32581 + Interview Questions in Mathematics Page 22 InterviewSolution

1051.	Question 2 (i)Choose the correct option and justify your choice.(i) 2tan3001+tan2300=(A) sin60∘(B) cos60∘(C) tan60∘(D) sin30∘
Answer» Question 2 (i) Choose the correct option and justify your choice. (i) $\frac{2 t a n 3 0^{0}}{1 + t a n^{2} 30^{0}} =$ (A) $s i n 60^{\circ}$ (B) $c o s 60^{\circ}$ (C) $t a n 60^{\circ}$ (D) $s i n 30^{\circ}$

Discussion

1052.	Q) The angular speed of the hour hand of a clock is
Answer» Q) The angular speed of the hour hand of a clock is

Discussion

1053.	What is the value of p if the distance between the points (4,p) and (1,0) is 5?
Answer» What is the value of p if the distance between the points (4,p) and (1,0) is 5?

Discussion

1054.

If the median of the following frequency distribution is 28.5 find the missing frequencies: Class interval: 0−10 10−20 20−30 30−40 40−50 50−60 Total Frequency: 5 f1 20 15 f2 5 60

Answer» If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval:	0−10	10−20	20−30	30−40	40−50	50−60	Total
Frequency:	5	f₁	20	15	f₂	5	60

Discussion

1055.	In parallelogram ABCD, A(2,3), B(7,3) and D(4,7). Then the coordinates of C is
Answer» In parallelogram ABCD, A(2,3), B(7,3) and D(4,7). Then the coordinates of C is

Discussion

1056.	The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated belowClass13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of atheletes who completed the race in less than 14.6 s is
Answer» The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated below $\begin{matrix} Class & 13.8 - 14 & 14 - 14.2 & 14.2 - 14.4 & 14.4 - 14.6 & 14.6 - 14.8 & 14.8 - 15 Frequency & 2 & 4 & 5 & 71 & 48 & 20 \end{matrix}$ The number of atheletes who completed the race in less than 14.6 s is

1056.

The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated belowClass13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of atheletes who completed the race in less than 14.6 s is

Answer»

The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated below

$\begin{matrix} Class & 13.8 - 14 & 14 - 14.2 & 14.2 - 14.4 & 14.4 - 14.6 & 14.6 - 14.8 & 14.8 - 15 Frequency & 2 & 4 & 5 & 71 & 48 & 20 \end{matrix}$

The number of atheletes who completed the race in less than 14.6 s is

Discussion

1057.	Write the next term of the AP:√8,√18,√32,....
Answer» Write the next term of the $A P : \sqrt{8}, \sqrt{18}, \sqrt{32}, . . . .$

Discussion

1058.	If (x + 1) is a factor of (2x2 + kx), then k = ?(a) 4(b) −3(c) 2(d) –2
Answer» If (x + 1) is a factor of (2x² + kx), then k = ? (a) 4 (b) −3 (c) 2 (d) –2

Discussion

1059.	The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Answer» The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.

Discussion

1060.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2-4ax-b2+4a2=0 [CBSE 2012]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x^{2} - 4 a x - b^{2} + 4 a^{2} = 0$ [CBSE 2012]

Discussion

1061.	Question 8 (i)A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find:(i) the inside surface area of the dome,[Assume π=227]
Answer» Question 8 (i) A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find: (i) the inside surface area of the dome, $[A s s u m e π = \frac{22}{7}]$

Discussion

1062.	Find the equation of the line which is passing through (0,0) with slope m.
Answer» Find the equation of the line which is passing through $(0, 0)$ with slope $m$ .

Discussion

1063.	Star Ltd was registered with a capital of ₹ 5,00,000 in shares of ₹ 10 each and issued 20,000 such shares at a premium of ₹ 2 per share, payable as ₹ 2 per share on application, ₹ 5 per share on allotment (including premium) and ₹ 2 per share on first call made three months later. All the money payable on application and allotment was duly received but when the first call was made, one shareholder paid the entire balance on his holding of 300 shares and another shareholder holding 1,000 shares failed to pay the first call money.Pass journal entries to record the above transactions and show how they will appear in the company's Balance Sheet.
Answer» Star Ltd was registered with a capital of ₹ 5,00,000 in shares of ₹ 10 each and issued 20,000 such shares at a premium of ₹ 2 per share, payable as ₹ 2 per share on application, ₹ 5 per share on allotment (including premium) and ₹ 2 per share on first call made three months later. All the money payable on application and allotment was duly received but when the first call was made, one shareholder paid the entire balance on his holding of 300 shares and another shareholder holding 1,000 shares failed to pay the first call money. Pass journal entries to record the above transactions and show how they will appear in the company's Balance Sheet.

