24740 + Interview Questions in Mathematics Page 180 InterviewSolution

8951.	(x+1) is a factor of the polynomial (a) x3−2x2+x+2 (b) x3+2x2+x−2 (c) x3+2x2−x−2 (d) x3+2x2−x+2
Answer» $(x + 1)$ is a factor of the polynomial (a) $x^{3} - 2 x^{2} + x + 2$ (b) $x^{3} + 2 x^{2} + x - 2$ (c) $x^{3} + 2 x^{2} - x - 2$ (d) $x^{3} + 2 x^{2} - x + 2$

Discussion

8952.	The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from the group,then the mean of of the remaining students is(a) 20 kg (b) 21 kg (c) 19 kg (d) 18 kg
Answer» The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from the group, then the mean of of the remaining students is (a) 20 kg (b) 21 kg (c) 19 kg (d) 18 kg

Discussion

8953.	If a, b are positive integers such that a < b and a b ab=25, then (a, b) = ____________.
Answer» If a, b are positive integers such that a < b and $[a b] [\begin{matrix} a \\ b \end{matrix}] = 25,$ then (a, b) = ____________.

Discussion

8954.	In the given figure, ABCD is a trapezium in which AB \|\| DC and DC = 40 cm and AB = 60 cm. If X and Y are, respectively, the mid-points of AD and BC, prove that:(i) XY = 50 cm(ii) DCYX is a trapezium(iii) ar (trap. DCYX) = 911 ar (trap. (XYBA)
Answer» In the given figure, ABCD is a trapezium in which AB \|\| DC and DC = 40 cm and AB = 60 cm. If X and Y are, respectively, the mid-points of AD and BC, prove that: (i) XY = 50 cm (ii) DCYX is a trapezium (iii) ar (trap. DCYX) = $\frac{9}{11}$ ar (trap. (XYBA)

Discussion

8955.	The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2.
Answer» The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m².

Discussion

8956.	In a circle of radius 5 centimetres, two chords of lengths 6 centimetres and 8 centimetres are drawn parallel to each other, on either side of the centre. What is the distance between these chords?
Answer» In a circle of radius 5 centimetres, two chords of lengths 6 centimetres and 8 centimetres are drawn parallel to each other, on either side of the centre. What is the distance between these chords?

8956.

In a circle of radius 5 centimetres, two chords of lengths 6 centimetres and 8 centimetres are drawn parallel to each other, on either side of the centre. What is the distance between these chords?

Answer»

In a circle of radius 5 centimetres, two chords of lengths 6 centimetres and 8 centimetres are drawn parallel to each other, on either side of the centre. What is the distance between these chords?

Discussion

8957.	If A={x:x is a prime number} and B={x:x≤10, x∈N}, then A∩B = ___.
Answer» If $A = {x : x is a prime number}$ and $B = {x : x \leq 10, x \in N},$ then $A \cap B$ = ___.

8957.

If A={x:x is a prime number} and B={x:x≤10, x∈N}, then A∩B = ___.

Answer»

If $A = {x : x is a prime number}$ and

$B = {x : x \leq 10, x \in N},$ then $A \cap B$ = ___.

Discussion

8958.	In the given figure, ABCD is a rhombus, then the value of 'x' is
Answer» In the given figure, ABCD is a rhombus, then the value of 'x' is

Discussion

8959.	A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?
Answer» A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

Discussion

8960.	how to identify a non real number in an algebraic expression
Answer» how to identify a non real number in an algebraic expression

Discussion

8961.	Question 49In the following question, fill in the blanks to make the statements true.The usual form of 2.39461×106 is ___
Answer» Question 49 In the following question, fill in the blanks to make the statements true. The usual form of $2.39461 \times 10^{6}$ is ___

8961.

Question 49In the following question, fill in the blanks to make the statements true.The usual form of 2.39461×106 is ___

Answer»

Question 49

In the following question, fill in the blanks to make the statements true.

The usual form of $2.39461 \times 10^{6}$ is ___

Discussion

8962.	94×106 = ______.
Answer» $94 \times 106$ = ______.

