32581 + Interview Questions in Mathematics Page 226 InterviewSolution

11251.	Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 2x2−11x+15
Answer» Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : $2 x^{2} - 11 x + 15$

11251.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 2x2−11x+15

Answer»

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$2 x^{2} - 11 x + 15$

Discussion

11252.	If the numbers 2n − 1, 3n + 2 and 6n − 1 are in AP, then find n and hence find the numbers.
Answer» If the numbers 2n − 1, 3n + 2 and 6n − 1 are in AP, then find n and hence find the numbers.

Discussion

11253.	What do we get when we subtract 57 from 137 ?
Answer» What do we get when we subtract $\frac{5}{7}$ from $\frac{13}{7}$ ?

Discussion

11254.	A quadratic polynomial __________
Answer» A quadratic polynomial __________

Discussion

11255.	If A′=[−2312] and B=[−1012], then find (A+2B)′.
Answer» If $A^{'} = [\begin{matrix} - 2 & 3 1 & 2 \end{matrix}]$ and $B = [\begin{matrix} - 1 & 0 1 & 2 \end{matrix}]$ , then find $(A + 2 B)^{'}$ .

Discussion

11256.

Record the following transactions in the Sales Book of Ganesh & Co. of Jaipur (Rajasthan), who deal in Furniture. Assume CGST 6% and SGST 6% :- 2017 June 4 Sold to Gupta Furniture House, New Delhi :- 120 Chairs ₹ 2,500 per Chair 25 Table ₹ 8,000 per Table Less: 5% 8 Sold to Raja Furniture House, Ahmedabad (Gujarat) :- 8 Almirahs ₹ 15,000 each 9 Steel Cabinets ₹ 20,000 each Less: Trade discount of 10% 12 Sold old Computer for ₹ 1,500 to Mohan & Co. on Credit. 20 Sold 4 Sofa sets ₹ 25,000 each to Varun & Co. for cash 25 Sold to New Furniture House, Jaipur:- 5 Sofa sets ₹ 20,000 each 10 Tables ₹ 8,000 each 28 Purchased from Ram Lal & Co. Jaipur on credit :- 50 chairs ₹ 2,000 each

Answer» Record the following transactions in the Sales Book of Ganesh & Co. of Jaipur (Rajasthan), who deal in Furniture. Assume CGST 6% and SGST 6% :-

2017
June 4	Sold to Gupta Furniture House, New Delhi :-
	120 Chairs ₹ 2,500 per Chair
	25 Table ₹ 8,000 per Table
	Less: 5%
8	Sold to Raja Furniture House, Ahmedabad (Gujarat) :-
	8 Almirahs ₹ 15,000 each
	9 Steel Cabinets ₹ 20,000 each
	Less: Trade discount of 10%
12	Sold old Computer for ₹ 1,500 to Mohan & Co. on Credit.
20	Sold 4 Sofa sets ₹ 25,000 each to Varun & Co. for cash
25	Sold to New Furniture House, Jaipur:-
	5 Sofa sets ₹ 20,000 each
	10 Tables ₹ 8,000 each
28	Purchased from Ram Lal & Co. Jaipur on credit :-
	50 chairs ₹ 2,000 each

Discussion

11257.	Find the next number in the following sequence: 37.00, 34.50, 32.00, 29.50...
Answer» Find the next number in the following sequence: 37.00, 34.50, 32.00, 29.50...

Discussion

11258.	Prove thatcosA−sinA+1cosA+sinA−1=cosecA+cotA
Answer» Prove that $\frac{c o s A - s i n A + 1}{c o s A + s i n A - 1} = c o s e c A + c o t A$

Discussion

11259.	If the volume of a hemisphere is 18π cm3, then its total surface area is __________.
Answer» If the volume of a hemisphere is 18π cm³, then its total surface area is __________.

Discussion

11260.	The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).
Answer» The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).

Discussion

11261.	Which one of the following option is always correct for x>0
Answer» Which one of the following option is always correct for $x > 0$

Discussion

11262.	With 200 roses, a person starts walking from his home to the temple which is 50 m far from his home. After walking each metre, he drops 2 roses. Form a series for the number of roses the person has after walking each metre.
Answer» With 200 roses, a person starts walking from his home to the temple which is 50 m far from his home. After walking each metre, he drops 2 roses. Form a series for the number of roses the person has after walking each metre.