Discussion

1064.	The arithmetic mean of the following data is 25, find the value of k. xi : 5 15 25 35 45 fi : 3 k 3 6 2
Answer» The arithmetic mean of the following data is 25, find the value of k. $x_{i}$ : 5 15 25 35 45 $f_{i}$ : 3 k 3 6 2

Discussion

1065.	While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.
Answer» While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.

Discussion

1066.	In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Answer» In an A.P. 17^th term is 7 more than its 10^th term. Find the common difference.

Discussion

1067.	If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and −ax2 + bx + c = 0 has real roots.
Answer» If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and −ax² + bx + c = 0 has real roots.

Discussion

1068.	16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water . Find the volume of the water filled in the box .
Answer» 16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions $16 cm \times 8 cm \times 8 cm$ and then the box is filled with water . Find the volume of the water filled in the box .

Discussion

1069.	If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?
Answer» If the linear equation $y = 7 x - 4$ is written in standard form, the standard form being $a x + b y + c = 0,$ then what are the possible value of $a, b, c$ ?

Discussion

1070.	An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another plane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will the two planes be after 112 hours?
Answer» An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another plane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will the two planes be after $1 \frac{1}{2}$ hours?

Discussion

1071.	How many three digits numbers divisible by 19 have the sum of their digits is 1
Answer» How many three digits numbers divisible by 19 have the sum of their digits is 1

Discussion

1072.	Find the sum of the first (i) 11 terms of the A.P.: 2,6,10,14,... (ii) 13 terms of the A.P.: -6,0,6,12,... (iii) 51 terms of the A.P.: whose second term is 2 and fourth term is 8.
Answer» Find the sum of the first (i) 11 terms of the A.P.: 2,6,10,14,... (ii) 13 terms of the A.P.: -6,0,6,12,... (iii) 51 terms of the A.P.: whose second term is 2 and fourth term is 8.

Discussion

1073.	If √x+√y=√2+√5, then √x−√y = ___
Answer» If $\sqrt{x} + \sqrt{y} = \sqrt{2} + \sqrt{5}$ , then $\sqrt{x} - \sqrt{y}$ = ___

Discussion

1074.	Solve the following quadratic equations by factorization:ax2+1-xa2+1=0
Answer» Solve the following quadratic equations by factorization: $a (x^{2} + 1) - x (a^{2} + 1) = 0$

Discussion

1075.	If n is any natural number, then 9n−5n ends with:
Answer» If $n$ is any natural number, then $9^{n} - 5^{n}$ ends with:

Discussion

1076.	Question 12Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Answer» Question 12 Two APs have the same common difference. The difference between their $100^{t h}$ terms is 100, what is the difference between their $1000^{t h}$ terms?

Discussion

1077.	(i) How many terms of the sequence 18, 16, 14, ... should be taken so that their sum is zero?(ii) How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?(iii) How many terms of the A.P. 9, 17, 25,... must be taken so that their sum is 636?(iv) How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
Answer» (i) How many terms of the sequence 18, 16, 14, ... should be taken so that their sum is zero? (ii) How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40? (iii) How many terms of the A.P. 9, 17, 25,... must be taken so that their sum is 636? (iv) How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?

Discussion

1078.	Which of the following equations are consistent?
Answer» Which of the following equations are consistent?

Discussion

1079.	The sum of first ten terms of an A.P. is four times the sum of its first five terms. What is the ratio of first term and common difference?
Answer» The sum of first ten terms of an A.P. is four times the sum of its first five terms. What is the ratio of first term and common difference?

Discussion

1080.	Reflection of the point (−10,7) in the x-axis is ____________
Answer» Reflection of the point $(- 10, 7)$ in the x-axis is ____________

Discussion

1081.	A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. They admit C into partnership for 1/5th share. C brings ₹ 30,000 as capital and ₹ 10,000 as goodwill. At the time of admission of C, goodwill appeared in the Balance Sheet of A and B at ₹ 3,000. New profit-sharing ratio of the partners will be 5 : 3 : 2. Pass necessary Journal entries.
Answer» A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. They admit C into partnership for 1/5th share. C brings ₹ 30,000 as capital and ₹ 10,000 as goodwill. At the time of admission of C, goodwill appeared in the Balance Sheet of A and B at ₹ 3,000. New profit-sharing ratio of the partners will be 5 : 3 : 2. Pass necessary Journal entries.

