24740 + Interview Questions in Mathematics Page 98 InterviewSolution

4851.	Question 5 (ii)Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:BP = BQ or B is equidistant from the arms of ∠A.
Answer» Question 5 (ii) Line l is the bisector of an angle $∠ A a n d B$ is any point on l. BP and BQ are perpendiculars from B to the arms of $∠ A$ (see the given figure). Show that: BP = BQ or B is equidistant from the arms of $∠ A .$

Discussion

4852.	It takes 8 days for 35 laborers to harvest coffee on a plantation. How long will 20 laborers take to harvest coffee on the same plantation.
Answer» It takes 8 days for 35 laborers to harvest coffee on a plantation. How long will 20 laborers take to harvest coffee on the same plantation.

Discussion

4853.	In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]
Answer» In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ [2 MARKS]

4853.

In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]

Answer»

In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ [2 MARKS]

Discussion

4854.	if m is a rational number and root n is irrational number then prove that (m + root n) is irrational
Answer» if m is a rational number and root n is irrational number then prove that (m + root n) is irrational

Discussion

4855.	A diagonal of a rectangle is inclined to one side of the rectangle at 35°. The Acute angle between the diagonal is
Answer» A diagonal of a rectangle is inclined to one side of the rectangle at 35°. The Acute angle between the diagonal is

Discussion

4856.	Prove the following trigonometric identities.1-cos A1+cos A=cot A-cosec A2
Answer» Prove the following trigonometric identities. $\frac{1 - \cos A}{1 + \cos A} = {(\cot A - cosec A)}^{2}$

Discussion

4857.	Two parallel chords, 10 cm apart, of lengths 8 cm and 12 cm, respectively are there in a circle. Find the distance of the shorter chord from the centre.
Answer» Two parallel chords, 10 cm apart, of lengths 8 cm and 12 cm, respectively are there in a circle. Find the distance of the shorter chord from the centre.

Discussion

4858.	From the adjoining figure, if ∠2 = 55∘ and ∠5 = 60∘, then the lines m and n are
Answer» From the adjoining figure, if $∠$ 2 = 55 $^{\circ}$ and $∠$ 5 = 60 $^{\circ}$ , then the lines m and n are

4858.

From the adjoining figure, if ∠2 = 55∘ and ∠5 = 60∘, then the lines m and n are

Answer»

From the adjoining figure, if $∠$ 2 = 55 $^{\circ}$ and $∠$ 5 = 60 $^{\circ}$ , then the lines m and n are

Discussion

4859.	How to write a congruence statement easily?
Answer» How to write a congruence statement easily?

Discussion

4860.	If a triangle, with one of its side 12 cm, is reduced by a scale factor of 13, then find the length of the corresponding side of the new triangle.
Answer» If a triangle, with one of its side 12 cm, is reduced by a scale factor of $\frac{1}{3}$ , then find the length of the corresponding side of the new triangle.

Discussion

4861.	Express each of the following in exponential form : (i) log80.125=−1 (ii) log100.01=−2 (iii) logaA=x (iv) log101=0
Answer» Express each of the following in exponential form : (i) $l o g_{8} 0.125 = - 1$ (ii) $l o g_{10} 0.01 = - 2$ (iii) $l o g_{a} A = x$ (iv) $l o g_{10} 1 = 0$

4861.

Express each of the following in exponential form : (i) log80.125=−1 (ii) log100.01=−2 (iii) logaA=x (iv) log101=0

Answer»

Express each of the following in exponential form :

(i) $l o g_{8} 0.125 = - 1$

(ii) $l o g_{10} 0.01 = - 2$

(iii) $l o g_{a} A = x$

(iv) $l o g_{10} 1 = 0$

Discussion

4862.	In a boarding house of 80 boys, there are food provisions for 30 days. If 20 more boys join the boarding house, how long will the provisions last ?
Answer» In a boarding house of 80 boys, there are food provisions for 30 days. If 20 more boys join the boarding house, how long will the provisions last ?

Discussion

4863.	If P(A) and P(¯¯¯¯A) are complementary events and P(A) = 0.15, then P(¯¯¯¯A)= ?
Answer» If $P (A)$ and $P (¯ ¯¯ ¯ A)$ are complementary events and $P (A)$ = 0.15, then $P (¯ ¯¯ ¯ A)$ = ?

