32581 + Interview Questions in Mathematics Page 209 InterviewSolution

10401.	The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it? [3 MARKS]
Answer» The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it? [3 MARKS]

Discussion

10402.	If tan θ=ab, find the value of cos θ+sin θ cos θ-sin θ.
Answer» If $\tan θ = \frac{a}{b}$ , find the value of $\frac{\cos θ + \sin θ}{\cos θ - \sin θ}$ .

Discussion

10403.	Which of the following sequence is not in arithmetic progression?
Answer» Which of the following sequence is not in arithmetic progression?

Discussion

10404.	Lines PQ and RS are parallel. It is given that ∠ RSP = 52∘, then find ∠ SPQ. __
Answer» Lines PQ and RS are parallel. It is given that $∠$ RSP = $52^{\circ}$ , then find $∠$ SPQ. __

10404.

Lines PQ and RS are parallel. It is given that ∠ RSP = 52∘, then find ∠ SPQ. __

Answer»

Lines PQ and RS are parallel. It is given that $∠$ RSP = $52^{\circ}$ , then find $∠$ SPQ.

__

Discussion

10405.	If (a, 0) is a point on the line represented by the equation 2x−3y=4,, find the value of a.
Answer» If (a, 0) is a point on the line represented by the equation $2 x - 3 y = 4,$ , find the value of a.

Discussion

10406.	If A3=0, then I+A+A2 equals
Answer» If $A^{3} = 0$ , then $I + A + A^{2}$ equals

Discussion

10407.	There are 7 students who like math, 9 students who like logical reasoning. If there are 15 students in the class and 1 student likes both math and logical reasoning, find the number of students who neither like math nor logical reasoning.
Answer» There are 7 students who like math, 9 students who like logical reasoning. If there are 15 students in the class and 1 student likes both math and logical reasoning, find the number of students who neither like math nor logical reasoning.

Discussion

10408.	Question 14 The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6: 05 am and 6: 40 am.
Answer» Question 14 The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6: 05 am and 6: 40 am.

Discussion

10409.	Which term of the G.P. : −10, 5√3, −56,.......... is −572 ?
Answer» Which term of the G.P. : $- 10, \frac{5}{\sqrt{3}}, - \frac{5}{6}, . . . . . . . . . . i s - \frac{5}{72} ?$

10409.

Which term of the G.P. : −10, 5√3, −56,.......... is −572 ?

Answer»

Which term of the G.P. :

$- 10, \frac{5}{\sqrt{3}}, - \frac{5}{6}, . . . . . . . . . . i s - \frac{5}{72} ?$

Discussion

10410.	Given that tan θ = 13, the value of cosec2θ-sec2θcosec2θ+sec2θ is(a) − 1(b) 1(c) 12(d) -12
Answer» Given that tan θ = $\frac{1}{\sqrt{3}}$ , the value of $\frac{\cos e c^{2} θ - s e c^{2} θ}{\cos e c^{2} θ + s e c^{2} θ}$ is (a) − 1 (b) 1 (c) $\frac{1}{2}$ (d) $- \frac{1}{2}$

Discussion

10411.	'A' takes 3 hours more than 'B' to walk 30km. But if A doubles his pace, he is ahead of B by 3/2 hours. Find their speed of walking.
Answer» 'A' takes 3 hours more than 'B' to walk 30km. But if A doubles his pace, he is ahead of B by 3/2 hours. Find their speed of walking.

Discussion

10412.	12.Dobernier triads
Answer» 12.Dobernier triads

Discussion

10413.	Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?
Answer» Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?

Discussion

10414.	If (2m+5),4,3m are in AP,then, find the value of m. 0.6
Answer» $If (2 m + 5), 4, 3 m are in AP,$ $then, find the value of m .$ 0.6

Discussion

10415.	A cup is in the shape of a hemisphere of radius 9cm. Find the volume of the cup.
Answer» A cup is in the shape of a hemisphere of radius 9cm. Find the volume of the cup.

