32581 + Interview Questions in Mathematics Page 147 InterviewSolution

7301.	Choose the area enclosed between the secant and the tangent.
Answer» Choose the area enclosed between the secant and the tangent.

Discussion

7302.	Three typists working 8 hours a day type a document in 10 days. If only 2 typists are workinghow many hours a day should they work to finish the job in 12 days?
Answer» Three typists working 8 hours a day type a document in 10 days. If only 2 typists are workinghow many hours a day should they work to finish the job in 12 days?

Discussion

7303.	Question 8If the triangle ABC in the above question is revolved about the side 5cm, then find the volume of the solid so obtained.Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
Answer» Question 8 If the triangle ABC in the above question is revolved about the side 5cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Discussion

7304.	Prove that the zeros of the quadratic polynomial x^2 +ax +a, a is not equal to zero both can not be negative
Answer» Prove that the zeros of the quadratic polynomial x^2 +ax +a, a is not equal to zero both can not be negative

Discussion

7305.	Prove the following trignometric identities: (sec2θ−1)(cosec2θ−1)=1
Answer» Prove the following trignometric identities: $(s e c^{2} θ - 1) (c o s e c^{2} θ - 1) = 1$

7305.

Prove the following trignometric identities: (sec2θ−1)(cosec2θ−1)=1

Answer»

Prove the following trignometric identities:

$(s e c^{2} θ - 1) (c o s e c^{2} θ - 1) = 1$

Discussion

7306.	What number must be added to each of the numbers 10,18,22,38 to make them in proportion?
Answer» What number must be added to each of the numbers $10, 18, 22, 38$ to make them in proportion?

7306.

What number must be added to each of the numbers 10,18,22,38 to make them in proportion?

Answer»

What number must be added to each of the numbers $10, 18, 22, 38$ to make them in proportion?

Discussion

7307.	Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.
Answer» Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.

Discussion

7308.	23. In the given figure, P, Q and R are the mid-points of sides AB, AC and BC of AABC respectively If ADBC, then prove that PQRD is a cyclic quadrilateral. D R [(C)" ()" ()oz .(v)61 .suy]
Answer» 23. In the given figure, P, Q and R are the mid-points of sides AB, AC and BC of AABC respectively If ADBC, then prove that PQRD is a cyclic quadrilateral. D R [(C)" ()" ()oz .(v)61 .suy]

Discussion

7309.	The radius of the circle of largest area that can be cut out from a rectangle of dimensions 10 cm×5 cm is
Answer» The radius of the circle of largest area that can be cut out from a rectangle of dimensions $10 cm \times 5 cm$ is

Discussion

7310.	Anna deposited ₹200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount(in ₹) she gets on maturity. 8421
Answer» Anna deposited ₹200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount(in ₹) she gets on maturity. 8421

Discussion

7311.	Write the conjugates of the following binomial surds(1) (2) (3) (4) (5) (6)
Answer» Write the conjugates of the following binomial surds (1) (2) (3) (4) (5) (6)

7311.

Write the conjugates of the following binomial surds(1) (2) (3) (4) (5) (6)

Answer»

Write the conjugates of the following binomial surds

(1)

(2)

(3)

(4)

(5)

(6)

Discussion

7312.	Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.
Answer» Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

Discussion

7313.	Q Given three points a(x1,x2,x3),b(y1,y2,y3),c(z1,z2,z3).And their determinant is zero the are these points collinear?
Answer» Q Given three points a(x1,x2,x3),b(y1,y2,y3),c(z1,z2,z3).And their determinant is zero the are these points collinear?

Discussion

7314.	If the equation cosx + 3cos2kx =4 has exactly one solution then what about k ?
Answer» If the equation cosx + 3cos2kx =4 has exactly one solution then what about k ?

Discussion

7315.	A truck carrier measures 10 m × 4 m × 5 m. What will be the volume of sand that can be filled into the truck?
Answer» A truck carrier measures 10 m × 4 m × 5 m. What will be the volume of sand that can be filled into the truck?

Discussion

7316.	◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.
Answer» ◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.