Discussion

4864.	Line-segment AB is parallel to another line-segment CD. O is the midpoint of AD.Show that(i) △AOB≅△DOC(ii) O is also the midpoint of BC.
Answer» Line-segment AB is parallel to another line-segment CD. O is the midpoint of AD. Show that $(i) △ A O B ≅ △ D O C$ (ii) O is also the midpoint of BC.

Discussion

4865.	If (3,1) is a solution of the equation 6x+by=25, then what is the value of b?
Answer» If $(3, 1)$ is a solution of the equation $6 x + b y = 25,$ then what is the value of $b$ ?

Discussion

4866.	Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60∘ and 45∘ .
Answer» Construct a triangle whose perimeter is $6.4 c m$ , and angles at the base are $60^{\circ} a n d 45^{\circ}$ .

Discussion

4867.	Question 101 It takes 213 m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth 913 m long?
Answer» Question 101 It takes $2 \frac{1}{3}$ m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth $9 \frac{1}{3}$ m long?

4867.

Question 101 It takes 213 m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth 913 m long?

Answer»

Question 101

It takes $2 \frac{1}{3}$ m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth $9 \frac{1}{3}$ m long?

Discussion

4868.	The sides of a triangle are 11cm, 15cm and 16cm. The altitude to the largest side is
Answer» The sides of a triangle are 11cm, 15cm and 16cm. The altitude to the largest side is

Discussion

4869.	A=B=45 1) SIN (A-B) =SIN A cos B - cos A sin B
Answer» A=B=451) SIN (A-B) =SIN A cos B - cos A sin B

Discussion

4870.	The pillars of an apartment are cylindrical in shape. If each pillar has a circular base of radius 40 cm and height 20 m, then find the volume of 7 such pillars.
Answer» The pillars of an apartment are cylindrical in shape. If each pillar has a circular base of radius 40 cm and height 20 m, then find the volume of 7 such pillars.

Discussion

4871.	Question 49In the question given below, fill in the blanks to make the statement true:1032−1022= ___ ×(103−102)= ___ .
Answer» Question 49 In the question given below, fill in the blanks to make the statement true: $103^{2} - 102^{2} =$ ___ $\times (103 - 102) =$ ___ .

Discussion

4872.	Fill In the Blanks The mean of the following distribution x : 3 5 7 4y : 2 a 5 bis 5. Then the value of b is ____________.
Answer» Fill In the Blanks The mean of the following distribution x : 3 5 7 4 y : 2 a 5 b is 5. Then the value of b is ____________.

Discussion

4873.	What is the simplified form of 60×4−2×8−1×560×(14) ?
Answer» What is the simplified form of $6^{0} \times 4^{- 2} \times 8^{- 1} \times 56^{0} \times (\frac{1}{4})$ ?

Discussion

4874.	Write the equation for the following statement:If you add 3 to one-third of z, you get 30.
Answer» Write the equation for the following statement: If you add 3 to one-third of z, you get 30.

Discussion

4875.	The coordinates of a point (-x, -y) lies in the
Answer» The coordinates of a point (-x, -y) lies in the

Discussion

4876.

A weather station recorded the temperatures of a place over a period of 7 days as follows:DayTemperature (in ∘C )Monday 45Tuesday38Wednesday40Thursday42Friday41Saturday37Sunday36Find the probability of a day having a temperature of more than 40 ∘ C.

Answer»

A weather station recorded the temperatures of a place over a period of 7 days as follows:

Day	Temperature (in $^{\circ}$ C )
Monday	45
Tuesday	38
Wednesday	40
Thursday	42
Friday	41
Saturday	37
Sunday	36

Find the probability of a day having a temperature of more than 40

^{\circ}

C.

Discussion

4877.	In a triangle ABC, AB, BC and AC are the sides, then which of the following holds true?
Answer» In a triangle ABC, AB, BC and AC are the sides, then which of the following holds true?