Discussion

11263.	Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1)
Answer» Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1)

Discussion

11264.	Question 5 (i) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) (cosecθ−cotθ)2=(1−cosθ)(1+cosθ)
Answer» Question 5 (i) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) $(c o s e c θ - c o t θ)^{2} = \frac{(1 - c o s θ)}{(1 + c o s θ)}$

Discussion

11265.	The areas of two similar triangles are 100 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other.
Answer» The areas of two similar triangles are 100 cm² and 49 cm² respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other.

Discussion

11266.	The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….
Answer» The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….

Discussion

11267.	Express each number as product of its prime factors:
Answer» Express each number as product of its prime factors:

11267.

Express each number as product of its prime factors:

Answer»

Express each number as product of its prime factors:

Discussion

11268.	The total remuneration paid to labourers, employed to harvest soyabeen is in direct variation with the number of labourers. If remuneration of 4 labourers is ₹ 1000, find the remuneration of 17 labourers.
Answer» The total remuneration paid to labourers, employed to harvest soyabeen is in direct variation with the number of labourers. If remuneration of 4 labourers is ₹ 1000, find the remuneration of 17 labourers.

Discussion

11269.	Question 6Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.
Answer» Question 6 Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.

Discussion

11270.	If the point P(x,y) is equidistant from the points A(5,1) and B(-1,5), then prove that 3x=2y
Answer» If the point P(x,y) is equidistant from the points A(5,1) and B(-1,5), then prove that 3x=2y

Discussion

11271.	In what ratio does the point p(24/7 ,y) divides the line segment joining the point (2 , -2) and (3,7) also find y
Answer» In what ratio does the point p(24/7 ,y) divides the line segment joining the point (2 , -2) and (3,7) also find y

Discussion

11272.	The second term of a G.P. is 100 and the common ratio is 1n, where n is a natural number. Pn is the product of first n terms of the G.P. P7 > P6 and P7 > P7 , what is the sum of all possible values of n?
Answer» The second term of a G.P. is 100 and the common ratio is $\frac{1}{n}$ , where n is a natural number. $P_{n}$ is the product of first n terms of the G.P. $P_{7}$ > $P_{6}$ and $P_{7}$ > $P_{7}$ , what is the sum of all possible values of n?

Discussion

11273.	Find the sum and product of the roots of the equation x2 – 2x – 15 = 0
Answer» Find the sum and product of the roots of the equation $x^{2}$ – 2x – 15 = 0

Discussion

11274.	Which graph has a vertical stretch factor of 12 when compared to the graph of y=x2?
Answer» Which graph has a vertical stretch factor of $\frac{1}{2}$ when compared to the graph of $y = x^{2}$ ?

Discussion

11275.	The annual rainfall record of a city for 66 days is given in the following table:Rainfall (in cm): 0 - 10 10 - 20 20 -30 30 - 40 40 - 50 50 - 60Number of days: 22 10 8 15 5 6Calculate the median rainfall using ogives of more than type and less than type.
Answer» The annual rainfall record of a city for 66 days is given in the following table: Rainfall (in cm): 0 - 10 10 - 20 20 -30 30 - 40 40 - 50 50 - 60 Number of days: 22 10 8 15 5 6 Calculate the median rainfall using ogives of more than type and less than type.

Discussion

11276.	Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to 13 of the larger part. Then find the length of the larger part.
Answer» Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to $\frac{1}{3}$ of the larger part. Then find the length of the larger part.

Discussion

11277.	2. As observed from a point 60 m above a lake, the angle of elevation of an advertising ballonas measure 30 and from the same point the angle of depression of the image of the ballon in theh,lake has measure 60. Calculate the height of the balloon above the lake.
Answer» 2. As observed from a point 60 m above a lake, the angle of elevation of an advertising ballonas measure 30 and from the same point the angle of depression of the image of the ballon in theh,lake has measure 60. Calculate the height of the balloon above the lake.