Discussion

7317.	Construct a Δ ABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60∘ i. Construct the locus of all points inside Δ ABC, which are equidistant from B and C. ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC. iii. Mark the point Q in your construction, which would make Δ QBC equal in area to Δ ABC, and isosceles. iv. Measure and record the length of CQ.
Answer» Construct a $Δ$ ABC, in which BC = 6 cm, AB = 9 cm and $∠$ ABC = 60 $^{\circ}$ i. Construct the locus of all points inside $Δ$ ABC, which are equidistant from B and C. ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC. iii. Mark the point Q in your construction, which would make $Δ$ QBC equal in area to $Δ$ ABC, and isosceles. iv. Measure and record the length of CQ.

7317.

Construct a Δ ABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60∘ i. Construct the locus of all points inside Δ ABC, which are equidistant from B and C. ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC. iii. Mark the point Q in your construction, which would make Δ QBC equal in area to Δ ABC, and isosceles. iv. Measure and record the length of CQ.

Answer»

Construct a $Δ$ ABC, in which BC = 6 cm, AB = 9 cm and $∠$ ABC = 60 $^{\circ}$

i. Construct the locus of all points inside $Δ$ ABC, which are equidistant from B and C.

ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC.

iii. Mark the point Q in your construction, which would make $Δ$ QBC equal in area to $Δ$ ABC, and isosceles.

iv. Measure and record the length of CQ.

Discussion

7318.	Draw two direct common tangents to two circles of radii 5.5 cm and 3.5 cm and their centres are 9 cm apart
Answer» Draw two direct common tangents to two circles of radii 5.5 cm and 3.5 cm and their centres are 9 cm apart

Discussion

7319.	If H.C.F and L.C.M of two polynomials are y and 3y respectively, then product of those polynomials is ______.
Answer» If H.C.F and L.C.M of two polynomials are y and 3y respectively, then product of those polynomials is ______.

Discussion

7320.	A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.
Answer» A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.

Discussion

7321.	Match the reciprocals.
Answer» Match the reciprocals.

Discussion

7322.	A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .
Answer» A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .

Discussion

7323.	For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where0≤r b.
Answer» For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where $0 \leq r$ $b$ .

Discussion

7324.

On 1st April, 2018, X started a business with ₹ 40,000 as his capital. On 31st March, 2019, his position was as follows: (₹) Creditors 30,000 Bills Payable 10,000 Bank 10,000 Debtors 50,000 Stock 40,000 Plant 68,000 Furniture 12,000 During the year 2018–19, X drew ₹ 24,000. On 1st October, 2018, he introduced further capital amounting to ₹ 30,000. You are required to ascertain profit or loss made by him during the year 2018–19.Adjustments:(a) Plant is to be depreciated at 10%.(b) A provision of 5% is to be made against debtors.Also prepare the Statement of Affairs as on 31st March, 2019.

Answer» On 1st April, 2018, X started a business with ₹ 40,000 as his capital. On 31st March, 2019, his position was as follows:

		(₹)
Creditors		30,000
Bills Payable		10,000
Bank		10,000
Debtors		50,000
Stock		40,000
Plant		68,000
Furniture		12,000

During the year 2018–19, X drew ₹ 24,000. On 1st October, 2018, he introduced further capital amounting to ₹ 30,000. You are required to ascertain profit or loss made by him during the year 2018–19.

Adjustments:

(a) Plant is to be depreciated at 10%.

(b) A provision of 5% is to be made against debtors.

Also prepare the Statement of Affairs as on 31st March, 2019.

Discussion

7325.	Question 3 5x + 9 = 5 + 3x
Answer» Question 3 5x + 9 = 5 + 3x

Discussion

7326.	If 6x4+8x3-5x2+ax+b is completely divisible by polynomial 2x2-5 then find the value of a and b
Answer» If 6x⁴+8x³-5x²+ax+b is completely divisible by polynomial 2x²-5 then find the value of a and b

Discussion

7327.	The length of the diagonal of a cube that can beinscribed in a sphere of radius 7.5 cm is
Answer» The length of the diagonal of a cube that can be inscribed in a sphere of radius 7.5 cm is

Discussion

7328.	Solve the following quadratic equations by factorization:x2-42x+6=0
Answer» Solve the following quadratic equations by factorization: $x^{2} - 4 \sqrt{2} x + 6 = 0$

Discussion

7329.	Question 5 If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 90∘, then OP = a √2.
Answer» Question 5 If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is $90^{\circ}$ , then OP = a $\sqrt{2}$ .

