.

.The sum of the first 2011 terms of a G.P. is 200. The sum of the first 4022 terms of the same series is 380.Find the sum of the first 6033 terms of the series

The diameter of a road roller is 60 cm and it is 140 cm long. It levelled an area of 79,200 cm2. How many turns did the road roller take to level the said area?

What did the Professor mean by "intelligent reading"?

For any three sets A,B &amp; C;A∪(B∪C)=

A solid cylinder is melted and cast into a cone of same radius.The heights of the cone and cylinder are in the ratio

int_(0)^(1) 1/sqrt(2-x-x^2)dx

Find the values of a and b if 5+2√37+4√3=a+b√3

What is the value of b if,(3,1) is a solution for the equation: 6x+by=25 ?

Question 2A diagonal of a rectangle is inclined to one side of the rectangle at 25∘. The acute angle between the diagonals is(a) 55∘(b) 50∘(c) 40∘(d) 25∘

Classify the following as linear, quadratic and cubic polynomials:(i)4x3+2x+6 (ii)x+5(iii)9x3 (iv)2x2+2x+7

If the angles of a triangle are 30°, 30° and 120°, then the triangle is ___.

What is the difference between else and elif construct of if statement?

Explain polynomial in one variable x of degree n

OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD

Find the area of the shaded region.

9. The numerator of a rational number is 17 more than its denominator. The numerator of its absolute is 7 more than its denominator. Find the rational number.

Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg):4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Computethe following:(i) (ii) (iii) (v)

Question 7A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Question 4 Construct the following and give justification : ​​​​​​​ An equilateral triangle, if its altitude is 3.2cm.

Using factor theorem, show that g(x) is a factor of p(x), when p(x)=3x3+x2−20x+12,g(x)=3x−2

If the radius and height of a cylinder are increased by 10% and decreased by 5% respectively, then what will be the percentage change in volume? [4 MARKS]

factorise 5-15(x+y)2

Question 11 (iii)In ΔABC and ΔDEF ,AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that AD || CF and AD = CF.

f(x)=√x²-25+1/√84-x²

Prove that ar(ΔAPB)=ar(ΔACQ)

The table below shows the sale of shirts of various sizes in a week. Shirt size3839404142Number sold6073899023 The size which is demanded the most is ___.

I have 14 apples with me, out of which 27 of them were spoilt. From the remaining good ones, I sold a few of them and was left with 15 of the fresh apples. I gave half of the remaining apples to my friend. Find the total number of apples which are left with me.

Using a protractor, draw an angle of measure 72°. With this angle as given, draw angles of measure 36° and 54°.

Fill in the blanks KE (J) m (kg) v (m/s) _____ 28 15 2000 10 _____ 9520 _____ 4

In a parallelogram ABCD diagonals AC and BD intersects at O and AC =12.8 cm and BD=7.6 cm, then the measure of OC and OD respectively equal to

Solve : 3power x power 2 :3power x=9:1

Question: 4Which of the following is an equation ?(a) x + 1(b) x - 1(c) x - 1 = 0(d) x + 1 &gt; 0

Which of the following numbers is a rational number between 14 and 35 ?

A solid cuboid of iron with dimensions 53cm\ast40cm\ast15cm is melted and recasted into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the lenght of pipe?

A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.

ntABCD is a rhombus in which angle A = 60 degree. Find the ratio AC : BD.n

For the equations 2x+3y=13 and 5x−4y=−2 where x≠0 & y≠0, the value of

For any three sets A,B & C;A∪(B∪C)=

Question 4 Construct the following and give justification : An equilateral triangle, if its altitude is 3.2cm.

Fill in the blanks KE (J) m (kg) v (m/s) ___ 28 15 2000 10 _ 9520 ___ 4

Question: 4Which of the following is an equation ?(a) x + 1(b) x - 1(c) x - 1 = 0(d) x + 1 > 0