32581 + Interview Questions in Mathematics Page 198 InterviewSolution

9851.	If (1+4p)4,(1−p)2,and (1−2p)2 are the probabilities of three mutually exclusive events , then the value of p is
Answer» If $\frac{(1 + 4 p)}{4}, \frac{(1 - p)}{2}, and \frac{(1 - 2 p)}{2}$ are the probabilities of three mutually exclusive events , then the value of p is

Discussion

9852.	Solve the following linear equations :(i) x – 11 =7(ii) z + 8 = 9(iii) 11x = 121
Answer» Solve the following linear equations : (i) x – 11 =7 (ii) z + 8 = 9 (iii) 11x = 121

Discussion

9853.	cosθ1−tanθ+sinθ1−cotθ = ___
Answer» $\frac{c o s θ}{1 - t a n θ} + \frac{s i n θ}{1 - c o t θ}$ = ___

Discussion

9854.	From an external point P , tangents PA = PB are drawn to a circle with centre O . If ∠PAB= 50°, then find ∠AOB.
Answer» From an external point P , tangents PA = PB are drawn to a circle with centre O . If $∠ P A B = 50^{°}$ , then find $∠ A O B$ .

Discussion

9855.	∠ABC=x and ∠ADC=2x. Find ∠COD
Answer» $∠ A B C = x a n d ∠ A D C = 2 x$ . Find $∠ C O D$

Discussion

9856.	On dividing x3−3x2+x+2 by a polynomial g(x), the quotient and remainder were x−2 and −2x+4, respectively. Find g(x).
Answer» On dividing $x^{3} - 3 x^{2} + x + 2$ by a polynomial g(x), the quotient and remainder were $x - 2$ and $- 2 x + 4$ , respectively. Find g(x).

Discussion

9857.	Solve: (xx+2)2−7(xx+2)+12=0;x≠−2.
Answer» Solve: ${(\frac{x}{x + 2})}^{2} - 7 (\frac{x}{x + 2}) + 12 = 0; x \neq - 2.$

9857.

Solve: (xx+2)2−7(xx+2)+12=0;x≠−2.

Answer»

Solve: ${(\frac{x}{x + 2})}^{2} - 7 (\frac{x}{x + 2}) + 12 = 0; x \neq - 2.$

Discussion

9858.	The present age of a father is three years more than three times the age of the son. Three years hence father’s age will be 10 years more than twice the age of the son. Determine their present ages.
Answer» The present age of a father is three years more than three times the age of the son. Three years hence father’s age will be 10 years more than twice the age of the son. Determine their present ages.

Discussion

9859.	The dimensions of a rectangular block with Vermeer calliper having least count 0.1mm 5.0mm10.0mm10.0mm the maximum percentage error in the measurement of volume of the block is
Answer» The dimensions of a rectangular block with Vermeer calliper having least count 0.1mm 5.0mm10.0mm10.0mm the maximum percentage error in the measurement of volume of the block is

Discussion

9860.	If a,b and c are in continued proportion, then ac= _____.
Answer» If $a, b$ and $c$ are in continued proportion, then $\frac{a}{c} =$ _____.

Discussion

9861.	What is radius?
Answer» What is radius?

Discussion

9862.	How many terms of the AP 3,7,11,15,... willl make the sum 406 ? (a) 10 (b) 12 (c) 14 (d) 20
Answer» How many terms of the AP 3,7,11,15,... willl make the sum 406 ? (a) 10 (b) 12 (c) 14 (d) 20

Discussion

9863.	A person has a rectangular garden whose area is 100 sq m.He fences 3 sides with 30m barbed wire.On the fourth side,the wall of his house is constructed.Find dimensions of the garden.
Answer» A person has a rectangular garden whose area is 100 sq m.He fences 3 sides with 30m barbed wire.On the fourth side,the wall of his house is constructed.Find dimensions of the garden.

Discussion

9864.	If (secθ−tanθ)=13, the value of;(secθ+tanθ) is:
Answer» If $(s e c θ - t a n θ) = \frac{1}{3}$ , the value of; $(s e c θ + t a n θ)$ is:

Discussion

9865.	Find the smallest value of a and b such that 3a=2b?
Answer» Find the smallest value of $a$ and $b$ such that $3 a = 2 b ?$

Discussion

9866.	Question 92 (xx)Factorise the following using the identity a2−b2=(a+b)(a−b).y4−625
Answer» Question 92 (xx) Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$ $y^{4} - 625$

9866.