Discussion

4878.	Two coins are tossed simultaneously. The probability of getting atmost one head is
Answer» Two coins are tossed simultaneously. The probability of getting atmost one head is

Discussion

4879.	The simplest rationalising factor of 3√500 is
Answer» The simplest rationalising factor of $\sqrt[3]{500}$ is

Discussion

4880.	If BDEF and FDCE are parallelograms, then ___ lies equidistant to points B and C. (Fill in one among A/F/E/D).
Answer» If BDEF and FDCE are parallelograms, then ___ lies equidistant to points B and C. (Fill in one among A/F/E/D).

Discussion

4881.	Prepare Bank Reconcilation Statement form the following particulars and show balance as per Cash Book:(i) Balance as per Pass Book on 31st March, 2018 overdrawn ₹ 10,000.(ii) Cheques drawn in the last week of March, 2018 but not cleared till 3rd April, 2018 ₹ 20,000.(iii) Interst on bank overdraft not entered in the Cash Book ₹ 1,500.(iv) Cheques of ₹ 20,000 deposited in the bank in March, 2018 but not collected and credited till 3rd April, 2018.(v) ₹ 100 Insurance premium paid by the bank under a standing order has not been entered in the Cash Book.(iv) A draft of ₹ 10,000 favouring Atul & Co. was issued by the bank charging commission of ₹ 200. However, in the Cash Book entry was passed by ₹ 10,000.
Answer» Prepare Bank Reconcilation Statement form the following particulars and show balance as per Cash Book: (i) Balance as per Pass Book on 31st March, 2018 overdrawn ₹ 10,000. (ii) Cheques drawn in the last week of March, 2018 but not cleared till 3rd April, 2018 ₹ 20,000. (iii) Interst on bank overdraft not entered in the Cash Book ₹ 1,500. (iv) Cheques of ₹ 20,000 deposited in the bank in March, 2018 but not collected and credited till 3rd April, 2018. (v) ₹ 100 Insurance premium paid by the bank under a standing order has not been entered in the Cash Book. (iv) A draft of ₹ 10,000 favouring Atul & Co. was issued by the bank charging commission of ₹ 200. However, in the Cash Book entry was passed by ₹ 10,000.

Discussion

4882.	If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.
Answer» If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.

Discussion

4883.	The point of concurrence of angle bisectors of a triangle is known as ____________.
Answer» The point of concurrence of angle bisectors of a triangle is known as ____________.

Discussion

4884.	In what time will a sum of ₹8000 amount to ₹8360 at 6% per annum simple interest?(a) 8 months(b) 9 months(c) 114 months(d) 112 years
Answer» In what time will a sum of ₹8000 amount to ₹8360 at 6% per annum simple interest? (a) 8 months (b) 9 months (c) $1 \frac{1}{4}$ months (d) $1 \frac{1}{2}$ years

Discussion

4885.	_______ is a line passing through the point (3, 0).
Answer» _______ is a line passing through the point (3, 0).

Discussion

4886.	The radius of a cone is 5 cm and vertical height is 12 cm.Find the area of the curved surface.
Answer» The radius of a cone is 5 cm and vertical height is 12 cm.Find the area of the curved surface.

Discussion

4887.	Identify the region that represents x2.
Answer» Identify the region that represents x $^{2}$ .

Discussion

4888.	On which axis do the x² following point lie? a) 7,0 b) 0,5 c) 0,1 d) -4,0
Answer» On which axis do the x² following point lie? a) 7,0 b) 0,5 c) 0,1 d) -4,0

4888.

On which axis do the x² following point lie? a) 7,0 b) 0,5 c) 0,1 d) -4,0

Answer»

On which axis do the x² following point lie?

a) 7,0 b) 0,5 c) 0,1 d) -4,0

Discussion

4889.	Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________. 8
Answer» Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________. 8

Discussion

4890.	A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625π m2, then the height of the tent is____m.
Answer» A circular ground of radius 50 $m$ has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is $625 π m^{2}$ , then the height of the tent is____ $m$ .

Discussion

4891.	Find the value of x in each of the following figures if l∥m.
Answer» Find the value of $x$ in each of the following figures if $l ∥ m$ .

4891.

Find the value of x in each of the following figures if l∥m.

Answer»

Find the value of $x$ in each of the following figures if $l ∥ m$ .