Discussion

10416.	15.300 workers were engaged to finish a piece of work in a certain number of days. If 8 workers dropped on the second day, 8 more workers dropped on the third day and so on. It took 8 more days to finish the work now. The number of days in which the work was completed is 1. 35 2. 30 3. 25 4. 28
Answer» 15.300 workers were engaged to finish a piece of work in a certain number of days. If 8 workers dropped on the second day, 8 more workers dropped on the third day and so on. It took 8 more days to finish the work now. The number of days in which the work was completed is 1. 35 2. 30 3. 25 4. 28

Discussion

10417.	Collecting data on GDP from the government resources will be termed as a ___ data
Answer» Collecting data on GDP from the government resources will be termed as a ___ data

Discussion

10418.	A triangle ABC is drawn to circumscribe a circle of radius 2cm such that the segments BD and into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively . If area of the ∆ABC = 21 cm². Find the sides AB and AC.
Answer» A triangle ABC is drawn to circumscribe a circle of radius 2cm such that the segments BD and into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively . If area of the ∆ABC = 21 cm². Find the sides AB and AC.

Discussion

10419.	In a month, 60 machines working together can print 500 posters. A job of printing 4,200 posters was assigned. How many machines should be utilized to complete the work in a month?
Answer» In a month, 60 machines working together can print 500 posters. A job of printing 4,200 posters was assigned. How many machines should be utilized to complete the work in a month?

Discussion

10420.	If x= 3+22, then find the value of x-1x.
Answer» If $x = 3 + 2 \sqrt{2}$ , then find the value of $\sqrt{x} - \frac{1}{\sqrt{x}}$ .

Discussion

10421.	The sale price of a motorcycle including 7% sales tax is Rs 38520. Find the list price. If a discount of 10% on the list price were given, what would have been the sale price?
Answer» The sale price of a motorcycle including 7% sales tax is Rs 38520. Find the list price. If a discount of 10% on the list price were given, what would have been the sale price?

Discussion

10422.	From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is 52 and tangent of depression of the foot of the lower is 14. Find the height of the lower.
Answer» From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is $\frac{5}{2}$ and tangent of depression of the foot of the lower is $\frac{1}{4}$ . Find the height of the lower.

Discussion

10423.	In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm. QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
Answer» In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm. QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

Discussion

10424.	In what ratio does the point (2411,y) divide the line segment joining the points P (2, -2) and Q(3, 7)? Also find the value of y.
Answer» In what ratio does the point $(\frac{24}{11}, y)$ divide the line segment joining the points P (2, -2) and Q(3, 7)? Also find the value of y.

Discussion

10425.	The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30∘. The measure of the obtuse angle is a) 100∘ b) 150∘ c) 105∘ d) 120∘
Answer» The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is $30^{\circ}$ . The measure of the obtuse angle is a) $100^{\circ}$ b) $150^{\circ}$ c) $105^{\circ}$ d) $120^{\circ}$

Discussion

10426.	Prepare an Accounting Equation from the following:(i) Started business with cash ₹ 1,00,000.(ii) Purchased goods for cash ₹ 20,000 and on credit ₹ 30,000.(iii) Sold goods for cash costing ₹ 10,000 and on credit costing ₹ 15,000 both at a profit of 20%.
Answer» Prepare an Accounting Equation from the following: (i) Started business with cash ₹ 1,00,000. (ii) Purchased goods for cash ₹ 20,000 and on credit ₹ 30,000. (iii) Sold goods for cash costing ₹ 10,000 and on credit costing ₹ 15,000 both at a profit of 20%.

Discussion

10427.	If 5x = sec θ and 5x=tan θ, find the value of 5x2-1x2.
Answer» If 5x = sec θ and $\frac{5}{x} = \tan θ$ , find the value of $5 (x^{2} - \frac{1}{x^{2}})$ .