Discussion

7330.	In complex numbers if the form is a+bi where a and b are real numbers and variables for I the value given is -1 ,I square =-1 is it not a constant?
Answer» In complex numbers if the form is a+bi where a and b are real numbers and variables for I the value given is -1 ,I square =-1 is it not a constant?

Discussion

7331.	Out of the four number given, first three are in GP and last three are in AP whose common difference is 6. If the first and last numbers are same,then first term will be
Answer» Out of the four number given, first three are in GP and last three are in AP whose common difference is 6. If the first and last numbers are same,then first term will be

Discussion

7332.	In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region
Answer» In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

Discussion

7333.	If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in cm2) is:
Answer» If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in $c m^{2}$ ) is:

Discussion

7334.	Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square.
Answer» Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square.

Discussion

7335.	a conical shaped container whose radius of base is r cm and height is h cm is full of water the sphere of radius R is completely immersed in the container in such a way that the surface of sphere touches the base of the cone and its surfaces the portion of the water which comes out of the cone is(1)R^2/r^2h(2)r^2/R^2h(3)4R^2/r^2h(4)4r^2/R^2h
Answer» a conical shaped container whose radius of base is r cm and height is h cm is full of water the sphere of radius R is completely immersed in the container in such a way that the surface of sphere touches the base of the cone and its surfaces the portion of the water which comes out of the cone is (1)R^2/r^2h (2)r^2/R^2h (3)4R^2/r^2h (4)4r^2/R^2h

Discussion

7336.	A company manufactures bicycles. Its cost and revenue functions are C(x) = 39,000 + 30x and R(x) = 43x, respectively, where x is the number of bicycles produced and sold in a week. How many bicycles must be sold by the company to realize some profit?
Answer» A company manufactures bicycles. Its cost and revenue functions are C(x) = 39,000 + 30x and R(x) = 43x, respectively, where x is the number of bicycles produced and sold in a week. How many bicycles must be sold by the company to realize some profit?

Discussion

7337.	A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.
Answer» A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.

Discussion

7338.	Question 14 After rationalizing the denominator of 73√3−2√2, we get the denominator as A) 13 B) 19 C) 5 D) 35
Answer» Question 14 After rationalizing the denominator of $\frac{7}{3 \sqrt{3} - 2 \sqrt{2}}$ , we get the denominator as A) 13 B) 19 C) 5 D) 35

Discussion

7339.	The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is 32. Find the number.
Answer» The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is 32. Find the number.

Discussion

7340.	If sin a-cos a is equal to-\sqrt2sin a then cos a + sin a is equal to
Answer» If sin a-cos a is equal to-\sqrt2sin a then cos a + sin a is equal to

Discussion

7341.	A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1,2 or 3)
Answer» A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1,2 or 3)

Discussion

7342.	Find the values of k for which the following equation has equal roots: [4 MARKS] (k−12)x2+2(k−12)x+2=0
Answer» Find the values of k for which the following equation has equal roots: [4 MARKS] $(k - 12) x^{2} + 2 (k - 12) x + 2 = 0$

Discussion

7343.	An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
Answer» An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

Discussion

7344.	O is the centre of the circle and line XY shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?
Answer» O is the centre of the circle and line XY shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?

Discussion

7345.	How many terms of the series 18 + 15 + 12 + ...... when added together will give 45 ?
Answer» How many terms of the series 18 + 15 + 12 + ...... when added together will give 45 ?

Discussion

7346.	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 find AB2 in terms of PD and DE.
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 find $A B^{2}$ in terms of PD and DE.

7346.

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 find AB2 in terms of PD and DE.

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 find $A B^{2}$ in terms of PD and DE.