Discussion

11278.	47.Solve the equation : \|\|x+3\|-5\|=2
Answer» 47.Solve the equation : \|\|x+3\|-5\|=2

Discussion

11279.	Solve −5(x+4)>30;x ϵ Z
Answer» Solve $- 5 (x + 4) > 30; x ϵ Z$

Discussion

11280.	47 If p(x)=ax3-bx2-3x+18 is divided by x+1 and x+2 then the remainder are 12 and -20 respectively. The values of a and b are respectively ?
Answer» 47 If p(x)=ax3-bx2-3x+18 is divided by x+1 and x+2 then the remainder are 12 and -20 respectively. The values of a and b are respectively ?

Discussion

11281.	15 find the equation of the circle which passes through the vertices of the triangle formed by L1 = x + y +1 =0 ; L2 =3x + y -5 =0 ; L3= 2x + y -5 =0.
Answer» 15 find the equation of the circle which passes through the vertices of the triangle formed by L1 = x + y +1 =0 ; L2 =3x + y -5 =0 ; L3= 2x + y -5 =0.

Discussion

11282.	Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
Answer» Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

11282.

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

Answer»

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

Discussion

11283.	Find the value of constant ‘m’ if : y = – 1 is a root of quadratic equation 7+4(m+2)y–y2 = 0. __
Answer» Find the value of constant ‘m’ if : y = – 1 is a root of quadratic equation $7 + 4 (m + 2) y - y^{2}$ = 0. __

Discussion

11284.	In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to
Answer» In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to

11284.

In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to

Answer»

In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to

Discussion

11285.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

11286.	In figure,AX bisects ∠BAC as well as ∠BDC. State the three facts needed to ensure that ΔACD ≅ ΔABD
Answer» In figure,AX bisects ∠BAC as well as ∠BDC. State the three facts needed to ensure that ΔACD ≅ ΔABD

Discussion

11287.	The houses in a row are numbered consecutively from 1 to 49. Show that there is a value m such that the sum of numbers of the houses preceding the house marked m is equal to the sum of the numbers of houses following it. Find the value 'm'.
Answer» The houses in a row are numbered consecutively from 1 to 49. Show that there is a value m such that the sum of numbers of the houses preceding the house marked m is equal to the sum of the numbers of houses following it. Find the value 'm'.

Discussion

11288.	Which of the following is true for the given pair of triangles?
Answer» Which of the following is true for the given pair of triangles?

Discussion

11289.	The roots of the quadratic equation x2+5x-14=0 is
Answer» The roots of the quadratic equation $x^{2}$ +5x-14=0 is

Discussion

11290.	It is a KVPY question Let a1,a2,a3,a4 be real number such that a1+a2+a3+a4=0 and a1^2+a2^2+a3^2+a4^2=1 then the smallest possible value of the expression (a1-a2)^2+(a2-a3)^2+(a3-a4)^2+(a4-a1)^2 lies in which interval. Not sure about the chapter..
Answer» It is a KVPY question Let a1,a2,a3,a4 be real number such that a1+a2+a3+a4=0 and a1^2+a2^2+a3^2+a4^2=1 then the smallest possible value of the expression (a1-a2)^2+(a2-a3)^2+(a3-a4)^2+(a4-a1)^2 lies in which interval. Not sure about the chapter..

Discussion

11291.	3. A point A is at a distance of \sqrt{29} from the pointB(6,-3). Find the coordinates of A, if its ordinateis half of its abscissa.
Answer» 3. A point A is at a distance of \sqrt{29} from the pointB(6,-3). Find the coordinates of A, if its ordinateis half of its abscissa.

Discussion

11292.	In the given figure, RS \|\| DB \|\| PQ. If CP = PD = 11 cm and DR = RA = 3 cm. Then the values of x and y are respectively. (a) 12, 10(b) 14, 6(c) 10, 7(d) 16, 8
Answer» In the given figure, RS \|\| DB \|\| PQ. If CP = PD = 11 cm and DR = RA = 3 cm. Then the values of x and y are respectively. (a) 12, 10 (b) 14, 6 (c) 10, 7 (d) 16, 8

Discussion

11293.	Solve each of the following equations by using the method of completing the square:x2-2+1x+2=0
Answer» Solve each of the following equations by using the method of completing the square: $x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

Discussion

11294.	Are there numbers x and y such that?
Answer» Are there numbers x and y such that?

11294.

Are there numbers x and y such that?

