24740 + Interview Questions in Mathematics Page 124 InterviewSolution

6151.	Find the LCM and HCF of 26, 91 and verify that LCM × HCF = product of the two numbers.
Answer» Find the LCM and HCF of 26, 91 and verify that LCM $\times$ HCF = product of the two numbers.

Discussion

6152.	A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows:87718367857769766585855470688073786885738178817775Find mean, median and mode (mg/dl) of the above data.
Answer» A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows: $\begin{matrix} 87 & 71 & 83 & 67 & 85 77 & 69 & 76 & 65 & 85 85 & 54 & 70 & 68 & 80 73 & 78 & 68 & 85 & 73 81 & 78 & 81 & 77 & 75 \end{matrix}$ Find mean, median and mode (mg/dl) of the above data.

Discussion

6153.	The vertices of a ΔABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB at D, such that AD/AB= 14 . Calculate the area of the ΔADC.
Answer» The vertices of a $Δ$ ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB at D, such that AD/AB= $\frac{1}{4}$ . Calculate the area of the $Δ$ ADC.

Discussion

6154.	Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.
Answer» Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

Discussion

6155.	Find the square of √5−2
Answer» Find the square of $\sqrt{5} - 2$

Discussion

6156.	In=∫eaxxndx, then In,(n∈N,n≥2) is:
Answer» $I_{n} = \int \frac{e^{a x}}{x^{n}} d x$ , then $I_{n}, (n \in N, n \geq 2)$ is:

Discussion

6157.	Question 4 For the pair of equations λx+3y+7=0 and 2x + 6y – 14 = 0. To have infinitely many solutions, the value of l should be 1. Is the statement true ? Give reasons
Answer» Question 4 For the pair of equations $λ$ x+3y+7=0 and 2x + 6y – 14 = 0. To have infinitely many solutions, the value of l should be 1. Is the statement true ? Give reasons

Discussion

6158.	10. DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas. Prove that the diagonal DF bisects GE.
Answer» 10. DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas. Prove that the diagonal DF bisects GE.

Discussion

6159.	Find the quotient when the polynomial 2x3+2x2+2 is divided by x−3 using synthetic division method.
Answer» Find the quotient when the polynomial $2 x^{3} + 2 x^{2} + 2$ is divided by $x - 3$ using synthetic division method.

Discussion

6160.	In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If ∠BOD=160∘, find the measure of ∠BPD , as shown in the given figure.
Answer» In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If $∠ B O D = 160^{\circ}$ , find the measure of $∠ B P D$ , as shown in the given figure.

Discussion

6161.	If a2 + b2 + c2 = 250 and ab + bc + ca = 3 find a + b + c.
Answer» If a² + b² + c² = 250 and ab + bc + ca = 3 find a + b + c.

Discussion

6162.	In the given figure, RS is the diameter of the circle. NM is parallel to RS and ∠MRS=29o. Calculate ∠NRM
Answer» In the given figure, RS is the diameter of the circle. NM is parallel to RS and $∠ M R S = 29^{o}$ . Calculate $∠ N R M$

6162.

In the given figure, RS is the diameter of the circle. NM is parallel to RS and ∠MRS=29o. Calculate ∠NRM

Answer»

In the given figure, RS is the diameter of the circle. NM is parallel to RS and $∠ M R S = 29^{o}$ . Calculate $∠ N R M$

Discussion

6163.	Question 5 Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC.
Answer» Question 5 Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC.

Discussion

6164.	In the given circle, identify the center, radii, diameter and chords.
Answer» In the given circle, identify the center, radii, diameter and chords.

6164.

In the given circle, identify the center, radii, diameter and chords.

Answer»

In the given circle, identify the center, radii, diameter and chords.