Discussion

10428.	Question 15 If the probability of an event is P, then the probability of its completmentry event will be (a) P - 1 (b) P (c) 1 - P (d) 1−1P
Answer» Question 15 If the probability of an event is P, then the probability of its completmentry event will be (a) P - 1 (b) P (c) 1 - P (d) $1 - \frac{1}{P}$

Discussion

10429.	If P(−5, −3), Q(−4, −6), R(2, −3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area. [CBSE 2015]
Answer» If P(−5, −3), Q(−4, −6), R(2, −3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area. [CBSE 2015]

Discussion

10430.	If α and β are the zeros of the quadratic polynomial f(x)=x2−p(x+1)-c, show that (α+1)(β+1)=1−c
Answer» If $α a n d β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - p (x + 1)$ -c, show that $(α + 1) (β + 1) = 1 - c$

Discussion

10431.	If the area of a sector of a circle is 518 of the area of the circle, then the sector angle is equal to(a) 60°(b) 90°(c) 100°(d) 120°
Answer» If the area of a sector of a circle is $\frac{5}{18}$ of the area of the circle, then the sector angle is equal to (a) 60° (b) 90° (c) 100° (d) 120°

Discussion

10432.	The quadratic equation x2-6x+a=0 and x2-cx+6=0 have one root in common. The other roots of the first and second equations are integers in 4:3, then find the common root.
Answer» The quadratic equation x²-6x+a=0 and x²-cx+6=0 have one root in common. The other roots of the first and second equations are integers in 4:3, then find the common root.

Discussion

10433.	A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant. [CBSE 2015]
Answer» A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant. [CBSE 2015]

Discussion

10434.	The sum of digits of every possible 8 digit number is noted. Which sum occurs most often?
Answer» The sum of digits of every possible 8 digit number is noted. Which sum occurs most often?

Discussion

10435.	In the given figure, S and T are points on the sides PQ and PR respectively of ∆PQR such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ∆PST and ∆PQR.
Answer» In the given figure, S and T are points on the sides PQ and PR respectively of ∆PQR such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ∆PST and ∆PQR.

Discussion

10436.	A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.
Answer» A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.

10436.

A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.

Answer»

A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.

Discussion

10437.	29. three vertices of a parallelogram are A (-2,2),B(6,2)and C(4,3).plot these points on a graph paper and hence use it to find the co ordinates of the fourth vertex D . Also ,find the coordinate of the mid point of the CD .
Answer» 29. three vertices of a parallelogram are A (-2,2),B(6,2)and C(4,3).plot these points on a graph paper and hence use it to find the co ordinates of the fourth vertex D . Also ,find the coordinate of the mid point of the CD .

Discussion

10438.	Question 27In a throw of a die, the probability of getting the number 7 is:(a) 12(b) 16(c) 1(d) 0
Answer» Question 27 In a throw of a die, the probability of getting the number 7 is: (a) $\frac{1}{2}$ (b) $\frac{1}{6}$ (c) 1 (d) 0

10438.

Question 27In a throw of a die, the probability of getting the number 7 is:(a) 12(b) 16(c) 1(d) 0

Answer»

Question 27

In a throw of a die, the probability of getting the number 7 is:

(a) $\frac{1}{2}$

(b) $\frac{1}{6}$

(c) 1

(d) 0

Discussion

10439.	A straight line AB is 8 cm long. Locate by construction the locus of a point which is:(i) Equidistant from A and B.(ii) Always 4 cm from the line AB.(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.
Answer» A straight line AB is 8 cm long. Locate by construction the locus of a point which is: (i) Equidistant from A and B. (ii) Always 4 cm from the line AB. (iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

10439.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:(i) Equidistant from A and B.(ii) Always 4 cm from the line AB.(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Answer»

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

(i) Equidistant from A and B.

(ii) Always 4 cm from the line AB.

