32581 + Interview Questions in Mathematics Page 178 InterviewSolution

8851.	For any AP, the expression for the nth term is always a ___ expression in n.
Answer» For any AP, the expression for the $n^{t h}$ term is always a ___ expression in $n$ .

Discussion

8852.	Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.
Answer» Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.

Discussion

8853.	IF 4x^3 + 7x^2 - 3x - 6 IS DIVIDED BY x + 1 , THEN FIND IT'S REMAINDER.
Answer» IF 4x^3 + 7x^2 - 3x - 6 IS DIVIDED BY x + 1 , THEN FIND IT'S REMAINDER.

Discussion

8854.	Number of the real solution of the equation \|x-3\|+2\|x+1\|=4
Answer» Number of the real solution of the equation \|x-3\|+2\|x+1\|=4

Discussion

8855.	Variance of certain number of scores is 16 and the mean is 10 then the coefficient of variation is?
Answer» Variance of certain number of scores is 16 and the mean is 10 then the coefficient of variation is?

Discussion

8856.	Question 11The angle of elevation of the top of a tower is 30∘. If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.
Answer» Question 11 The angle of elevation of the top of a tower is $30^{\circ}$ . If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.

Discussion

8857.	Find the ratio of the sides AB : BC : AC.
Answer» Find the ratio of the sides AB : BC : AC.

Discussion

8858.	The number of 5 digits numbers which are divisible by 3, using the digits 1,2,3,4,5,6,7,8 and 9 when repetition of digits is allowed.
Answer» The number of 5 digits numbers which are divisible by 3, using the digits 1,2,3,4,5,6,7,8 and 9 when repetition of digits is allowed.

Discussion

8859.	Match the following sets with cardianality of their power set.
Answer» Match the following sets with cardianality of their power set.

Discussion

8860.	The horizontal distance between two poles is 15 m. The angle of depression of the top of the first pole as seen from the top of the second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. 3=1.732 [CBSE 2013]
Answer» The horizontal distance between two poles is 15 m. The angle of depression of the top of the first pole as seen from the top of the second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. $(\sqrt{3} = 1.732)$ [CBSE 2013]

Discussion

8861.	The mode of the given data 1, 7, 2, 4, 5, 9, 8, 3 is
Answer» The mode of the given data 1, 7, 2, 4, 5, 9, 8, 3 is

Discussion

8862.	Question 10Verify whether the following are true or false.(i) -3 is a zero of x - 3(ii) −13 is a zero of 3x + 1(iii) −45 is a zero of 4 - 5y(iv) 0 and 2 are the zeroes of t2–t(v) -3 is a zero of y2+y–6
Answer» Question 10 Verify whether the following are true or false. (i) -3 is a zero of x - 3 (ii) $- \frac{1}{3}$ is a zero of 3x + 1 (iii) $- \frac{4}{5}$ is a zero of 4 - 5y (iv) 0 and 2 are the zeroes of $t^{2} - t$ (v) -3 is a zero of $y^{2} + y - 6$

Discussion

8863.	Addition of matrices is defined if order of the matrices is ______________.
Answer» Addition of matrices is defined if order of the matrices is ______________.

Discussion

8864.	If two lines are parallel to each other the system of equation is
Answer» If two lines are parallel to each other the system of equation is

Discussion

8865.	Question 14D and E are the mid-points of the sides AB and AC, respectively, of ΔABC.DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is(a) ∠DAE=∠EFC(b) AE=EF(c) DE=EF(d) ∠ADE=∠ECF
Answer» Question 14 D and E are the mid-points of the sides AB and AC, respectively, of $Δ A B C . D E$ is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is (a) $∠ D A E = ∠ E F C$ (b) $A E = E F$ (c) $D E = E F$ (d) $∠ A D E = ∠ E C F$

Discussion

8866.	A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from 60∘ to 45∘. Calculate the speed of the boat.
Answer» A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from $60^{\circ} t o 45^{\circ}$ . Calculate the speed of the boat.

Discussion

8867.	37. (x_2,y+5)=(-2,1÷ 3)are two equal ordered pairs then X is equal to
Answer» 37. (x_2,y+5)=(-2,1÷ 3)are two equal ordered pairs then X is equal to

Discussion

8868.	Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?
Answer» Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?