Question 92 (xx)Factorise the following using the identity a2−b2=(a+b)(a−b).y4−625

Answer»

Question 92 (xx)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$y^{4} - 625$

Discussion

9867.	How many terms of the series(a) 2 + 4 + 8 + …….makes the sum 1022(b) 3 + 9 + 27 + ……. make the sum of 1092(c) 2 + 6 + 18 + ……. make the sum 728
Answer» How many terms of the series (a) 2 + 4 + 8 + …….makes the sum 1022 (b) 3 + 9 + 27 + ……. make the sum of 1092 (c) 2 + 6 + 18 + ……. make the sum 728

9867.

How many terms of the series(a) 2 + 4 + 8 + …….makes the sum 1022(b) 3 + 9 + 27 + ……. make the sum of 1092(c) 2 + 6 + 18 + ……. make the sum 728

Answer»

How many terms of the series

(a) 2 + 4 + 8 + …….makes the sum 1022

(b) 3 + 9 + 27 + ……. make the sum of 1092

(c) 2 + 6 + 18 + ……. make the sum 728

Discussion

9868.	∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?
Answer» $\sum$ fx = 5x + 2, $\sum$ f = 12. If the mean of the distribution is 6, what is the value of x?

Discussion

9869.	If x, y, z are different from zero and 1+x1111+y1111+z=0, then the value of x−1 + y−1 + z−1 is(a) xyz(b) x−1 y−1 z−1(c) − x − y − z(d) − 1
Answer» If x, y, z are different from zero and $\|\begin{matrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{matrix}\| = 0$ , then the value of x⁻¹ + y⁻¹ + z⁻¹ is (a) xyz (b) x⁻¹ y⁻¹ z⁻¹ (c) − x − y − z (d) − 1

Discussion

9870.	What must be added to 3x3 + x2 − 22x + 9 so that the result is exactly divisible by 3x2 + 7x − 6?
Answer» What must be added to 3x³ + x² − 22x + 9 so that the result is exactly divisible by 3x² + 7x − 6?

Discussion

9871.	The points whose abscissa and ordinate have different signs will lie in(a) I and II quadrants(b) II and III quadrants(c) I and III quadrants(d) II and IV quadrants
Answer» The points whose abscissa and ordinate have different signs will lie in (a) I and II quadrants (b) II and III quadrants (c) I and III quadrants (d) II and IV quadrants

Discussion

9872.	Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.
Answer» Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.

Discussion

9873.	Solve each of the following systems of equations by the method of cross-multiplication :ax + by = a2bx + ay = b2
Answer» Solve each of the following systems of equations by the method of cross-multiplication : ax + by = a² bx + ay = b²

Discussion

9874.	∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?
Answer» $\sum$ fx = 5x + 2, $\sum$ f = 12. If the mean of the distribution is 6, what is the value of x?

Discussion

9875.	What is theta and tan theta?
Answer» What is theta and tan theta?

Discussion

9876.	Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Answer» Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).

Discussion

9877.	42. X positive integers are multipled together what is the probability that last digit of the number is 5?
Answer» 42. X positive integers are multipled together what is the probability that last digit of the number is 5?

Discussion

9878.	Cot theta + tan theta=cosec theta ×sec theta
Answer» Cot theta + tan theta=cosec theta ×sec theta

Discussion

9879.	If the equation x2−px+216=0 has one root as a square of the other, find the value of p
Answer» If the equation $x^{2} - p x + 216 = 0$ has one root as a square of the other, find the value of p

Discussion

9880.	The sum of the first 8 terms of an arithmetic progression is 328. The ratio of term 5th to term 25th of the AP is 23:123. What is the value of the 77th term of the AP?
Answer» The sum of the first 8 terms of an arithmetic progression is 328. The ratio of term 5th to term 25th of the AP is 23:123. What is the value of the 77th term of the AP?

Discussion

9881.	If sin θ=45, what is the value of cotθ + cosecθ?
Answer» If $\sin θ = \frac{4}{5}$ , what is the value of cotθ + cosecθ?

Discussion

9882.	In the given figure, RQ and TP are perpendicular to PQ, also TS⊥PR prove that ST. RQ = PS. PQ.
Answer» In the given figure, RQ and TP are perpendicular to PQ, also $T S ⊥ P R$ prove that ST. RQ = PS. PQ.

Discussion

9883.	A shuttle cock used for playing badminton has the shape of the combination of :
Answer» A shuttle cock used for playing badminton has the shape of the combination of :

Discussion

9884.	Find the value of k for which each of the following system of equations have infinitely many solutions :kx-2y+6=04x-3y+9=0
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $k x - 2 y + 6 = 0 4 x - 3 y + 9 = 0$

Discussion

9885.	How long will a girl take to walk around the boundary of a square field of area 9 hectars at the rate of 6 kilometers per hour?
Answer» How long will a girl take to walk around the boundary of a square field of area $9$ hectars at the rate of $6$ kilometers per hour?