(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Discussion

10440.	Question - 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) a=−1, d=12
Answer» Question - 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) $a = - 1, d = \frac{1}{2}$

Discussion

10441.	Using factor theorem, show that X-y, y-z, z-x are the factors of x(y^2 -x^2 )+ y^2(z^2-x^2) z(x^2-y^2)
Answer» Using factor theorem, show that X-y, y-z, z-x are the factors of x(y^2 -x^2 )+ y^2(z^2-x^2) z(x^2-y^2)

Discussion

10442.	In tossing of 3 coins, the probability of getting exactly 1 head is:
Answer» In tossing of 3 coins, the probability of getting exactly 1 head is:

Discussion

10443.	3.Find the ratio in which (7/3,-1) divides the line joining the points (1, 5) and (3,-4)
Answer» 3.Find the ratio in which (7/3,-1) divides the line joining the points (1, 5) and (3,-4)

Discussion

10444.	F(x)=x^2+4x+1. then prove that F(x)>/1 when x-4 (/--this stands for equal to)
Answer» F(x)=x^2+4x+1. then prove that F(x)>/1 when x-4 (/--this stands for equal to)

Discussion

10445.	How many points are there on the x-axis, at a distance 5 from the point (1, 3)? What are their coordinates? What about such points on the y-axis?
Answer» How many points are there on the x-axis, at a distance 5 from the point (1, 3)? What are their coordinates? What about such points on the y-axis?

Discussion

10446.	If the sqaure difference of the zeros of the quadratic polynomial F(x)= x^2 +px+45 is equal to 144, find the value of p.
Answer» If the sqaure difference of the zeros of the quadratic polynomial F(x)= x^2 +px+45 is equal to 144, find the value of p.

10446.

If the sqaure difference of the zeros of the quadratic polynomial F(x)= x^2 +px+45 is equal to 144, find the value of p.

Answer»

If the sqaure difference of the zeros of the quadratic polynomial

F(x)= x^2 +px+45 is equal to 144, find the value of p.

Discussion

10447.	A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.
Answer» A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.

Discussion

10448.	If the straight line lx+my=1 is the normal of the hyperbola y²=4ax then prove that al³+2alm²=m²
Answer» If the straight line lx+my=1 is the normal of the hyperbola y²=4ax then prove that al³+2alm²=m²

Discussion

10449.	In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.
Answer» In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

Discussion

10450.	Radius of a circle is 10 cm. Area of a sector of the sector is 100 cm2 . Find the area of its corresponding major sector. ( π = 3.14 )
Answer» Radius of a circle is 10 cm. Area of a sector of the sector is 100 cm² . Find the area of its corresponding major sector. ( $π$ = 3.14 )

Discussion

Explore topic-wise InterviewSolutions in .

The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it? [3 MARKS]

If tan θ=ab, find the value of cos θ+sin θ cos θ-sin θ.

Which of the following sequence is not in arithmetic progression?

Lines PQ and RS are parallel. It is given that ∠ RSP = 52∘, then find ∠ SPQ. __

If (a, 0) is a point on the line represented by the equation 2x−3y=4,, find the value of a.

If A3=0, then I+A+A2 equals

There are 7 students who like math, 9 students who like logical reasoning. If there are 15 students in the class and 1 student likes both math and logical reasoning, find the number of students who neither like math nor logical reasoning.

Question 14 The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6: 05 am and 6: 40 am.

Which term of the G.P. : −10, 5√3, −56,.......... is −572 ?

Given that tan θ = 13, the value of cosec2θ-sec2θcosec2θ+sec2θ is(a) − 1(b) 1(c) 12(d) -12

'A' takes 3 hours more than 'B' to walk 30km. But if A doubles his pace, he is ahead of B by 3/2 hours. Find their speed of walking.

12.Dobernier triads

Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?

If (2m+5),4,3m are in AP,then, find the value of m. 0.6

A cup is in the shape of a hemisphere of radius 9cm. Find the volume of the cup.