Discussion

6165.	Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:(i) f(x)=3x+1, x=-13(ii) f(x)=x2-1, x=1, -1(iii) g(x)=3x2-2, x=23, -23(iv) p(x)=x3-6x2+11x-6, x=1, 2,3(v) f(x)=5x-π, x=45(vi) f(x)=x2, x=0(vii) f(x)=lx+m, x=-m1(viii) f(x)=2x+1, x=12
Answer» Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases: (i) $f (x) = 3 x + 1, x = - \frac{1}{3}$ (ii) $f (x) = x^{2} - 1, x = 1, - 1$ (iii) $g (x) = 3 x^{2} - 2, x = \frac{2}{\sqrt{3}}, - \frac{2}{\sqrt{3}}$ (iv) $p (x) = x^{3} - 6 x^{2} + 11 x - 6, x = 1, 2, 3$ (v) $f (x) = 5 x - π, x = \frac{4}{5}$ (vi) $f (x) = x^{2}, x = 0$ (vii) $f (x) = l x + m, x = - \frac{m}{1}$ (viii) $f (x) = 2 x + 1, x = \frac{1}{2}$

Discussion

6166.	The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Assume π =
Answer» The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder. Assume π =

Discussion

6167.	Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100m2 of area is painted. How many cans of paint will she need to paint the room?
Answer» Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint $100 m^{2}$ of area is painted. How many cans of paint will she need to paint the room?

Discussion

6168.	Factorise: (81−16x2)
Answer» Factorise: $(81 - 16 x^{2})$

Discussion

6169.	If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm, DF = 5cm and ∠D = 75°. Are two triangles congruent?
Answer» If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm, DF = 5cm and ∠D = 75°. Are two triangles congruent?

Discussion

6170.	Give one example each of a binomial of degree 35 and of a monomial of degree 100.
Answer» Give one example each of a binomial of degree 35 and of a monomial of degree 100.

Discussion

6171.	How many heads will you get as the most probable outcome when 4 coins are tossed? What is the probability for this outcome? [3 MARKS]
Answer» How many heads will you get as the most probable outcome when 4 coins are tossed? What is the probability for this outcome? [3 MARKS]

Discussion

6172.	If x+√15=4, then find the value of x+1x.
Answer» If $x + \sqrt{15} = 4,$ then find the value of $x + \frac{1}{x}$ .

Discussion

6173.	Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is [Use π=227]
Answer» Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are $10 c m$ and $7 c m$ respectively. The area of aluminium sheet required to make the cone is [Use $π = \frac{22}{7}$ ]

Discussion

6174.	ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are
Answer» ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are

6174.

ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are

Answer»

ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are

Discussion

6175.	Which of the following lies in the fourth quadrant:1-(-4,3)2-(0,0)3-(3,-4)
Answer» Which of the following lies in the fourth quadrant: 1-(-4,3) 2-(0,0) 3-(3,-4)

Discussion

6176.	In the given figure ABCO is a parallelogram. AB, CD and OD are equal in length. If ∠ BAO=110∘, then find the measure of ∠ BCD.
Answer» $In the given figure ABCO is a parallelogram. AB, CD and OD are equal in length. If ∠ B A O = 110^{\circ}, then find the measure of ∠ B C D .$

Discussion

6177.	Ram appeared in his mid-term examination and his marks in different subjects were:-SubjectMarksScience75Maths85Hindi75English75Social Science65The mode of the above data is ___75
Answer» Ram appeared in his mid-term examination and his marks in different subjects were:- $\begin{matrix} Subject & Marks Science & 75 Maths & 85 Hindi & 75 English & 75 Social Science & 65 \end{matrix}$ The mode of the above data is ___ 75

6177.

Ram appeared in his mid-term examination and his marks in different subjects were:-SubjectMarksScience75Maths85Hindi75English75Social Science65The mode of the above data is ___75

Answer»

Ram appeared in his mid-term examination and his marks in different subjects were:-

$\begin{matrix} Subject & Marks Science & 75 Maths & 85 Hindi & 75 English & 75 Social Science & 65 \end{matrix}$

The mode of the above data is ___

75

Discussion

6178.	In the figure, if chords AB and CD of the circle intersect each other at right angles, then x+y=
Answer» In the figure, if chords AB and CD of the circle intersect each other at right angles, then $x + y =$

6178.

