32581 + Interview Questions in Mathematics Page 88 InterviewSolution

4351.	The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?
Answer» The figure given below shows a relation from $P$ to $Q .$ Find the relation, domain and range from the arrow diagram given?

4351.

The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?

Answer»

The figure given below shows a relation from $P$ to $Q .$ Find the relation, domain and range from the arrow diagram given?

Discussion

4352.	If 132300=22×33×52×ab, then which of the following is true ?
Answer» If $132300 = 2^{2} \times 3^{3} \times 5^{2} \times a^{b},$ then which of the following is true ?

Discussion

4353.	Represent the given set in Roster form. A = {x: x is a prime number, 52 < x < 112}
Answer» Represent the given set in Roster form. A = {x: x is a prime number, $\frac{5}{2}$ < x < $\frac{11}{2}$ }

4353.

Represent the given set in Roster form. A = {x: x is a prime number, 52 < x < 112}

Answer»

Represent the given set in Roster form.

A = {x: x is a prime number, $\frac{5}{2}$ < x < $\frac{11}{2}$ }

Discussion

4354.	A cuboidal water tank measuring 80 cm × 60 cm × 60 cm is filled from a pipe of cross sectional area 1.5 cm2. If speed of water is 3.2 m/s, then how long does it take to fill the tank?
Answer» A cuboidal water tank measuring 80 cm × 60 cm × 60 cm is filled from a pipe of cross sectional area 1.5 $c m^{2}$ . If speed of water is 3.2 m/s, then how long does it take to fill the tank?

Discussion

4355.	In the figure, C is the centre of the circle and AB is its diameter, Δ PDC is an isosceles triangle with PC = PD, Then AB2=___
Answer» In the figure, C is the centre of the circle and AB is its diameter, $Δ$ PDC is an isosceles triangle with PC = PD, Then $A B^{2}$ =___

4355.

In the figure, C is the centre of the circle and AB is its diameter, Δ PDC is an isosceles triangle with PC = PD, Then AB2=___

Answer»

In the figure, C is the centre of the circle and AB is its diameter, $Δ$ PDC is an isosceles triangle with PC = PD, Then $A B^{2}$ =___

Discussion

4356.	Evaluate the expression: 78−74+12The decimal form of the number is
Answer» Evaluate the expression: $\frac{7}{8} - \frac{7}{4} + \frac{1}{2}$ The decimal form of the number is

Discussion

4357.	A die is thrown once. The probability of getting a prime number is (a) 23 (b) 13 (c) 12(d) 16
Answer» A die is thrown once. The probability of getting a prime number is (a) $\frac{2}{3}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{1}{6}$

Discussion

4358.	What is the radius (in cm) of the tyre in a car, if it covers 0.396 km in 300 rotations? (Use π = 227)
Answer» What is the radius (in cm) of the tyre in a car, if it covers 0.396 km in 300 rotations? (Use π = $\frac{22}{7}$ )

Discussion

4359.	18. Verify that the numbers given alongside alongside of the polynomial are their zeroes. also verify the relationship between the zeros and the coefficient.x4+2x3-7X*2-8x+12; -3, -2, 1, 2
Answer» 18. Verify that the numbers given alongside alongside of the polynomial are their zeroes. also verify the relationship between the zeros and the coefficient.x4+2x3-7X*2-8x+12; -3, -2, 1, 2

Discussion

4360.	ABCD is a square with P and Q are the midpoints of BC and CD respectively. A point is selected at random in the square. Calculate the probability that it lies inside the triangle PCQ.
Answer» ABCD is a square with P and Q are the midpoints of BC and CD respectively. A point is selected at random in the square. Calculate the probability that it lies inside the triangle PCQ.