Discussion

1082.	(d/dx)(dy/dx)=(d²y)/(dx)²Is this correct?
Answer» (d/dx)(dy/dx)=(d²y)/(dx)² Is this correct?

Discussion

1083.	Mark the correct alternative in the following question:If the sum of a number and its two-fifth is 70. The number is(a) 70 (b) 50 (c) 60 (d) 90
Answer» Mark the correct alternative in the following question: If the sum of a number and its two-fifth is 70. The number is (a) 70 (b) 50 (c) 60 (d) 90

Discussion

1084.	Prove the following trignometric identities: (1+cot2 A) sin2 A=1
Answer» Prove the following trignometric identities: $(1 + c o t^{2} A) s i n^{2} A = 1$

1084.

Prove the following trignometric identities: (1+cot2 A) sin2 A=1

Answer»

Prove the following trignometric identities:

$(1 + c o t^{2} A) s i n^{2} A = 1$

Discussion

1085.	Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?
Answer» Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?

Discussion

1086.	Question 2Write whether the following statement is True or False?The graph of the linear equation x + 2y = 7 passes through the point (0, 7).
Answer» Question 2 Write whether the following statement is True or False? The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

Discussion

1087.	In a triangle ABC, AB =20 cm, ∠A=30∘, AC = 18 cm. Find the area of the triangle
Answer» In a triangle ABC, AB =20 cm, $∠ A = 30^{\circ}$ , AC = 18 cm. Find the area of the triangle

1087.

In a triangle ABC, AB =20 cm, ∠A=30∘, AC = 18 cm. Find the area of the triangle

Answer»

In a triangle ABC, AB =20 cm, $∠ A = 30^{\circ}$ , AC = 18 cm. Find the area of the triangle

Discussion

1088.	In the given figure, ABCD is a cyclic quadrilateral, B and D are the centres of two congruent circles. If the radius of each circle is 7 cm, then the area of the shaded region is equal to [use π=227]
Answer» In the given figure, $A B C D$ is a cyclic quadrilateral, $B$ and $D$ are the centres of two congruent circles. If the radius of each circle is $7 cm$ , then the area of the shaded region is equal to $[use π = \frac{22}{7}]$

Discussion

1089.	(cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.
Answer» (cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.

Discussion

1090.	Write the condition to be satisfied by q so that a rational number pq has a terminating decimal expansions.
Answer» Write the condition to be satisfied by q so that a rational number $\frac{p}{q}$ has a terminating decimal expansions.

Discussion

1091.	A cylindrical tank is filled with water to level of 3 m. A hole is opened atheight of 52.5 cm from bottom. The ratio of the area of the hole to that ofcross-sectional area of the cylinder is 0.1. The square of the speed with whichwater is coming out from the orifice is (Take g = 10 ms^{-2}) (a) 50 m^2s^{-2} (b) 40 m^2s^{-2} (c) 51.5 m^2s^{-2} (d) 50.5 m^2s^-
Answer» A cylindrical tank is filled with water to level of 3 m. A hole is opened atheight of 52.5 cm from bottom. The ratio of the area of the hole to that ofcross-sectional area of the cylinder is 0.1. The square of the speed with whichwater is coming out from the orifice is (Take g = 10 ms^{-2}) (a) 50 m^2s^{-2} (b) 40 m^2s^{-2} (c) 51.5 m^2s^{-2} (d) 50.5 m^2s^-

Discussion

1092.	Find out the wrong number in the series given below :1,2,6,15,31,56,91
Answer» Find out the wrong number in the series given below : $1, 2, 6, 15, 31, 56, 91$

Discussion

1093.	In the given figure, OACB is a quadrant of 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 the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) Quadrant OACB (ii) Shaded region

1093.

In the given figure, OACB is a quadrant of 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 the given figure, OACB is a quadrant of 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

1094.	In a school of 1900 students, there are 800 girls. Find the probability that a student chosen at random is a boy.
Answer» In a school of 1900 students, there are 800 girls. Find the probability that a student chosen at random is a boy.

Discussion

1095.	Complétez avec les prépositions convenables.
Answer» Complétez avec les prépositions convenables.

Discussion

1096.	22. If one zero of the quadratic polynomial x-7x+5k is -2 then find the value of k
Answer» 22. If one zero of the quadratic polynomial x-7x+5k is -2 then find the value of k

Discussion

1097.	'3x - 7' is the polynomial in ___ variable.
Answer» '3x - 7' is the polynomial in ___ variable.