In the figure, if chords AB and CD of the circle intersect each other at right angles, then x+y=

Answer»

In the figure, if chords AB and CD of the circle intersect each other at right angles, then $x + y =$

Discussion

6179.	As you can see from the frequency distribution table below, digits 3 and 9 have the highest frequency. A frequency distribution is defined as
Answer» As you can see from the frequency distribution table below, digits 3 and 9 have the highest frequency. A frequency distribution is defined as

6179.

As you can see from the frequency distribution table below, digits 3 and 9 have the highest frequency. A frequency distribution is defined as

Answer»

As you can see from the frequency distribution table below, digits 3 and 9 have the highest frequency.

A frequency distribution is defined as

Discussion

6180.	A diagonal of a rectangle makes an angle of 25° with one side of the rectangle. The acute angle between the diagonals is
Answer» A diagonal of a rectangle makes an angle of $25 °$ with one side of the rectangle. The acute angle between the diagonals is

Discussion

6181.	Two parallel sides of a trapezium are of lengths 57 cm and 39 cm. The distance between the parallel sides is 28 cm. Find the area of the trapezium.
Answer» Two parallel sides of a trapezium are of lengths 57 cm and 39 cm. The distance between the parallel sides is 28 cm. Find the area of the trapezium.

Discussion

6182.	if one vertex of an equilateral triangle is 1 +i and centroid is at origin then find other two vertices of triangle.
Answer» if one vertex of an equilateral triangle is 1 +i and centroid is at origin then find other two vertices of triangle.

Discussion

6183.	A coin is tossed 500 times with the following frequencies of two outcomes:head = 245 timestail = 255 timesWhat is the probability of getting a head in the next throw?
Answer» A coin is tossed 500 times with the following frequencies of two outcomes: head = 245 times tail = 255 times What is the probability of getting a head in the next throw?

Discussion

6184.	Question 74In the following question, state whether the given statements are true (T) or false (F).50=5
Answer» Question 74 In the following question, state whether the given statements are true (T) or false (F). $5^{0} = 5$

6184.

Question 74In the following question, state whether the given statements are true (T) or false (F).50=5

Answer»

Question 74

In the following question, state whether the given statements are true (T) or false (F).

$5^{0} = 5$

Discussion

6185.	Prepare Bank Reconciliation Statement from the following:On 31st March, 2019, a merchant's Cash Book showed a credit bank balance of ₹ 10,500 but due to the following reasons the Pass Book showed a difference:(i) A cheque of ₹ 540 issued to Mohan has not been presented for payment.(ii) A post-dated cheque for ₹ 100 has been debited in the bank column of the Cash Book but under no circumstances was it possible to present it.(iii) Four cheque of ₹ 1,200 sent to the bank have not been collected so far. A cheque of ₹ 400 deposited in the bank has been dishonoured.(iv) As per instructions, the bank paid ₹ 50 as Fire Insurance premium but the entry has not been made in the Cash Book.(v) There was a debit in the Pass Book of ₹ 15 in respect of bank charges and a credit of ₹ 25 for interest on Current Account but no record exists in the Cash Book.(vi) Cheque of ₹ 5,000 dated 15th April, 2019 issued to M & Co. was dishonoured being post dated. It was also not recorded in the books of account yet.
Answer» Prepare Bank Reconciliation Statement from the following: On 31st March, 2019, a merchant's Cash Book showed a credit bank balance of ₹ 10,500 but due to the following reasons the Pass Book showed a difference: (i) A cheque of ₹ 540 issued to Mohan has not been presented for payment. (ii) A post-dated cheque for ₹ 100 has been debited in the bank column of the Cash Book but under no circumstances was it possible to present it. (iii) Four cheque of ₹ 1,200 sent to the bank have not been collected so far. A cheque of ₹ 400 deposited in the bank has been dishonoured. (iv) As per instructions, the bank paid ₹ 50 as Fire Insurance premium but the entry has not been made in the Cash Book. (v) There was a debit in the Pass Book of ₹ 15 in respect of bank charges and a credit of ₹ 25 for interest on Current Account but no record exists in the Cash Book. (vi) Cheque of ₹ 5,000 dated 15th April, 2019 issued to M & Co. was dishonoured being post dated. It was also not recorded in the books of account yet.