Discussion

4361.	A man wishes to swim across the river 0.5 km wide. If he can swim at the rate of 2 km/h in still water and the river flows at the rate of 1 km/h . The angle made by the direction ( w.r.t. to the flowbof the river) along which he should swim so as to reach a point exactly opposite hospital starting point, should be : 1) 60°2) 120°3) 145°4) 90°
Answer» A man wishes to swim across the river 0.5 km wide. If he can swim at the rate of 2 km/h in still water and the river flows at the rate of 1 km/h . The angle made by the direction ( w.r.t. to the flowbof the river) along which he should swim so as to reach a point exactly opposite hospital starting point, should be : 1) 60° 2) 120° 3) 145° 4) 90°

Discussion

4362.	Solve the following equation by factorisation: √3 x 2+10x+7√3=0
Answer» Solve the following equation by factorisation: √3 x ²+10x+7√3=0

4362.

Solve the following equation by factorisation: √3 x 2+10x+7√3=0

Answer»

Solve the following equation by factorisation:

√3 x ²+10x+7√3=0

Discussion

4363.	Question 7 Express the following in the form pq, where p and q are integers and q≠0 (i) 0.2 (ii) 0.888… (iii) 5.¯2 (iv) 0¯¯¯¯¯¯¯¯¯¯.001 (v)0.2555… (vi)0.1¯¯¯¯¯¯34 (vii) 0.00323232... (viii) 0.404040…
Answer» Question 7 $Express the following in the form$ $\frac{p}{q}$ , $where p and q are integers and q \neq 0$ (i) 0.2 (ii) 0.888… (iii) $5. ¯ 2$ (iv) $0 ¯ ¯¯¯¯¯¯¯¯ ¯ .001$ (v)0.2555… (vi) $0.1 ¯ ¯¯¯¯ ¯ 34$ (vii) 0.00323232... (viii) 0.404040…

Discussion

4364.	Express 0.¯4 as a rational number in simplest form.
Answer» Express $0. ¯ 4$ as a rational number in simplest form.

Discussion

4365.	If the coordinates of points A and B are (−2, −2) and (2, −4) respectively, find the coordinates of the point Psuch that AP=37AB, where P lies on the line segment AB. [CBSE 2015]
Answer» If the coordinates of points A and B are (−2, −2) and (2, −4) respectively, find the coordinates of the point P such that $A P = \frac{3}{7} A B$ , where P lies on the line segment AB. [CBSE 2015]

Discussion

4366.	Write the sequence with nth term:(i) an = 3 + 4n(ii) an = 5 + 2n(iii) an = 6 − n(iv) an = 9 − 5nShow that all of the above sequences form A.P.
Answer» Write the sequence with nth term: (i) a_n = 3 + 4n (ii) a_n = 5 + 2n (iii) a_n = 6 − n (iv) a_n = 9 − 5n Show that all of the above sequences form A.P.

Discussion

4367.	If alpha and beta are the zeroes of x^2-5x+k.if alpha-beta=1,find k
Answer» If alpha and beta are the zeroes of x^2-5x+k.if alpha-beta=1,find k

Discussion

4368.	A dividend of 12% was declared on ₹ 100 share selling at a certain price. If the rate of return is 8%. Then the market value of share is ₹ ___
Answer» A dividend of 12% was declared on ₹ 100 share selling at a certain price. If the rate of return is 8%. Then the market value of share is ₹ ___

Discussion

4369.	Two poles of heights 6 in and 11 in stand on a plane ground. If the distance between th,tir feet is 12 m, find the distance between their tops.
Answer» Two poles of heights 6 in and 11 in stand on a plane ground. If the distance between th,tir feet is 12 m, find the distance between their tops.

Discussion

4370.	Question 4 (i)Find the value(s) of p for the pair of equations 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.
Answer» Question 4 (i) Find the value(s) of p for the pair of equations 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.