Discussion

8963.	ABCD is a parallelogram. If AO = 10, OC = 3x + 4, BO = 8, OD = 2y + 2, then find the value of x+y.5
Answer» ABCD is a parallelogram. If AO = 10, OC = 3x + 4, BO = 8, OD = 2y + 2, then find the value of $x + y .$ 5

Discussion

8964.	In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.
Answer» In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.

Discussion

8965.	3. PQRS is a cyclic quad if angle QPR=35 then the value of angle PSR is
Answer» 3. PQRS is a cyclic quad if angle QPR=35 then the value of angle PSR is

Discussion

8966.	In Fig. 8.40, ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.
Answer» In Fig. 8.40, ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.

Discussion

8967.	Find the length of the side of a cube whose total surface area is 1536 cm2.
Answer» Find the length of the side of a cube whose total surface area is $1536 c m^{2}$ .

Discussion

8968.	If zeroes of x^2-5x+k are reciprocals of each other, then find k
Answer» If zeroes of x^2-5x+k are reciprocals of each other, then find k

Discussion

8969.	Question 12The diagonals AC and BD of a parallelogram ABCD intersect each other. The point O. If ∠DAC=32∘ and ∠AOB=70∘,then∠DBC is equal to(A) 24∘ (B) 86∘(C) 38∘(D) 32∘
Answer» Question 12 The diagonals AC and BD of a parallelogram ABCD intersect each other. The point O. If $∠ D A C = 32^{\circ} a n d ∠ A O B = 70^{\circ}, t h e n ∠ D B C$ is equal to (A) $24^{\circ}$ (B) $86^{\circ}$ (C) $38^{\circ}$ (D) $32^{\circ}$

Discussion

8970.	32. if the centre of a regular hexagon is at origin and one of the vertex on argand diagram is 1+2 I, then it's perimeter is
Answer» 32. if the centre of a regular hexagon is at origin and one of the vertex on argand diagram is 1+2 I, then it's perimeter is

Discussion

8971.	Which of the following pairs of linear equations are consistent/inconsistent? (i) x + 3y – 5 = 0, 2x + y = 0 (ii) 2x + y = 1, 2y = 2 – 4x (iii) 2x – y = 2, 2y – 4x = 2
Answer» Which of the following pairs of linear equations are consistent/inconsistent? (i) x + 3y – 5 = 0, 2x + y = 0 (ii) 2x + y = 1, 2y = 2 – 4x (iii) 2x – y = 2, 2y – 4x = 2

Discussion

8972.	If the sum of two numbers is 11 and there cubes sum is 737 .Find the numbers
Answer» If the sum of two numbers is 11 and there cubes sum is 737 .Find the numbers

Discussion

8973.	Expand (3a+2b)(2a−3b)
Answer» Expand $(3 a + \frac{2}{b}) (2 a - \frac{3}{b})$

Discussion

8974.	An irrational number between 3 and 4 is .
Answer» An irrational number between 3 and 4 is .

Discussion

8975.	The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm2. If the volume of the tube is 176 cm3, find the inner and outer radii of the tube.
Answer» The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm². If the volume of the tube is 176 cm³, find the inner and outer radii of the tube.

Discussion

8976.	Find the rational number which is terminating?
Answer» Find the rational number which is terminating?

Discussion

8977.	The ratio of the sum and the product of the roots of 5x2–14x+8=0 is
Answer» The ratio of the sum and the product of the roots of $5 x^{2} - 14 x + 8 = 0$ is

Discussion

8978.	Fill In The Blanks Two chords AB and CD of a circle are each at a distance of 6 cm from the centre. the ratio of their lengths is ________.
Answer» Fill In The Blanks Two chords AB and CD of a circle are each at a distance of 6 cm from the centre. the ratio of their lengths is ________.