Discussion

8869.	If a line passing through (1,1) divides the segment between the axes in the ratio 3:4, then the equation of the line is
Answer» If a line passing through $(1, 1)$ divides the segment between the axes in the ratio 3:4, then the equation of the line is

Discussion

8870.	Show that one and only one out of n,n+4,n+8,n+12 and n + 16 is divisible by 5
Answer» Show that one and only one out of n,n+4,n+8,n+12 and n + 16 is divisible by 5

Discussion

8871.	the dimensional formula of∫ tdt is
Answer» the dimensional formula of∫ tdt is

Discussion

8872.

On April 1st, 2016, X started a business with ₹ 40,000 as his capital. On March 31st, 2017, 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 2016-17 X drew ₹ 24,000. On 1st October 2016, he introduced further capital amounting to ₹ 30,000. You are required to ascertain profit or loss made by him during the year 2016-17.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 March 31st 2017.

Answer» On April 1st, 2016, X started a business with ₹ 40,000 as his capital. On March 31st, 2017, 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 2016-17 X drew ₹ 24,000. On 1st October 2016, he introduced further capital amounting to ₹ 30,000. You are required to ascertain profit or loss made by him during the year 2016-17.

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 March 31st 2017.

Discussion

8873.	if water falls from a tap, then the volume rate of flow of water at depth h,(A_{0 }is the area of cross-section of the mouth and A_0/2 is the corresponding area at depth h) 1. A_0\sqrt{2gh} 2. A_0\sqrt{2gh/3} 3. 2A_0\sqrt{gh} 4. A_0\sqrt{3gh
Answer» if water falls from a tap, then the volume rate of flow of water at depth h,(A_{0 }is the area of cross-section of the mouth and A_0/2 is the corresponding area at depth h) 1. A_0\sqrt{2gh} 2. A_0\sqrt{2gh/3} 3. 2A_0\sqrt{gh} 4. A_0\sqrt{3gh

Discussion

8874.

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life-time (in days) Less than 50 Less than 100 Less than 150 Less than 200 Less than 250 Less than 300 Number of bulbs 7 21 52 79 91 100 From this table, construct the frequency distribution table.

Answer» The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

Life-time (in days)	Less than 50	Less than 100	Less than 150	Less than 200	Less than 250	Less than 300
Number of bulbs	7	21	52	79	91	100

From this table, construct the frequency distribution table.

Discussion

8875.	In △PQR, PQ = 12 cm, PR = 13 cm and ∠Q=90∘. Find the value of 12tan P and cot P.
Answer» In $△$ PQR, PQ = 12 cm, PR = 13 cm and $∠ Q = 90^{\circ}$ . Find the value of 12tan P and cot P.

Discussion

8876.	The 24th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.
Answer» The 24th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Discussion

8877.	Which of the following graph represents y=−x2?
Answer» Which of the following graph represents $y = - x^{2}$ ?

Discussion

8878.	If P(n): 2×42n+1+33n+1 is divisible by λ for all n ∈ N is true, then find the value of λ.
Answer» If P(n): $2 \times 4^{2 n + 1} + 3^{3 n + 1}$ is divisible by $λ$ for all n $\in$ N is true, then find the value of $λ$ .

Discussion

8879.	The marks obtained by 40 students in a class are presented in the form of a table. Find the mean marks using direct method.Marks obtainedNumber of students0−10310−20420−301330−401540−505
Answer» The marks obtained by 40 students in a class are presented in the form of a table. Find the mean marks using direct method. $\begin{matrix} Marks obtained & Number of students 0 - 10 & 3 10 - 20 & 4 20 - 30 & 13 30 - 40 & 15 40 - 50 & 5 \end{matrix}$

Discussion

8880.	How much more is the sum of the natural numbers from 21 to 40 than the sum of the natural numbers from 1 to 20?
Answer» How much more is the sum of the natural numbers from 21 to 40 than the sum of the natural numbers from 1 to 20?

Discussion

8881.	Find the quotient and remainder whenfx=x4-5x+6 is divided by gx=2-x2
Answer» Find the quotient and remainder when $f (x) = x^{4} - 5 x + 6$ is divided by $g (x) = 2 - x^{2}$

Discussion

8882.	If the sides of two similar triangles are in the ratio of 4 : 9, then the areas of these triangles are in the ratio ____.
Answer» If the sides of two similar triangles are in the ratio of 4 : 9, then the areas of these triangles are in the ratio ____.

Discussion

8883.	The HCF of 6(x2−4) and 15(x+2)(x+7) is:
Answer» $The HCF of 6 (x^{2} - 4) and 15 (x + 2) (x + 7) is :$

Discussion

8884.	A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin?
Answer» A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin?