Discussion

4371.	Very-Short-Answer QuestionsIf 1 is a root of the equation ay2+ay+3=0 and y2+y+b=0 then find the value of ab. [CBSE 2012]
Answer» Very-Short-Answer Questions If 1 is a root of the equation $a y^{2} + a y + 3 = 0$ and $y^{2} + y + b = 0$ then find the value of ab. [CBSE 2012]

Discussion

4372.	The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.
Answer» The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

Discussion

4373.	The volume of a cone is 3080 cm3 and height is 15 cm. Find the radius of the cone.
Answer» The volume of a cone is 3080 cm³ and height is 15 cm. Find the radius of the cone.

Discussion

4374.	The differential equation of all non-horizontal lines in a plane is __________________.
Answer» The differential equation of all non-horizontal lines in a plane is __________________.

Discussion

4375.	Evaluate (8a3−27b3)(64x3+y3), where (64x3+y3)≠0.
Answer» Evaluate $\frac{(8 a^{3} - 27 b^{3})}{(64 x^{3} + y^{3})}$ , where $(64 x^{3} + y^{3}) \neq 0$ .

Discussion

4376.	An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Answer» An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Discussion

4377.	In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) quadrant OACB(ii) shaded region.
Answer» In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.

Discussion

4378.	sec θ+tan θ−1tan θ−sec θ+1= ________
Answer» $\frac{s e c θ + t a n θ - 1}{t a n θ - s e c θ + 1} =$ ________

Discussion

4379.	Show that ( – 1) is a factor of 3 – 72 + 14 – 8. Hence factorise the above expression completely.
Answer» Show that ( – 1) is a factor of ³ – 7² + 14 – 8. Hence factorise the above expression completely.

Discussion

4380.	Find the median class of the following distribution:
Answer» Find the median class of the following distribution:

4380.

Find the median class of the following distribution:

Answer»

Find the median class of the following distribution:

Discussion

4381.	Wherever possible, write each of the following as a single matrix (i)[1234]+[−1−21−7] (ii)[234467]−[0236−10] (iii)[012467]+[3468]
Answer» Wherever possible, write each of the following as a single matrix $(i) [\begin{matrix} 1 & 2 3 & 4 \end{matrix}] + [\begin{matrix} - 1 & - 2 1 & - 7 \end{matrix}]$ $(i i) [\begin{matrix} 2 & 3 & 4 4 & 6 & 7 \end{matrix}] - [\begin{matrix} 0 & 2 & 3 6 & - 1 & 0 \end{matrix}]$ $(i i i) [\begin{matrix} 0 & 1 & 2 4 & 6 & 7 \end{matrix}] + [\begin{matrix} 3 & 4 6 & 8 \end{matrix}]$

Discussion

4382.	Two circles of radii 8 cm and 3 cm have their centers 13 cm apart. Find the length of a direct common tangent to the two circles. __
Answer» Two circles of radii 8 cm and 3 cm have their centers 13 cm apart. Find the length of a direct common tangent to the two circles. __

Discussion

4383.	26. Probability getting 1 in throw of a dice in eventh throw
Answer» 26. Probability getting 1 in throw of a dice in eventh throw

Discussion

4384.	Calculate the distance between A (7, 3) and B on the -axis whose abscissa is 11.
Answer» Calculate the distance between A (7, 3) and B on the -axis whose abscissa is 11.

Discussion

4385.	what is meant by q_o?
Answer» what is meant by q_o?

Discussion

4386.	Q. In a military code, SYSTEM is written as SYSMET, and NEARER is written as AENRER. Then using the same code, how will FRACTION get coded?
Answer» Q. In a military code, SYSTEM is written as SYSMET, and NEARER is written as AENRER. Then using the same code, how will FRACTION get coded?

Discussion

4387.	If √3 is an irrational number, then which of the following is an irrational number?
Answer» If $\sqrt{3}$ is an irrational number, then which of the following is an irrational number?

Discussion

4388.	Solve for x and y:12x+13y=213x+12y=136
Answer» Solve for x and y: $\frac{1}{2 x} + \frac{1}{3 y} = 2 \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}$

Discussion

4389.	Difference of 7th and 12th terms in an arithmetic sequence is 20, the common difference is
Answer» Difference of 7th and 12th terms in an arithmetic sequence is 20, the common difference is

Discussion

4390.	A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the(i) inside surface area of the dome,(ii) volume of the air inside the dome.
Answer» A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome.