Discussion

9886.	The number of tangents that can be drawn from an external point to a circle is [CBSE 2011, 12](1) 1(2) 2(3) 3(4) 4
Answer» The number of tangents that can be drawn from an external point to a circle is [CBSE 2011, 12] (1) 1 (2) 2 (3) 3 (4) 4

Discussion

9887.	The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___
Answer» The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___

Discussion

9888.	How many terms of the A.P. 27, 24, 21, ... are required to get the sum as 0?
Answer» How many terms of the A.P. 27, 24, 21, ... are required to get the sum as 0?

Discussion

9889.	Solve each of the following systems of equations by the method of cross-multiplication :xa-b+aba-b=ya+b-aba+bx+y=2a2
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $x (a - b + \frac{a b}{a - b}) = y (a + b - \frac{a b}{a + b}) x + y = 2 a^{2}$

Discussion

9890.	From the given figure, determine tan A.
Answer» From the given figure, determine tan A.

Discussion

9891.	In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that ∠ PQR=58∘, calculate ∠ RPQ.
Answer» In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that $∠ P Q R = 58^{\circ},$ calculate $∠ R P Q .$

9891.

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that ∠ PQR=58∘, calculate ∠ RPQ.

Answer»

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that $∠ P Q R = 58^{\circ},$ calculate $∠ R P Q .$

Discussion

9892.	for what value of n the nth term of the following 2 A.P.s are same? i) 1,7,13,19... ii) 69,68,67
Answer» for what value of n the nth term of the following 2 A.P.s are same? i) 1,7,13,19... ii) 69,68,67

Discussion

9893.	The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find(i) the difference between the heights of the light-house and the building.(ii) the distance between the light-house and the building .
Answer» The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find (i) the difference between the heights of the light-house and the building. (ii) the distance between the light-house and the building .

Discussion

9894.	Dinesh brought an article for Rs.374, which included a discount of 15% on the marked price and a sales tax of 10% on the reduced price. Find the marked price of the article.
Answer» Dinesh brought an article for Rs.374, which included a discount of 15% on the marked price and a sales tax of 10% on the reduced price. Find the marked price of the article.

Discussion

9895.	Prove that there is ona and only one tangent at any point on the circumference of a circle.
Answer» Prove that there is ona and only one tangent at any point on the circumference of a circle.

Discussion

9896.	The following are the marks obtained by 9 students in Mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median is(a) 9 (b) 10.5 (c) 12.67 (d) 14.67
Answer» The following are the marks obtained by 9 students in Mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median is (a) 9 (b) 10.5 (c) 12.67 (d) 14.67

Discussion

9897.	If A=[543−1],B=[2104] and C=[−3210] then find A + B - C
Answer» If $A = [\begin{matrix} 5 & 4 3 & - 1 \end{matrix}], B = [\begin{matrix} 2 & 1 0 & 4 \end{matrix}]$ and $C = [\begin{matrix} - 3 & 2 1 & 0 \end{matrix}]$ then find A + B - C

Discussion

9898.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:1x-1x-2=3, x≠0, 2 [CBSE 2010]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $\frac{1}{x} - \frac{1}{x - 2} = 3, x \neq 0, 2$ [CBSE 2010]

Discussion

9899.	One cubic metre of copper is melted and recast into a square cross-section bar 36 m long. An exact cube is cut off from this bar. If 1 cubic metre of copper costs Rs 108, then the cost of thiscube is(a) 50 paise(c) One rupee(b) 75 paise(d) 1.50 rupee
Answer» One cubic metre of copper is melted and recast into a square cross-section bar 36 m long. An exact cube is cut off from this bar. If 1 cubic metre of copper costs Rs 108, then the cost of thiscube is(a) 50 paise(c) One rupee(b) 75 paise(d) 1.50 rupee

Discussion

9900.	Question 21 (i) Find the sum: 1 + (-2) + (-5) + (-8) + . . . + (-236)
Answer» Question 21 (i) Find the sum: 1 + (-2) + (-5) + (-8) + . . . + (-236)

Discussion

Explore topic-wise InterviewSolutions in .

If (1+4p)4,(1−p)2,and (1−2p)2 are the probabilities of three mutually exclusive events , then the value of p is

Solve the following linear equations :(i) x – 11 =7(ii) z + 8 = 9(iii) 11x = 121

cosθ1−tanθ+sinθ1−cotθ = ___

From an external point P , tangents PA = PB are drawn to a circle with centre O . If ∠PAB= 50°, then find ∠AOB.