Discussion

8885.	If the ratio of sum of m terms and n terms of an A.P. is m2:n2, then the ratio of its mth and nth terms will be :
Answer» If the ratio of sum of m terms and n terms of an A.P. is $m^{2}$ : $n^{2}$ , then the ratio of its $m^{t h}$ and $n^{t h}$ terms will be :

Discussion

8886.	The median class for the following data isMarksBelow 10Below 20Below 30Below 40Below 50No. of students 510233140
Answer» The median class for the following data is $\begin{matrix} Marks & Below 10 & Below 20 & Below 30 & Below 40 & Below 50 No. of students & 5 & 10 & 23 & 31 & 40 \end{matrix}$

Discussion

8887.	Question 18 The sum of first five multiples of3 is : A) 45 B) 55 C) 65 D) 75
Answer» Question 18 The sum of first five multiples of3 is : A) 45 B) 55 C) 65 D) 75

Discussion

8888.	Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Answer» Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Discussion

8889.	28 Aauniform metel ring wth centre Chas two pts. A and B wth diff temprature. If angle ACB is 180 then the rate of heat flow is 1.2W . If angle ACB is 90 , then the rate of heat flow is
Answer» 28 Aauniform metel ring wth centre Chas two pts. A and B wth diff temprature. If angle ACB is 180 then the rate of heat flow is 1.2W . If angle ACB is 90 , then the rate of heat flow is

Discussion

8890.	Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using a similarity criterion for two triangles, show that
Answer» Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using a similarity criterion for two triangles, show that

Discussion

8891.	R divides the line segment joining P(1,2) and Q(-3, 4) in the ratio K : 1, Find the co-ordinates of R.
Answer» R divides the line segment joining P(1,2) and Q(-3, 4) in the ratio K : 1, Find the co-ordinates of R.

Discussion

8892.	There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,(1) a natural number.(2) a number less than 1.(3) a whole number.(4) a number is greater than 5.figure
Answer» There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows, (1) a natural number. (2) a number less than 1. (3) a whole number. (4) a number is greater than 5. figure

Discussion

8893.	What will be the mean of 201, 205, 209, 305 and 410 ?266
Answer» What will be the mean of 201, 205, 209, 305 and 410 ? 266

Discussion

8894.	Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.
Answer» Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.

Discussion

8895.	The prime factorisation of a and b area=22×3×5 and b=2×32.What is the LCM of a and b?180
Answer» The prime factorisation of a and b are $a = 2^{2} \times 3 \times 5 and b = 2 \times 3^{2} .$ What is the LCM of a and b? 180

Discussion

8896.	Do the following pair of linear equations have no solution? Justify your answer.2x + 4y = 3 and 12y + 6x = 6
Answer» Do the following pair of linear equations have no solution? Justify your answer. 2x + 4y = 3 and 12y + 6x = 6

Discussion

8897.	FFind the value of k, for which one root of the quadratic equation kx2-14x+8=0 is six times the other.
Answer» FFind the value of k, for which one root of the quadratic equation kx2-14x+8=0 is six times the other.

Discussion

8898.	A thief is running on a train with 12km/hr .the police car Is moving with 80 km /h.if the train is 60km/h .what is the speed of the thief w.r.t police car?
Answer» A thief is running on a train with 12km/hr .the police car Is moving with 80 km /h.if the train is 60km/h .what is the speed of the thief w.r.t police car?

8898.

A thief is running on a train with 12km/hr .the police car Is moving with 80 km /h.if the train is 60km/h .what is the speed of the thief w.r.t police car?

Answer»

A thief is running on a train with 12km/hr .the police car

Is moving with 80 km /h.if the train is 60km/h .what is the speed of the thief w.r.t police car?

Discussion

8899.	If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that ab=cd.
Answer» If the roots of the equation (a² + b²)x² − 2 (ac + bd)x + (c² + d²) = 0 are equal, prove that $\frac{a}{b} = \frac{c}{d}$ .

Discussion

8900.	Find the values of p and q for which the following system of linear equations has infinite number of solutions:2x+3y=9p+qx+2p-qy=3p+q+1
Answer» Find the values of p and q for which the following system of linear equations has infinite number of solutions: $2 x + 3 y = 9 (p + q) x + (2 p - q) y = 3 (p + q + 1)$

Discussion

Explore topic-wise InterviewSolutions in .

For any AP, the expression for the nth term is always a ___ expression in n.

Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.

IF 4x^3 + 7x^2 - 3x - 6 IS DIVIDED BY x + 1 , THEN FIND IT'S REMAINDER.