Discussion

8979.	A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.
Answer» A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

Discussion

8980.	Let →a and →b be two non-zero vectors perpendicular to each other and \|→a\|=\|→b\|. If \|→a×→b\|=\|→a\|, then the angle between the vectors (→a+→b+(→a×→b)) and →a is equal to:
Answer» Let $\to a$ and $\to b$ be two non-zero vectors perpendicular to each other and $\| \to a \| = \| \to b \| .$ If $\| \to a \times \to b \| = \| \to a \|$ , then the angle between the vectors $(\to a + \to b + (\to a \times \to b))$ and $\to a$ is equal to:

Discussion

8981.	By grouping the terms in x4 - 2x3 - 6x + 12, we get
Answer» By grouping the terms in x⁴ - 2x³ - 6x + 12, we get

Discussion

8982.	The length (or boundary or perimeter) of a circle is called its __ .
Answer» The length (or boundary or perimeter) of a circle is called its __ .

Discussion

8983.	Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.
Answer» Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.

Discussion

8984.

Find the mean weight from the following table. Weight (kg) 29 30 31 32 33 No. of children 02 01 04 03 05

Answer»

Find the mean weight from the following table.

Weight (kg)	29	30	31	32	33
No. of children	02	01	04	03	05

Discussion

8985.	1. In a cyclic quadrilateral ABCD ,the bisectors of opposite angles A& C meet the circle at points P & Q respectively.prove that PQ is a diameter of the circle.
Answer» 1. In a cyclic quadrilateral ABCD ,the bisectors of opposite angles A& C meet the circle at points P & Q respectively.prove that PQ is a diameter of the circle.

Discussion

8986.	Using factor theorem, factorize each of the following polynomials y3−2y2 - 29y -42
Answer» Using factor theorem, factorize each of the following polynomials $y^{3} - 2 y^{2}$ - 29y -42

8986.

Using factor theorem, factorize each of the following polynomials y3−2y2 - 29y -42

Answer»

Using factor theorem, factorize each of the following polynomials

$y^{3} - 2 y^{2}$ - 29y -42

Discussion

8987.	Using synthetic division, solve (x4+2x3+3x2+4x+5)÷(x+2).Write the quotient and the remainder.
Answer» Using synthetic division, solve $(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$ . Write the quotient and the remainder.

Discussion

8988.	For constructing an angle of 60∘, we need to draw __ arc/arcs.
Answer» For constructing an angle of $60^{\circ}$ , we need to draw __ arc/arcs.

Discussion

8989.	In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar (\|\|gm XQRY) : ar (ΔQSR) =(i) 1 : 4(ii) 2 : 1(iii) 1 : 2(iv) 1 : 1
Answer» In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar (\|\|^gm XQRY) : ar (ΔQSR) = (i) 1 : 4 (ii) 2 : 1 (iii) 1 : 2 (iv) 1 : 1

Discussion

8990.	The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 88 m2. The volume of the cuboid is ___ m3
Answer» The dimensions of a cuboid are in the ratio of $1 : 2 : 3$ and its total surface area is $88 m^{2}$ . The volume of the cuboid is ___ $m^{3}$

Discussion

8991.	Write a program that prints the minimum and maximum of five numbers entered by the user.
Answer» Write a program that prints the minimum and maximum of five numbers entered by the user.

Discussion

8992.	Question 174ABCD is a trapezium such that AB∥CD, ∠A:∠D=2:1,∠B:∠C=7:5. Find the angles of the trapezium.
Answer» Question 174 ABCD is a trapezium such that $A B ∥ C D$ , $∠ A : ∠ D = 2 : 1, ∠ B : ∠ C = 7 : 5$ . Find the angles of the trapezium.

Discussion

8993.	23.If a ray OC stands on a line AB and also ANGLE AOC = ANGLE BOC then prove that angle AOC = 90
Answer» 23.If a ray OC stands on a line AB and also ANGLE AOC = ANGLE BOC then prove that angle AOC = 90

Discussion

8994.	In the figure, angle BAD = 75o, angle DCF = x and angle DEF = y.The values of x and y are
Answer» In the figure, angle BAD = 75^o, angle DCF = x and angle DEF = y.The values of x and y are

8994.

In the figure, angle BAD = 75o, angle DCF = x and angle DEF = y.The values of x and y are

Answer»

In the figure, angle BAD = 75^o, angle DCF = x and angle DEF = y.The values of x and y are

Discussion

8995.	If cotA=7/8, find (1/sin A) (1/sinA)÷(1+cosA) (1-cosA).
Answer» If cotA=7/8, find (1/sin A) (1/sinA)÷(1+cosA) (1-cosA).