∠ABC=x and ∠ADC=2x. Find ∠COD

On dividing x3−3x2+x+2 by a polynomial g(x), the quotient and remainder were x−2 and −2x+4, respectively. Find g(x).

Solve: (xx+2)2−7(xx+2)+12=0;x≠−2.

The present age of a father is three years more than three times the age of the son. Three years hence father’s age will be 10 years more than twice the age of the son. Determine their present ages.

The dimensions of a rectangular block with Vermeer calliper having least count 0.1mm 5.0mm10.0mm10.0mm the maximum percentage error in the measurement of volume of the block is

If a,b and c are in continued proportion, then ac= _____.

What is radius?

How many terms of the AP 3,7,11,15,... willl make the sum 406 ? (a) 10 (b) 12 (c) 14 (d) 20

A person has a rectangular garden whose area is 100 sq m.He fences 3 sides with 30m barbed wire.On the fourth side,the wall of his house is constructed.Find dimensions of the garden.

If (secθ−tanθ)=13, the value of;(secθ+tanθ) is:

Find the smallest value of a and b such that 3a=2b?

Question 92 (xx)Factorise the following using the identity a2−b2=(a+b)(a−b).y4−625

How many terms of the series(a) 2 + 4 + 8 + …….makes the sum 1022(b) 3 + 9 + 27 + ……. make the sum of 1092(c) 2 + 6 + 18 + ……. make the sum 728

∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?

If x, y, z are different from zero and 1+x1111+y1111+z=0, then the value of x−1 + y−1 + z−1 is(a) xyz(b) x−1 y−1 z−1(c) − x − y − z(d) − 1

What must be added to 3x3 + x2 − 22x + 9 so that the result is exactly divisible by 3x2 + 7x − 6?

The points whose abscissa and ordinate have different signs will lie in(a) I and II quadrants(b) II and III quadrants(c) I and III quadrants(d) II and IV quadrants

Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.

Solve each of the following systems of equations by the method of cross-multiplication :ax + by = a2bx + ay = b2

∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?

What is theta and tan theta?

Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).

42. X positive integers are multipled together what is the probability that last digit of the number is 5?

Cot theta + tan theta=cosec theta ×sec theta

If the equation x2−px+216=0 has one root as a square of the other, find the value of p

The sum of the first 8 terms of an arithmetic progression is 328. The ratio of term 5th to term 25th of the AP is 23:123. What is the value of the 77th term of the AP?

If sin θ=45, what is the value of cotθ + cosecθ?

In the given figure, RQ and TP are perpendicular to PQ, also TS⊥PR prove that ST. RQ = PS. PQ.

A shuttle cock used for playing badminton has the shape of the combination of :

Find the value of k for which each of the following system of equations have infinitely many solutions :kx-2y+6=04x-3y+9=0

How long will a girl take to walk around the boundary of a square field of area 9 hectars at the rate of 6 kilometers per hour?

The number of tangents that can be drawn from an external point to a circle is [CBSE 2011, 12](1) 1(2) 2(3) 3(4) 4

The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___

How many terms of the A.P. 27, 24, 21, ... are required to get the sum as 0?

Solve each of the following systems of equations by the method of cross-multiplication :xa-b+aba-b=ya+b-aba+bx+y=2a2

From the given figure, determine tan A.

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that ∠ PQR=58∘, calculate ∠ RPQ.

for what value of n the nth term of the following 2 A.P.s are same? i) 1,7,13,19... ii) 69,68,67

The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find(i) the difference between the heights of the light-house and the building.(ii) the distance between the light-house and the building .

Dinesh brought an article for Rs.374, which included a discount of 15% on the marked price and a sales tax of 10% on the reduced price. Find the marked price of the article.

Prove that there is ona and only one tangent at any point on the circumference of a circle.

The following are the marks obtained by 9 students in Mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median is(a) 9 (b) 10.5 (c) 12.67 (d) 14.67

If A=[543−1],B=[2104] and C=[−3210] then find A + B - C

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:1x-1x-2=3, x≠0, 2 [CBSE 2010]

One cubic metre of copper is melted and recast into a square cross-section bar 36 m long. An exact cube is cut off from this bar. If 1 cubic metre of copper costs Rs 108, then the cost of thiscube is(a) 50 paise(c) One rupee(b) 75 paise(d) 1.50 rupee

Question 21 (i) Find the sum: 1 + (-2) + (-5) + (-8) + . . . + (-236)