Answer»

Are there numbers x and y such that?

Discussion

11295.	In a triangle ABC, if 2a=√3b+c, then
Answer» In a triangle $A B C,$ if $2 a = \sqrt{3} b + c,$ then

Discussion

11296.	2 years ago, a man’s age was 3 times the square of his son’s age. 3 years hence, his age will be 4 times his son’s age. Find their present ages.
Answer» 2 years ago, a man’s age was 3 times the square of his son’s age. 3 years hence, his age will be 4 times his son’s age. Find their present ages.

Discussion

11297.	In an isosceles ΔABC, the base AB is produced both the ways to P and Q such that AP×BQ=AC2. Prove that ΔAPC∼ΔBCQ.
Answer» In an isosceles $Δ A B C$ , the base AB is produced both the ways to P and Q such that $A P \times B Q = A C^{2}$ . Prove that $Δ A P C \sim Δ B C Q$ .

Discussion

11298.

Write the correct alternative for the following questions.(1) If the Face Value of a share is Rs 100 and Market value is Rs 75, then which of the following statements is correct ? (A) The share is at premium of Rs 175 (B) The share is at discount of Rs 25 (C) The share is at premium of Rs 25 (D) The share is at discount of Rs 75 (2) What is the amount of dividend received per share of face value Rs 10 and dividend declared is 50%. (A) Rs 50 (B) Rs 5 (C) Rs 500 (D) Rs 100 (3) The NAV of a unit in mutual fund scheme is Rs 10.65 then find the amount required to buy 500 such units. (A) 5325 (B) 5235 (C) 532500 (D) 53250 (4) Rate of GST on brokerage is ... (A) 5% (B) 12% (C) 18% (D) 28% (5) To find the cost of one share at the time of buying the amount of Brokerage and GST is to be ... the MV of share . (A) added to (B) substracted from (C) Multiplied with (D) divided by

Answer» Write the correct alternative for the following questions.

(1) If the Face Value of a share is Rs 100 and Market value is Rs 75, then which of the following statements is correct ?

(A) The share is at premium of Rs 175	(B) The share is at discount of Rs 25
(C) The share is at premium of Rs 25	(D) The share is at discount of Rs 75

(2) What is the amount of dividend received per share of face value Rs 10 and dividend declared is 50%.

(A) Rs 50

(B) Rs 5

(C) Rs 500

(D) Rs 100

(3) The NAV of a unit in mutual fund scheme is Rs 10.65 then find the amount required to buy 500 such units.

(A) 5325

(B) 5235

(C) 532500

(D) 53250

(4) Rate of GST on brokerage is ...

(A) 5%

(B) 12%

(C) 18%

(D) 28%

(5) To find the cost of one share at the time of buying the amount of Brokerage and GST is to be ... the MV of share .

(A) added to	(B) substracted from
(C) Multiplied with	(D) divided by

Discussion

11299.	Question 11In figure , O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 and OT intersect the circle at E, if AB is the tangent to the circle at E, find the length of AB.
Answer» Question 11 In figure , O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 and OT intersect the circle at E, if AB is the tangent to the circle at E, find the length of AB.

Discussion

11300.

On comparing the ratios, find out whether the following pair of linear equations are consistent, or inconsistent.

Answer»

On comparing the ratios, find out whether the following pair of linear equations are consistent, or inconsistent.

Discussion

Explore topic-wise InterviewSolutions in .

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 2x2−11x+15

If the numbers 2n − 1, 3n + 2 and 6n − 1 are in AP, then find n and hence find the numbers.

What do we get when we subtract 57 from 137 ?

A quadratic polynomial __________

If A′=[−2312] and B=[−1012], then find (A+2B)′.

Find the next number in the following sequence: 37.00, 34.50, 32.00, 29.50...

Prove thatcosA−sinA+1cosA+sinA−1=cosecA+cotA

If the volume of a hemisphere is 18π cm3, then its total surface area is __________.

The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).

Which one of the following option is always correct for x&gt;0

With 200 roses, a person starts walking from his home to the temple which is 50 m far from his home. After walking each metre, he drops 2 roses. Form a series for the number of roses the person has after walking each metre.

Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1)

Question 5 (i) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) (cosecθ−cotθ)2=(1−cosθ)(1+cosθ)

The areas of two similar triangles are 100 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other.

The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….

Express each number as product of its prime factors:

The total remuneration paid to labourers, employed to harvest soyabeen is in direct variation with the number of labourers. If remuneration of 4 labourers is ₹ 1000, find the remuneration of 17 labourers.

Question 6Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

If the point P(x,y) is equidistant from the points A(5,1) and B(-1,5), then prove that 3x=2y

In what ratio does the point p(24/7 ,y) divides the line segment joining the point (2 , -2) and (3,7) also find y

The second term of a G.P. is 100 and the common ratio is 1n, where n is a natural number. Pn is the product of first n terms of the G.P. P7 &gt; P6 and P7 &gt; P7 , what is the sum of all possible values of n?

Find the sum and product of the roots of the equation x2 – 2x – 15 = 0

Which graph has a vertical stretch factor of 12 when compared to the graph of y=x2?

The annual rainfall record of a city for 66 days is given in the following table:Rainfall (in cm): 0 - 10 10 - 20 20 -30 30 - 40 40 - 50 50 - 60Number of days: 22 10 8 15 5 6Calculate the median rainfall using ogives of more than type and less than type.

Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to 13 of the larger part. Then find the length of the larger part.

2. As observed from a point 60 m above a lake, the angle of elevation of an advertising ballonas measure 30 and from the same point the angle of depression of the image of the ballon in theh,lake has measure 60. Calculate the height of the balloon above the lake.

47.Solve the equation : ||x+3|-5|=2

Solve −5(x+4)&gt;30;x ϵ Z

47 If p(x)=ax3-bx2-3x+18 is divided by x+1 and x+2 then the remainder are 12 and -20 respectively. The values of a and b are respectively ?

15 find the equation of the circle which passes through the vertices of the triangle formed by L1 = x + y +1 =0 ; L2 =3x + y -5 =0 ; L3= 2x + y -5 =0.

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

Find the value of constant ‘m’ if : y = – 1 is a root of quadratic equation 7+4(m+2)y–y2 = 0. __

In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to

How many irrational numbers exist between two rational numbers?

In figure,AX bisects ∠BAC as well as ∠BDC. State the three facts needed to ensure that ΔACD ≅ ΔABD

The houses in a row are numbered consecutively from 1 to 49. Show that there is a value m such that the sum of numbers of the houses preceding the house marked m is equal to the sum of the numbers of houses following it. Find the value 'm'.

Which of the following is true for the given pair of triangles?

The roots of the quadratic equation x2+5x-14=0 is

It is a KVPY question Let a1,a2,a3,a4 be real number such that a1+a2+a3+a4=0 and a1^2+a2^2+a3^2+a4^2=1 then the smallest possible value of the expression (a1-a2)^2+(a2-a3)^2+(a3-a4)^2+(a4-a1)^2 lies in which interval. Not sure about the chapter..

3. A point A is at a distance of \sqrt{29} from the pointB(6,-3). Find the coordinates of A, if its ordinateis half of its abscissa.

In the given figure, RS || DB || PQ. If CP = PD = 11 cm and DR = RA = 3 cm. Then the values of x and y are respectively. (a) 12, 10(b) 14, 6(c) 10, 7(d) 16, 8

Solve each of the following equations by using the method of completing the square:x2-2+1x+2=0

Are there numbers x and y such that?

In a triangle ABC, if 2a=√3b+c, then

2 years ago, a man’s age was 3 times the square of his son’s age. 3 years hence, his age will be 4 times his son’s age. Find their present ages.

In an isosceles ΔABC, the base AB is produced both the ways to P and Q such that AP×BQ=AC2. Prove that ΔAPC∼ΔBCQ.

Question 11In figure , O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 and OT intersect the circle at E, if AB is the tangent to the circle at E, find the length of AB.

On comparing the ratios, find out whether the following pair of linear equations are consistent, or inconsistent.

Which one of the following option is always correct for x>0

The second term of a G.P. is 100 and the common ratio is 1n, where n is a natural number. Pn is the product of first n terms of the G.P. P7 > P6 and P7 > P7 , what is the sum of all possible values of n?

Solve −5(x+4)>30;x ϵ Z