Discussion

8996.	In the above figure, if AB∥CD and ∠APQ = 120∘, what is the ratio of ∠APQ to ∠CQP?
Answer» In the above figure, if AB $∥$ CD and $∠$ APQ = 120 $^{\circ}$ , what is the ratio of $∠$ APQ to $∠$ CQP?

Discussion

8997.

Following information is obtained from the books of Vinay, who maintained his books of account under Single Entry System: I. Receipts for the year ended 31st March, 2018: ₹ From Debtors 88,125 Cash Sales 20,625 Paid by Vinay 12,500 1,21,250 2. Payments during the year: New plant bought 3,125 Drawings 7,500 Salaries 5,625 Wages 33,625 Interest paid 375 Rent paid 6,625 Light and power 2,375 Sundry Expenses 10,625 Sundry Creditors 38,125 1,08,000 Vinay banks all receipts and makes payments by means of cheque. Assests and Liabilities As at 31st March,2017 (₹) As at 31st March, 2018 (Rs) Sundry Creditors 12.625 12,000 Sundry Debtors 18,750 30,625 Bank 3,125 ? Stock 31,250 15,625 Plant 37,500 36,575 From the above information, prepare Trading and Profit and Loss Account for the year ended 31st March, 2018 and Balance Sheet as on that date.

Answer» Following information is obtained from the books of Vinay, who maintained his books of account under Single Entry System:


I. Receipts for the year ended 31st March, 2018:	₹
From Debtors	88,125
Cash Sales	20,625
Paid by Vinay	12,500
	1,21,250
2. Payments during the year:
New plant bought	3,125
Drawings	7,500
Salaries	5,625
Wages	33,625
Interest paid	375
Rent paid	6,625
Light and power	2,375
Sundry Expenses	10,625
Sundry Creditors	38,125
	1,08,000

Vinay banks all receipts and makes payments by means of cheque.


Assests and Liabilities	As at 31st March,2017 (₹)	As at 31st March, 2018 (Rs)
Sundry Creditors	12.625	12,000
Sundry Debtors	18,750	30,625
Bank	3,125	?
Stock	31,250	15,625
Plant	37,500	36,575

From the above information, prepare Trading and Profit and Loss Account for the year ended 31st March, 2018 and Balance Sheet as on that date.

Discussion

8998.	Mettez le dialogue en ordre. C'est le chien de Mme. Lapierre. Qui - est ce? Qu'est - ce que c'est? C'est Mme Lapierre.
Answer» Mettez le dialogue en ordre. C'est le chien de Mme. Lapierre. Qui - est ce? Qu'est - ce que c'est? C'est Mme Lapierre.

Discussion

8999.	The Heron's formula to find the area of a triangle is:
Answer» The Heron's formula to find the area of a triangle is:

Discussion

9000.	If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then(a) ∠APB = ∠AQB(b) ∠APB + ∠AQB = 180° or ∠APB = ∠AQB(c) ∠APB + ∠AQB = 90°(d) ∠APB + ∠AQB = 180°
Answer» If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then (a) ∠APB = ∠AQB (b) ∠APB + ∠AQB = 180° or ∠APB = ∠AQB (c) ∠APB + ∠AQB = 90° (d) ∠APB + ∠AQB = 180°

Discussion

Explore topic-wise InterviewSolutions in .

(x+1) is a factor of the polynomial (a) x3−2x2+x+2 (b) x3+2x2+x−2 (c) x3+2x2−x−2 (d) x3+2x2−x+2

The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from the group,then the mean of of the remaining students is(a) 20 kg (b) 21 kg (c) 19 kg (d) 18 kg

If a, b are positive integers such that a < b and a b ab=25, then (a, b) = ____________.

In the given figure, ABCD is a trapezium in which AB || DC and DC = 40 cm and AB = 60 cm. If X and Y are, respectively, the mid-points of AD and BC, prove that:(i) XY = 50 cm(ii) DCYX is a trapezium(iii) ar (trap. DCYX) = 911 ar (trap. (XYBA)

The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2.

In a circle of radius 5 centimetres, two chords of lengths 6 centimetres and 8 centimetres are drawn parallel to each other, on either side of the centre. What is the distance between these chords?