15.300 workers were engaged to finish a piece of work in a certain number of days. If 8 workers dropped on the second day, 8 more workers dropped on the third day and so on. It took 8 more days to finish the work now. The number of days in which the work was completed is 1. 35 2. 30 3. 25 4. 28

Collecting data on GDP from the government resources will be termed as a ___ data

A triangle ABC is drawn to circumscribe a circle of radius 2cm such that the segments BD and into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively . If area of the ∆ABC = 21 cm². Find the sides AB and AC.

In a month, 60 machines working together can print 500 posters. A job of printing 4,200 posters was assigned. How many machines should be utilized to complete the work in a month?

If x= 3+22, then find the value of x-1x.

The sale price of a motorcycle including 7% sales tax is Rs 38520. Find the list price. If a discount of 10% on the list price were given, what would have been the sale price?

From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is 52 and tangent of depression of the foot of the lower is 14. Find the height of the lower.

In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm. QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

In what ratio does the point (2411,y) divide the line segment joining the points P (2, -2) and Q(3, 7)? Also find the value of y.

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30∘. The measure of the obtuse angle is a) 100∘ b) 150∘ c) 105∘ d) 120∘

Prepare an Accounting Equation from the following:(i) Started business with cash ₹ 1,00,000.(ii) Purchased goods for cash ₹ 20,000 and on credit ₹ 30,000.(iii) Sold goods for cash costing ₹ 10,000 and on credit costing ₹ 15,000 both at a profit of 20%.

If 5x = sec θ and 5x=tan θ, find the value of 5x2-1x2.

Question 15 If the probability of an event is P, then the probability of its completmentry event will be (a) P - 1 (b) P (c) 1 - P (d) 1−1P

If P(−5, −3), Q(−4, −6), R(2, −3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area. [CBSE 2015]

If α and β are the zeros of the quadratic polynomial f(x)=x2−p(x+1)-c, show that (α+1)(β+1)=1−c

If the area of a sector of a circle is 518 of the area of the circle, then the sector angle is equal to(a) 60°(b) 90°(c) 100°(d) 120°

The quadratic equation x​​​​​​2​​​​​-6x+a=0 and x​​​​​​2​​​​​-cx+6=0 have one root in common. The other roots of the first and second equations are integers in 4:3, then find the common root.

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant. [CBSE 2015]

The sum of digits of every possible 8 digit number is noted. Which sum occurs most often?

In the given figure, S and T are points on the sides PQ and PR respectively of ∆PQR such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ∆PST and ∆PQR.

A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.

29. three vertices of a parallelogram are A (-2,2),B(6,2)and C(4,3).plot these points on a graph paper and hence use it to find the co ordinates of the fourth vertex D . Also ,find the coordinate of the mid point of the CD .

Question 27In a throw of a die, the probability of getting the number 7 is:(a) 12(b) 16(c) 1(d) 0

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:(i) Equidistant from A and B.(ii) Always 4 cm from the line AB.(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Question - 2 (iv) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (iv) a=−1, d=12

Using factor theorem, show that X-y, y-z, z-x are the factors of x(y^2 -x^2 )+ y^2(z^2-x^2) z(x^2-y^2)

In tossing of 3 coins, the probability of getting exactly 1 head is:

3.Find the ratio in which (7/3,-1) divides the line joining the points (1, 5) and (3,-4)

F(x)=x^2+4x+1. then prove that F(x)>/1 when x-4 (/--this stands for equal to)

How many points are there on the x-axis, at a distance 5 from the point (1, 3)? What are their coordinates? What about such points on the y-axis?

If the sqaure difference of the zeros of the quadratic polynomial F(x)= x^2 +px+45 is equal to 144, find the value of p.

A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.

If the straight line lx+my=1 is the normal of the hyperbola y²=4ax then prove that al³+2alm²=m²

In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

Radius of a circle is 10 cm. Area of a sector of the sector is 100 cm2 . Find the area of its corresponding major sector. ( π = 3.14 )

The quadratic equation x2-6x+a=0 and x2-cx+6=0 have one root in common. The other roots of the first and second equations are integers in 4:3, then find the common root.