Discussion

1098.	Find the values of k for which the given equation has real and equal roots: [3 MARKS](k+1)x2−2(k−1)x+1=0
Answer» Find the values of k for which the given equation has real and equal roots: [3 MARKS] $(k + 1) x^{2} - 2 (k - 1) x + 1 = 0$

Discussion

1099.	How many revolution would a cycle wheel of diameter 1.6m make to cover a distance of 352metres
Answer» How many revolution would a cycle wheel of diameter 1.6m make to cover a distance of 352metres

Discussion

1100.

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.___

Answer»

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.

___

Discussion

Explore topic-wise InterviewSolutions in .

Question 2 (i)Choose the correct option and justify your choice.(i) 2tan3001+tan2300=(A) sin60∘(B) cos60∘(C) tan60∘(D) sin30∘

Q) The angular speed of the hour hand of a clock is

What is the value of p if the distance between the points (4,p) and (1,0) is 5?

If the median of the following frequency distribution is 28.5 find the missing frequencies: Class interval: 0−10 10−20 20−30 30−40 40−50 50−60 Total Frequency: 5 f1 20 15 f2 5 60

In parallelogram ABCD, A(2,3), B(7,3) and D(4,7). Then the coordinates of C is

The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated belowClass13.8−1414−14.214.2−14.414.4−14.614.6−14.814.8−15Frequency245714820The number of atheletes who completed the race in less than 14.6 s is

Write the next term of the AP:√8,√18,√32,....

If (x + 1) is a factor of (2x2 + kx), then k = ?(a) 4(b) −3(c) 2(d) –2

The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2-4ax-b2+4a2=0 [CBSE 2012]

Question 8 (i)A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find:(i) the inside surface area of the dome,[Assume π=227]

Find the equation of the line which is passing through (0,0) with slope m.

The arithmetic mean of the following data is 25, find the value of k. xi : 5 15 25 35 45 fi : 3 k 3 6 2

While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.

In an A.P. 17th term is 7 more than its 10th term. Find the common difference.

If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and −ax2 + bx + c = 0 has real roots.

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water . Find the volume of the water filled in the box .

If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?

An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another plane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will the two planes be after 112 hours?

How many three digits numbers divisible by 19 have the sum of their digits is 1

Find the sum of the first (i) 11 terms of the A.P.: 2,6,10,14,... (ii) 13 terms of the A.P.: -6,0,6,12,... (iii) 51 terms of the A.P.: whose second term is 2 and fourth term is 8.

If √x+√y=√2+√5, then √x−√y = ___

Solve the following quadratic equations by factorization:ax2+1-xa2+1=0

If n is any natural number, then 9n−5n ends with:

Question 12Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

Which of the following equations are consistent?

The sum of first ten terms of an A.P. is four times the sum of its first five terms. What is the ratio of first term and common difference?

Reflection of the point (−10,7) in the x-axis is ____________

(d/dx)(dy/dx)=(d²y)/(dx)²Is this correct?

Mark the correct alternative in the following question:If the sum of a number and its two-fifth is 70. The number is(a) 70 (b) 50 (c) 60 (d) 90

Prove the following trignometric identities: (1+cot2 A) sin2 A=1

Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?

Question 2Write whether the following statement is True or False?The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

In a triangle ABC, AB =20 cm, ∠A=30∘, AC = 18 cm. Find the area of the triangle

In the given figure, ABCD is a cyclic quadrilateral, B and D are the centres of two congruent circles. If the radius of each circle is 7 cm, then the area of the shaded region is equal to [use π=227]

(cos1°) (cos2°) (cos3°) ... (cos 88°) (cos89°) (cos90°) = ___.

Write the condition to be satisfied by q so that a rational number pq has a terminating decimal expansions.

Find out the wrong number in the series given below :1,2,6,15,31,56,91

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

In a school of 1900 students, there are 800 girls. Find the probability that a student chosen at random is a boy.

Complétez avec les prépositions convenables.

22. If one zero of the quadratic polynomial x-7x+5k is -2 then find the value of k

'3x - 7' is the polynomial in ___ variable.

Find the values of k for which the given equation has real and equal roots: [3 MARKS](k+1)x2−2(k−1)x+1=0

How many revolution would a cycle wheel of diameter 1.6m make to cover a distance of 352metres

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.___

While dividing a segment in a given ratio, we can not draw the ray at angles __ and _.