If A={x:x is a prime number} and B={x:x≤10, x∈N}, then A∩B = ___.

In the given figure, ABCD is a rhombus, then the value of 'x' is

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

how to identify a non real number in an algebraic expression

Question 49In the following question, fill in the blanks to make the statements true.The usual form of 2.39461×106 is ___

94×106 = ______.

ABCD is a parallelogram. If AO = 10, OC = 3x + 4, BO = 8, OD = 2y + 2, then find the value of x+y.5

In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.

3. PQRS is a cyclic quad if angle QPR=35 then the value of angle PSR is

In Fig. 8.40, ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.

Find the length of the side of a cube whose total surface area is 1536 cm2.

If zeroes of x^2-5x+k are reciprocals of each other, then find k

Question 12The diagonals AC and BD of a parallelogram ABCD intersect each other. The point O. If ∠DAC=32∘ and ∠AOB=70∘,then∠DBC is equal to(A) 24∘ (B) 86∘(C) 38∘(D) 32∘

32. if the centre of a regular hexagon is at origin and one of the vertex on argand diagram is 1+2 I, then it's perimeter is

Which of the following pairs of linear equations are consistent/inconsistent? (i) x + 3y – 5 = 0, 2x + y = 0 (ii) 2x + y = 1, 2y = 2 – 4x (iii) 2x – y = 2, 2y – 4x = 2

If the sum of two numbers is 11 and there cubes sum is 737 .Find the numbers

Expand (3a+2b)(2a−3b)

An irrational number between 3 and 4 is .

The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm2. If the volume of the tube is 176 cm3, find the inner and outer radii of the tube.

Find the rational number which is terminating?

The ratio of the sum and the product of the roots of 5x2–14x+8=0 is

Fill In The Blanks Two chords AB and CD of a circle are each at a distance of 6 cm from the centre. the ratio of their lengths is ________.

A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

Let →a and →b be two non-zero vectors perpendicular to each other and |→a|=|→b|. If |→a×→b|=|→a|, then the angle between the vectors (→a+→b+(→a×→b)) and →a is equal to:

By grouping the terms in x4 - 2x3 - 6x + 12, we get

The length (or boundary or perimeter) of a circle is called its __ .

Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.

Find the mean weight from the following table. Weight (kg) 29 30 31 32 33 No. of children 02 01 04 03 05

1. In a cyclic quadrilateral ABCD ,the bisectors of opposite angles A& C meet the circle at points P & Q respectively.prove that PQ is a diameter of the circle.

Using factor theorem, factorize each of the following polynomials y3−2y2 - 29y -42

Using synthetic division, solve (x4+2x3+3x2+4x+5)÷(x+2).Write the quotient and the remainder.

For constructing an angle of 60∘, we need to draw __ arc/arcs.

In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar (||gm XQRY) : ar (ΔQSR) =(i) 1 : 4(ii) 2 : 1(iii) 1 : 2(iv) 1 : 1

The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 88 m2. The volume of the cuboid is ___ m3

Write a program that prints the minimum and maximum of five numbers entered by the user.

Question 174ABCD is a trapezium such that AB∥CD, ∠A:∠D=2:1,∠B:∠C=7:5. Find the angles of the trapezium.

23.If a ray OC stands on a line AB and also ANGLE AOC = ANGLE BOC then prove that angle AOC = 90

In the figure, angle BAD = 75o, angle DCF = x and angle DEF = y.The values of x and y are

If cotA=7/8, find (1/sin A) (1/sinA)÷(1+cosA) (1-cosA).

In the above figure, if AB∥CD and ∠APQ = 120∘, what is the ratio of ∠APQ to ∠CQP?

Mettez le dialogue en ordre. C'est le chien de Mme. Lapierre. Qui - est ce? Qu'est - ce que c'est? C'est Mme Lapierre.

The Heron's formula to find the area of a triangle is:

If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then(a) ∠APB = ∠AQB(b) ∠APB + ∠AQB = 180° or ∠APB = ∠AQB(c) ∠APB + ∠AQB = 90°(d) ∠APB + ∠AQB = 180°