4390.

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the(i) inside surface area of the dome,(ii) volume of the air inside the dome.

Answer»

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the

(i) inside surface area of the dome,

(ii) volume of the air inside the dome.

Discussion

4391.	IfA=[12−29], then -2A=_______________
Answer» If $A = [\begin{matrix} 1 & 2 - 2 & 9 \end{matrix}]$ , then -2A=_______________

Discussion

4392.	42. As observed from the top of the light house of height 'h m the angles of depression of two ships approaching it are α and β If one ship is coming from west and the other is coming from south. fnd the dstance the ships
Answer» 42. As observed from the top of the light house of height 'h m the angles of depression of two ships approaching it are α and β If one ship is coming from west and the other is coming from south. fnd the dstance the ships

Discussion

4393.	Solve each of the following systems of equations by the method of cross-multiplication :xa=ybax+by=a2+b2
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $\frac{x}{a} = \frac{y}{b} a x + b y = a^{2} + b^{2}$

Discussion

4394.	Question 1 (ii)Solve the following pair of linear equations by the elimination method and the substitution method:3x + 4y = 10 and 2x - 2y = 2
Answer» Question 1 (ii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x - 2y = 2

Discussion

4395.	Question 4Given 15 cot A = 8, find sin A and sec A.
Answer» Question 4 Given 15 cot A = 8, find sin A and sec A.

Discussion

4396.	9. In an AP the pth term is q and (p+q) th term is 0.Then the q th term is
Answer» 9. In an AP the pth term is q and (p+q) th term is 0.Then the q th term is

Discussion

4397.	Solve for x and y:x2-y9=6 x7+y3=5 −117 y=−1
Answer» Solve for x and y: $\frac{x}{2} - \frac{y}{9} = 6 \frac{x}{7} + \frac{y}{3} = 5$ −117 y=−1

Discussion

4398.	Prove that the points (3, −2), (4, 0), (6, −3) and (5, −5) are the vertices of a parallelogram.
Answer» Prove that the points (3, −2), (4, 0), (6, −3) and (5, −5) are the vertices of a parallelogram.

Discussion

4399.	If h is hcf of 4052 and 12576 .h=4052a+12576b.find h+a+b
Answer» If h is hcf of 4052 and 12576 .h=4052a+12576b.find h+a+b

Discussion

4400.	A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.[Use=227]
Answer» A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. $[U s e = \frac{22}{7}]$

Discussion

Explore topic-wise InterviewSolutions in .

The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?

If 132300=22×33×52×ab, then which of the following is true ?

Represent the given set in Roster form. A = {x: x is a prime number, 52 &lt; x &lt; 112}

A cuboidal water tank measuring 80 cm × 60 cm × 60 cm is filled from a pipe of cross sectional area 1.5 cm2. If speed of water is 3.2 m/s, then how long does it take to fill the tank?

In the figure, C is the centre of the circle and AB is its diameter, Δ PDC is an isosceles triangle with PC = PD, Then AB2=___

Evaluate the expression: 78−74+12The decimal form of the number is

A die is thrown once. The probability of getting a prime number is (a) 23 (b) 13 (c) 12(d) 16

What is the radius (in cm) of the tyre in a car, if it covers 0.396 km in 300 rotations? (Use π = 227)

18. Verify that the numbers given alongside alongside of the polynomial are their zeroes. also verify the relationship between the zeros and the coefficient.x*4+2x*3-7X*2-8x+12; -3, -2, 1, 2

ABCD is a square with P and Q are the midpoints of BC and CD respectively. A point is selected at random in the square. Calculate the probability that it lies inside the triangle PCQ.