Discussion

6186.	In each of the figures below, find the area of the shaded part
Answer» In each of the figures below, find the area of the shaded part

6186.

In each of the figures below, find the area of the shaded part

Answer»

In each of the figures below, find the area of the shaded part

Discussion

6187.	Who introduced the word rational number?
Answer» Who introduced the word rational number?

Discussion

6188.	ABC is a right angled triangle in which ∠A = 90° and AB = AC, Show that ∠B = ∠C.
Answer» ABC is a right angled triangle in which ∠A = 90° and AB = AC, Show that ∠B = ∠C.

Discussion

6189.	If A={1,2} and B={3,4}, then A∪B = ___.
Answer» If $A = {1, 2}$ and $B = {3, 4},$ then $A \cup B$ = ___.

Discussion

6190.	Question 18 If ABC is a right angled triangle such that AB = AC and bisector of angle C intersects the side AB at D, then prove that AC + AD = BC.
Answer» Question 18 If ABC is a right angled triangle such that AB = AC and bisector of angle C intersects the side AB at D, then prove that AC + AD = BC.

Discussion

6191.	If 13x - 2y + 34 = 19 - 2y is represented in the form of ax + by + c = 0, then what is the value of b?
Answer» If 13x - 2y + 34 = 19 - 2y is represented in the form of ax + by + c = 0, then what is the value of b?

Discussion

6192.	65×65 is equal to(a) 365(b) 6×05(c) 65(d) 125
Answer» $\sqrt[5]{6} \times \sqrt[5]{6}$ is equal to (a) $\sqrt[5]{36}$ (b) $\sqrt[5]{6 \times 0}$ (c) $\sqrt[5]{6}$ (d) $\sqrt[5]{12}$

Discussion

6193.	Derivation of formula of total surface area of cube
Answer» Derivation of formula of total surface area of cube

Discussion

6194.	In a ΔABC, if ∠B=∠C=45∘, which is the longest side?
Answer» In a $Δ A B C, i f ∠ B = ∠ C = 45^{\circ},$ which is the longest side?

Discussion

6195.	In the adjoining fig. □ABCD is a trapezium AB \|\| CD and its area is 33 cm2 . From the information given in the figure find the lengths of all sides of the □ABCD. Fill in the empty boxes to get the solution.
Answer» In the adjoining fig. $□$ ABCD is a trapezium AB \|\| CD and its area is 33 cm² . From the information given in the figure find the lengths of all sides of the $□$ ABCD. Fill in the empty boxes to get the solution.

Discussion

6196.	Find the cube of 2a+12a ( a≠0) .
Answer» Find the cube of $2 a + \frac{1}{2 a}$ ( $a \neq$ 0) .

Discussion

6197.	Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m. (Take 3=1.73.)
Answer» Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m. (Take $\sqrt{3} = 1.73$ .)

Discussion

6198.	If a row can fit 6 balls, arrange 13 balls in a box.
Answer» If a row can fit 6 balls, arrange 13 balls in a box.

Discussion

6199.	Identify the Venn diagram for B'.
Answer» Identify the Venn diagram for B'.

Discussion

6200.	In the figure, AOB is a straight line. If ∠AOC+∠BOD=850, then∠COD
Answer» In the figure, AOB is a straight line. If $∠ A O C + ∠ B O D = 85^{0}$ , then $∠ C O D$

6200.

In the figure, AOB is a straight line. If ∠AOC+∠BOD=850, then∠COD

Answer»

In the figure, AOB is a straight line. If $∠ A O C + ∠ B O D = 85^{0}$ , then $∠ C O D$

Discussion

Explore topic-wise InterviewSolutions in .

Find the LCM and HCF of 26, 91 and verify that LCM × HCF = product of the two numbers.

A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows:87718367857769766585855470688073786885738178817775Find mean, median and mode (mg/dl) of the above data.

The vertices of a ΔABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB at D, such that AD/AB= 14 . Calculate the area of the ΔADC.