Discussion

4892.	Evaluate each of the following:(i) (2/3) – (3/5)(ii) (-4/7) – (2/-3)
Answer» Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3)

4892.

Evaluate each of the following:(i) (2/3) – (3/5)(ii) (-4/7) – (2/-3)

Answer»

Evaluate each of the following:

(i) (2/3) – (3/5)

(ii) (-4/7) – (2/-3)

Discussion

4893.	The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?
Answer» The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?

4893.

The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?

Answer»

The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?

Discussion

4894.	In triangle PQR, ST is a line intersecting PQ and PR in S and T respectively such that ST \|\|QR. If PS=x, SQ=2, PT=x+3,TR=x-3.What is the value of x?
Answer» In triangle PQR, ST is a line intersecting PQ and PR in S and T respectively such that ST \|\|QR. If PS=x, SQ=2, PT=x+3,TR=x-3.What is the value of x?

Discussion

4895.	Question 3(i)Find the value of:(30+4−1)×22
Answer» Question 3(i) Find the value of: $(3^{0} + 4^{- 1}) \times 2^{2}$

4895.

Question 3(i)Find the value of:(30+4−1)×22

Answer»

Question 3(i)

Find the value of:

$(3^{0} + 4^{- 1}) \times 2^{2}$

Discussion

4896.	Let →a,→b and →c are three unit vectors such that →a+→b+→c is also a unit vector. If pairwise angle between →a,→b and →c are θ1,θ2 and θ3 respectively such that sin2(θ12)+sin2(θ22)+sin2(θ32)=α, then the value of α2 is
Answer» Let $\to a, \to b$ and $\to c$ are three unit vectors such that $\to a + \to b + \to c$ is also a unit vector. If pairwise angle between $\to a, \to b$ and $\to c$ are $θ_{1}, θ_{2}$ and $θ_{3}$ respectively such that ${sin}^{2} (\frac{θ_{1}}{2}) + {sin}^{2} (\frac{θ_{2}}{2}) + {sin}^{2} (\frac{θ_{3}}{2}) = α,$ then the value of $α^{2}$ is

Discussion

4897.	75. If 6^x = 7^x+1, then x = log6/7 n. Then the value of n
Answer» 75. If 6^x = 7^x+1, then x = log6/7 n. Then the value of n

Discussion

4898.	Which of the following fraction is terminating decimal?
Answer» Which of the following fraction is terminating decimal?

Discussion

4899.	Eleven bags of wheat flour, each marked 10 kg actually contained the following weights (in kg) of flour:10.05, 10.20, 10.00, 9.75, 10.00, 10.03, 9.95, 10.35, 9.90, 10.00, 10.08Find the probability that any of these bags chosen at random contains:(i) more than 10 kg of wheat flour.(ii) less than 9.5 kg of wheat flour.
Answer» Eleven bags of wheat flour, each marked 10 kg actually contained the following weights (in kg) of flour: 10.05, 10.20, 10.00, 9.75, 10.00, 10.03, 9.95, 10.35, 9.90, 10.00, 10.08 Find the probability that any of these bags chosen at random contains: (i) more than 10 kg of wheat flour. (ii) less than 9.5 kg of wheat flour.

Discussion

4900.	obtain all the zeroes of the polynomial 2x^3-x^3-4x=2 if two of its zeroes are root2 and -root2
Answer» obtain all the zeroes of the polynomial 2x^3-x^3-4x=2 if two of its zeroes are root2 and -root2

Discussion

Explore topic-wise InterviewSolutions in .

Question 5 (ii)Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:BP = BQ or B is equidistant from the arms of ∠A.

It takes 8 days for 35 laborers to harvest coffee on a plantation. How long will 20 laborers take to harvest coffee on the same plantation.

In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]

if m is a rational number and root n is irrational number then prove that (m + root n) is irrational

A diagonal of a rectangle is inclined to one side of the rectangle at 35°. The Acute angle between the diagonal is

Prove the following trigonometric identities.1-cos A1+cos A=cot A-cosec A2

Two parallel chords, 10 cm apart, of lengths 8 cm and 12 cm, respectively are there in a circle. Find the distance of the shorter chord from the centre.