Number of the real solution of the equation |x-3|+2|x+1|=4

Variance of certain number of scores is 16 and the mean is 10 then the coefficient of variation is?

Question 11The angle of elevation of the top of a tower is 30∘. If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.

Find the ratio of the sides AB : BC : AC.

The number of 5 digits numbers which are divisible by 3, using the digits 1,2,3,4,5,6,7,8 and 9 when repetition of digits is allowed.

Match the following sets with cardianality of their power set.

The horizontal distance between two poles is 15 m. The angle of depression of the top of the first pole as seen from the top of the second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. 3=1.732 [CBSE 2013]

The mode of the given data 1, 7, 2, 4, 5, 9, 8, 3 is

Question 10Verify whether the following are true or false.(i) -3 is a zero of x - 3(ii) −13 is a zero of 3x + 1(iii) −45 is a zero of 4 - 5y(iv) 0 and 2 are the zeroes of t2–t(v) -3 is a zero of y2+y–6

Addition of matrices is defined if order of the matrices is ______________.

If two lines are parallel to each other the system of equation is

A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from 60∘ to 45∘. Calculate the speed of the boat.

37. (x_2,y+5)=(-2,1÷ 3)are two equal ordered pairs then X is equal to

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?

If a line passing through (1,1) divides the segment between the axes in the ratio 3:4, then the equation of the line is

Show that one and only one out of n,n+4,n+8,n+12 and n + 16 is divisible by 5

the dimensional formula of∫ tdt is

if water falls from a tap, then the volume rate of flow of water at depth h,(A_{0 }is the area of cross-section of the mouth and A_0/2 is the corresponding area at depth h) 1. A_0\sqrt{2gh} 2. A_0\sqrt{2gh/3} 3. 2A_0\sqrt{gh} 4. A_0\sqrt{3gh

​​The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life-time (in days) Less than 50 Less than 100 Less than 150 Less than 200 Less than 250 Less than 300 Number of bulbs 7 21 52 79 91 100 From this table, construct the frequency distribution table.

In △PQR, PQ = 12 cm, PR = 13 cm and ∠Q=90∘. Find the value of 12tan P and cot P.

The 24th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Which of the following graph represents y=−x2?

If P(n): 2×42n+1+33n+1 is divisible by λ for all n ∈ N is true, then find the value of λ.

The marks obtained by 40 students in a class are presented in the form of a table. Find the mean marks using direct method.Marks obtainedNumber of students0−10310−20420−301330−401540−505

How much more is the sum of the natural numbers from 21 to 40 than the sum of the natural numbers from 1 to 20?

Find the quotient and remainder whenfx=x4-5x+6 is divided by gx=2-x2

If the sides of two similar triangles are in the ratio of 4 : 9, then the areas of these triangles are in the ratio ____.

The HCF of 6(x2−4) and 15(x+2)(x+7) is:

A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin?

If the ratio of sum of m terms and n terms of an A.P. is m2:n2, then the ratio of its mth and nth terms will be :

The median class for the following data isMarksBelow 10Below 20Below 30Below 40Below 50No. of students 510233140

Question 18 The sum of first five multiples of3 is : A) 45 B) 55 C) 65 D) 75

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

28 Aauniform metel ring wth centre Chas two pts. A and B wth diff temprature. If angle ACB is 180 then the rate of heat flow is 1.2W . If angle ACB is 90 , then the rate of heat flow is

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that

R divides the line segment joining P(1,2) and Q(-3, 4) in the ratio K : 1, Find the co-ordinates of R.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,(1) a natural number.(2) a number less than 1.(3) a whole number.(4) a number is greater than 5.figure

What will be the mean of 201, 205, 209, 305 and 410 ?266

Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.

The prime factorisation of a and b area=22×3×5 and b=2×32.What is the LCM of a and b?180

Do the following pair of linear equations have no solution? Justify your answer.2x + 4y = 3 and 12y + 6x = 6

FFind the value of k, for which one root of the quadratic equation kx2-14x+8=0 is six times the other.

A thief is running on a train with 12km/hr .the police car Is moving with 80 km /h.if the train is 60km/h .what is the speed of the thief w.r.t police car?

If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that ab=cd.

Find the values of p and q for which the following system of linear equations has infinite number of solutions:2x+3y=9p+qx+2p-qy=3p+q+1

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand. Life-time (in days) Less than 50 Less than 100 Less than 150 Less than 200 Less than 250 Less than 300 Number of bulbs 7 21 52 79 91 100 From this table, construct the frequency distribution table.