Discussion

7347.	The roots of 2x2–6x+8=0 are ___________.
Answer» The roots of $2 x^{2} - 6 x + 8 = 0$ are ___________.

Discussion

7348.	The sum of two numbers a and b is 15, and the sum of their reciprocals 1aand1bis310 Find the numbers a and b
Answer» The sum of two numbers a and b is 15, and the sum of their reciprocals $\frac{1}{a} a n d \frac{1}{b} i s \frac{3}{10}$ Find the numbers a and b

Discussion

7349.	If the 2nd term of an A.P, is 13 and 5th term is 25, what is its 7th term?(a) 30(b) 33(c) 37(d) 38
Answer» If the 2^nd term of an A.P, is 13 and 5^th term is 25, what is its 7^th term? (a) 30 (b) 33 (c) 37 (d) 38

Discussion

7350.	Which of the following is an expansion of the identity (a–b)3?
Answer» Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

Discussion

Explore topic-wise InterviewSolutions in .

Choose the area enclosed between the secant and the tangent.

Three typists working 8 hours a day type a document in 10 days. If only 2 typists are workinghow many hours a day should they work to finish the job in 12 days?

Question 8If the triangle ABC in the above question is revolved about the side 5cm, then find the volume of the solid so obtained.Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Prove that the zeros of the quadratic polynomial x^2 +ax +a, a is not equal to zero both can not be negative

Prove the following trignometric identities: (sec2θ−1)(cosec2θ−1)=1

What number must be added to each of the numbers 10,18,22,38 to make them in proportion?

23. In the given figure, P, Q and R are the mid-points of sides AB, AC and BC of AABC respectively If ADBC, then prove that PQRD is a cyclic quadrilateral. D R [(C)" ()" ()oz .(v)61 .suy]

The radius of the circle of largest area that can be cut out from a rectangle of dimensions 10 cm×5 cm is

Anna deposited ₹200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount(in ₹) she gets on maturity. 8421

Write the conjugates of the following binomial surds(1) (2) (3) (4) (5) (6)

Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

Q Given three points a(x1,x2,x3),b(y1,y2,y3),c(z1,z2,z3).And their determinant is zero the are these points collinear?

If the equation cosx + 3cos2kx =4 has exactly one solution then what about k ?

A truck carrier measures 10 m × 4 m × 5 m. What will be the volume of sand that can be filled into the truck?

◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.

Draw two direct common tangents to two circles of radii 5.5 cm and 3.5 cm and their centres are 9 cm apart

If H.C.F and L.C.M of two polynomials are y and 3y respectively, then product of those polynomials is ______.

Match the reciprocals.

A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .

For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where0≤r b.

Question 3 5x + 9 = 5 + 3x

If 6x4+8x3-5x2+ax+b is completely divisible by polynomial 2x2-5 then find the value of a and b

The length of the diagonal of a cube that can beinscribed in a sphere of radius 7.5 cm is

Solve the following quadratic equations by factorization:x2-42x+6=0

Question 5 If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 90∘, then OP = a √2.

In complex numbers if the form is a+bi where a and b are real numbers and variables for I the value given is -1 ,I square =-1 is it not a constant?

Out of the four number given, first three are in GP and last three are in AP whose common difference is 6. If the first and last numbers are same,then first term will be

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in cm2) is:

Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square.

A company manufactures bicycles. Its cost and revenue functions are C(x) = 39,000 + 30x and R(x) = 43x, respectively, where x is the number of bicycles produced and sold in a week. How many bicycles must be sold by the company to realize some profit?

A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.

Question 14 After rationalizing the denominator of 73√3−2√2, we get the denominator as A) 13 B) 19 C) 5 D) 35

The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is 32. Find the number.

If sin a-cos a is equal to-\sqrt2sin a then cos a + sin a is equal to

A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0,1,2 or 3)

Find the values of k for which the following equation has equal roots: [4 MARKS] (k−12)x2+2(k−12)x+2=0

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

O is the centre of the circle and line XY shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?

How many terms of the series 18 + 15 + 12 + ...... when added together will give 45 ?

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 find AB2 in terms of PD and DE.

The roots of 2x2–6x+8=0 are ___________.

The sum of two numbers a and b is 15, and the sum of their reciprocals 1aand1bis310 Find the numbers a and b

If the 2nd term of an A.P, is 13 and 5th term is 25, what is its 7th term?(a) 30(b) 33(c) 37(d) 38

Which of the following is an expansion of the identity (a–b)3?