From the adjoining figure, if ∠2 = 55∘ and ∠5 = 60∘, then the lines m and n are ​

How to write a congruence statement easily?

If a triangle, with one of its side 12 cm, is reduced by a scale factor of 13, then find the length of the corresponding side of the new triangle.

Express each of the following in exponential form : (i) log80.125=−1 (ii) log100.01=−2 (iii) logaA=x (iv) log101=0

In a boarding house of 80 boys, there are food provisions for 30 days. If 20 more boys join the boarding house, how long will the provisions last ?

If P(A) and P(¯¯¯¯A) are complementary events and P(A) = 0.15, then P(¯¯¯¯A)= ?

Line-segment AB is parallel to another line-segment CD. O is the midpoint of AD.Show that(i) △AOB≅△DOC(ii) O is also the midpoint of BC.

If (3,1) is a solution of the equation 6x+by=25, then what is the value of b?

Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60∘ and 45∘ .

Question 101 It takes 213 m of cloth to make a shirt. How many shirts can Radhika make from a piece of cloth 913 m long?

The sides of a triangle are 11cm, 15cm and 16cm. The altitude to the largest side is

A=B=45​​​​ 1) SIN (A-B) =SIN A cos B - cos A sin B

The pillars of an apartment are cylindrical in shape. If each pillar has a circular base of radius 40 cm and height 20 m, then find the volume of 7 such pillars.

Question 49In the question given below, fill in the blanks to make the statement true:1032−1022= ___ ×(103−102)= ___ .

Fill In the Blanks The mean of the following distribution x : 3 5 7 4y : 2 a 5 bis 5. Then the value of b is ____________.

What is the simplified form of 60×4−2×8−1×560×(14) ?

Write the equation for the following statement:If you add 3 to one-third of z, you get 30.

The coordinates of a point (-x, -y) lies in the

A weather station recorded the temperatures of a place over a period of 7 days as follows:DayTemperature (in ∘C )Monday 45Tuesday38Wednesday40Thursday42Friday41Saturday37Sunday36Find the probability of a day having a temperature of more than 40 ∘ C.

In a triangle ABC, AB, BC and AC are the sides, then which of the following holds true?

Two coins are tossed simultaneously. The probability of getting atmost one head is

The simplest rationalising factor of 3√500 is

If BDEF and FDCE are parallelograms, then ___ lies equidistant to points B and C. (Fill in one among A/F/E/D).

If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.

The point of concurrence of angle bisectors of a triangle is known as ____________.

In what time will a sum of ₹8000 amount to ₹8360 at 6% per annum simple interest?(a) 8 months(b) 9 months(c) 114 months(d) 112 years

_______ is a line passing through the point (3, 0).

The radius of a cone is 5 cm and vertical height is 12 cm.Find the area of the curved surface.

Identify the region that represents x2.

On which axis do the x² following point lie? a) 7,0 b) 0,5 c) 0,1 d) -4,0

Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________. 8

A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625π m2, then the height of the tent is____m.

Find the value of x in each of the following figures if l∥m.

Evaluate each of the following:(i) (2/3) – (3/5)(ii) (-4/7) – (2/-3)

The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?

In triangle PQR, ST is a line intersecting PQ and PR in S and T respectively such that ST ||QR. If PS=x, SQ=2, PT=x+3,TR=x-3.What is the value of x?

Question 3(i)Find the value of:(30+4−1)×22

Let →a,→b and →c are three unit vectors such that →a+→b+→c is also a unit vector. If pairwise angle between →a,→b and →c are θ1,θ2 and θ3 respectively such that sin2(θ12)+sin2(θ22)+sin2(θ32)=α, then the value of α2 is

75. If 6^x = 7^x+1, then x = log6/7 n. Then the value of n

Which of the following fraction is terminating decimal?

obtain all the zeroes of the polynomial 2x^3-x^3-4x=2 if two of its zeroes are root2 and -root2

From the adjoining figure, if ∠2 = 55∘ and ∠5 = 60∘, then the lines m and n are

A=B=45 1) SIN (A-B) =SIN A cos B - cos A sin B

Question 49In the question given below, fill in the blanks to make the statement true:1032−1022= _ ×(103−102)= _ .