Solve the following equation by factorisation: √3 x 2+10x+7√3=0

Question 7 Express the following in the form pq, where p and q are integers and q≠0 (i) 0.2 (ii) 0.888… (iii) 5.¯2 (iv) 0¯¯¯¯¯¯¯¯¯¯.001 (v)0.2555… (vi)0.1¯¯¯¯¯¯34 (vii) 0.00323232... (viii) 0.404040…

Express 0.¯4 as a rational number in simplest form.

If the coordinates of points A and B are (−2, −2) and (2, −4) respectively, find the coordinates of the point Psuch that AP=37AB, where P lies on the line segment AB. [CBSE 2015]

Write the sequence with nth term:(i) an = 3 + 4n(ii) an = 5 + 2n(iii) an = 6 − n(iv) an = 9 − 5nShow that all of the above sequences form A.P.

If alpha and beta are the zeroes of x^2-5x+k.if alpha-beta=1,find k

A dividend of 12% was declared on ₹ 100 share selling at a certain price. If the rate of return is 8%. Then the market value of share is ₹ ___

Two poles of heights 6 in and 11 in stand on a plane ground. If the distance between th,tir feet is 12 m, find the distance between their tops.

Question 4 (i)Find the value(s) of p for the pair of equations 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.

Very-Short-Answer QuestionsIf 1 is a root of the equation ay2+ay+3=0 and y2+y+b=0 then find the value of ab. [CBSE 2012]

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

The volume of a cone is 3080 cm3 and height is 15 cm. Find the radius of the cone.

The differential equation of all non-horizontal lines in a plane is __________________.

Evaluate (8a3−27b3)(64x3+y3), where (64x3+y3)≠0.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) quadrant OACB(ii) shaded region.

sec θ+tan θ−1tan θ−sec θ+1= ________

Show that ( – 1) is a factor of 3 – 72 + 14 – 8. Hence factorise the above expression completely.

Find the median class of the following distribution:

Wherever possible, write each of the following as a single matrix (i)[1234]+[−1−21−7] (ii)[234467]−[0236−10] (iii)[012467]+[3468]

Two circles of radii 8 cm and 3 cm have their centers 13 cm apart. Find the length of a direct common tangent to the two circles. __

26. Probability getting 1 in throw of a dice in eventh throw

Calculate the distance between A (7, 3) and B on the -axis whose abscissa is 11.

what is meant by q_o?

Q. In a military code, SYSTEM is written as SYSMET, and NEARER is written as AENRER. Then using the same code, how will FRACTION get coded?

If √3 is an irrational number, then which of the following is an irrational number?

Solve for x and y:12x+13y=213x+12y=136

Difference of 7th and 12th terms in an arithmetic sequence is 20, the common difference is

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the(i) inside surface area of the dome,(ii) volume of the air inside the dome.

IfA=[12−29], then -2A=_______________

42. As observed from the top of the light house of height 'h m the angles of depression of two ships approaching it are α and β If one ship is coming from west and the other is coming from south. fnd the dstance the ships

Solve each of the following systems of equations by the method of cross-multiplication :xa=ybax+by=a2+b2

Question 1 (ii)Solve the following pair of linear equations by the elimination method and the substitution method:3x + 4y = 10 and 2x - 2y = 2

Question 4Given 15 cot A = 8, find sin A and sec A.

9. In an AP the pth term is q and (p+q) th term is 0.Then the q th term is

Solve for x and y:x2-y9=6 x7+y3=5 −117 y=−1

Prove that the points (3, −2), (4, 0), (6, −3) and (5, −5) are the vertices of a parallelogram.

If h is hcf of 4052 and 12576 .h=4052*a+12576*b.find h+a+b

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.[Use=227]

Represent the given set in Roster form. A = {x: x is a prime number, 52 < x < 112}

18. Verify that the numbers given alongside alongside of the polynomial are their zeroes. also verify the relationship between the zeros and the coefficient.x4+2x3-7X*2-8x+12; -3, -2, 1, 2

If h is hcf of 4052 and 12576 .h=4052a+12576b.find h+a+b