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

Find the square of √5−2

In=∫eaxxndx, then In,(n∈N,n≥2) is:

Question 4 For the pair of equations λx+3y+7=0 and 2x + 6y – 14 = 0. To have infinitely many solutions, the value of l should be 1. Is the statement true ? Give reasons

10. DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas. Prove that the diagonal DF bisects GE.

Find the quotient when the polynomial 2x3+2x2+2 is divided by x−3 using synthetic division method.

In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If ∠BOD=160∘, find the measure of ∠BPD , as shown in the given figure.

If a2 + b2 + c2 = 250 and ab + bc + ca = 3 find a + b + c.

In the given figure, RS is the diameter of the circle. NM is parallel to RS and ∠MRS=29o. Calculate ∠NRM

Question 5 Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC.

In the given circle, identify the center, radii, diameter and chords.

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:(i) f(x)=3x+1, x=-13(ii) f(x)=x2-1, x=1, -1(iii) g(x)=3x2-2, x=23, -23(iv) p(x)=x3-6x2+11x-6, x=1, 2,3(v) f(x)=5x-π, x=45(vi) f(x)=x2, x=0(vii) f(x)=lx+m, x=-m1(viii) f(x)=2x+1, x=12

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Assume π =

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100m2 of area is painted. How many cans of paint will she need to paint the room?

Factorise: (81−16x2)

If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm, DF = 5cm and ∠D = 75°. Are two triangles congruent?

Give one example each of a binomial of degree 35 and of a monomial of degree 100.

How many heads will you get as the most probable outcome when 4 coins are tossed? What is the probability for this outcome? [3 MARKS]

If x+√15=4, then find the value of x+1x.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is [Use π=227]

ABC is an isosceles triangle in which AB = AC. If D and E are the mid points of AB and AC respectively, then the points D, B, C and E are

Which of the following lies in the fourth quadrant:1-(-4,3)2-(0,0)3-(3,-4)

In the given figure ABCO is a parallelogram. AB, CD and OD are equal in length. If ∠ BAO=110∘, then find the measure of ∠ BCD.

Ram appeared in his mid-term examination and his marks in different subjects were:-SubjectMarksScience75Maths85Hindi75English75Social Science65The mode of the above data is ___75

In the figure, if chords AB and CD of the circle intersect each other at right angles, then x+y=

As you can see from the frequency distribution table below, digits 3 and 9 have the highest frequency. A frequency distribution is defined as

A diagonal of a rectangle makes an angle of 25° with one side of the rectangle. The acute angle between the diagonals is

Two parallel sides of a trapezium are of lengths 57 cm and 39 cm. The distance between the parallel sides is 28 cm. Find the area of the trapezium.

if one vertex of an equilateral triangle is 1 +i and centroid is at origin then find other two vertices of triangle.

A coin is tossed 500 times with the following frequencies of two outcomes:head = 245 timestail = 255 timesWhat is the probability of getting a head in the next throw?

Question 74In the following question, state whether the given statements are true (T) or false (F).50=5

In each of the figures below, find the area of the shaded part

Who introduced the word rational number?

ABC is a right angled triangle in which ∠A = 90° and AB = AC, Show that ∠B = ∠C.

If A={1,2} and B={3,4}, then A∪B = ___.

Question 18 If ABC is a right angled triangle such that AB = AC and bisector of angle C intersects the side AB at D, then prove that AC + AD = BC.

If 13x - 2y + 34 = 19 - 2y is represented in the form of ax + by + c = 0, then what is the value of b?

65×65 is equal to(a) 365(b) 6×05(c) 65(d) 125

Derivation of formula of total surface area of cube

In a ΔABC, if ∠B=∠C=45∘, which is the longest side?

In the adjoining fig. □ABCD is a trapezium AB || CD and its area is 33 cm2 . From the information given in the figure find the lengths of all sides of the □ABCD. Fill in the empty boxes to get the solution.

Find the cube of 2a+12a ( a≠0) .

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m. (Take 3=1.73.)

If a row can fit 6 balls, arrange 13 balls in a box.

Identify the Venn diagram for B'.

In the figure, AOB is a straight line. If ∠AOC+∠BOD=850, then∠COD