24740 + Interview Questions in Mathematics Page 141 InterviewSolution

7001.	State whether the given statement is true or false. Justify your answer The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that AB=29AC.
Answer» State whether the given statement is true or false. Justify your answer The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that $A B = \frac{2}{9} A C .$

Discussion

7002.	Let 3a=4, 4b=5, 5c=6, 6d=7, 7e=8 and 8f=9. What is the value of the product abcdef?
Answer» Let $3^{a} = 4, 4^{b} = 5, 5^{c} = 6, 6^{d} = 7, 7^{e} = 8$ and $8^{f} = 9$ . What is the value of the product abcdef?

Discussion

7003.	If the sum of the lengths of the hypotenuse and a side of a right triangle is constant, the area of the triangle is maximum, when the angle between them is -
Answer» If the sum of the lengths of the hypotenuse and a side of a right triangle is constant, the area of the triangle is maximum, when the angle between them is -

Discussion

7004.	Prove that: If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Answer» Prove that: If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Discussion

7005.	In parallelogram ABCD, ∠A is 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram of AB = 5x -7 and CD = 3x + 1; find the length of CD.
Answer» In parallelogram ABCD, $∠$ A is 3 times $∠$ B. Find all the angles of the parallelogram. In the same parallelogram of AB = 5x -7 and CD = 3x + 1; find the length of CD.

Discussion

7006.	A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12cm × 8cm, how many bricks would be required.
Answer» A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12cm × 8cm, how many bricks would be required.

Discussion

7007.	If X¯ is the mean of x1,x2,.......,xn , then for a≠0, the mean of ax1,ax2,......,axn, x1a,x2a,...,xnn is (a) a+1aX¯(b) 12a+1aX¯(c) a+1nX¯n(d) a+1aX¯2n
Answer» If $\bar{X}$ is the mean of x₁,x₂,.......,x_n , then for $a \neq 0$ , the mean of ax₁,ax₂,......,ax_n, $\frac{x_{1}}{a}, \frac{x_{2}}{a}, . . ., \frac{x_{n}}{n} is$ $(a) (a + \frac{1}{a}) \bar{X} (b) \frac{1}{2} (a + \frac{1}{a}) \bar{X} (c) (a + \frac{1}{n}) \frac{\bar{X}}{n} (d) (a + \frac{1}{a}) \frac{\bar{X}}{2 n}$

Discussion

7008.	62. how to draw graph for \|2\|x\|-1\|=9
Answer» 62. how to draw graph for \|2\|x\|-1\|=9

Discussion

7009.	When p(x)=4x3−12x3+11x−5 is divided by (2x - 1), the remainder is
Answer» When $p (x) = 4 x^{3} - 12 x^{3} + 11 x - 5$ is divided by (2x - 1), the remainder is

Discussion

7010.	The rational number between 14 and 13 is .
Answer» The rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is .

Discussion

7011.	Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean X.
Answer» Following are the weights (in kg) of 10 new born babies in a hospital on a particular day: 3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean X.

Discussion

7012.	What is log?
Answer» What is log?

Discussion

7013.	12x – 7x2 + 4 – 2x3 is called a ___________ polynomial.
Answer» 12x – 7x² + 4 – 2x³ is called a ___________ polynomial.

Discussion

7014.	Parallelogram ABCD and Rectangle EBCF are between the same parallels. If the area of the parallelogram ABCD is 24 cm2, then the area of the rectangle EBCF is
Answer» Parallelogram ABCD and Rectangle EBCF are between the same parallels. If the area of the parallelogram ABCD is $24 c m^{2}$ , then the area of the rectangle EBCF is

Discussion

7015.	The component of a vector A=2\overset⇀ i+3\overset⇀ j along the vector B=\overset⇀ i+\overset⇀ j is a.5/\sqrt2 b.4\sqrt2 c.\sqrt2/3 d. None of these
Answer» The component of a vector A=2\overset⇀ i+3\overset⇀ j along the vector B=\overset⇀ i+\overset⇀ j is a.5/\sqrt2 b.4\sqrt2 c.\sqrt2/3 d. None of these

Discussion

7016.	Rim and SIM have the same weights. If each of them gains weight by 3kg then how will their new weights be compared ?
Answer» Rim and SIM have the same weights. If each of them gains weight by 3kg then how will their new weights be compared ?

Discussion

7017.	Woody buys 19 boxes of pencil and one of thestudents buys 13 boxes of pencil.What is the total number of boxes of pencil they have?
Answer» $Woody buys \frac{1}{9} boxes of pencil and one of the$ $students buys \frac{1}{3} boxes of pencil.$ What is the total number of boxes of pencil they have?

Discussion

7018.	The height of two buildings is 50 cm and 40 cm respectively. If the distance between their base is 24 cm, then find the distance between their top.
Answer» The height of two buildings is 50 cm and 40 cm respectively. If the distance between their base is 24 cm, then find the distance between their top.

Discussion

7019.	If we take a circle and a sphere of the same radius, then the surface area of the sphere is ___ times the area of the circle.
Answer» If we take a circle and a sphere of the same radius, then the surface area of the sphere is ___ times the area of the circle.

Discussion

7020.	After rationalising the denominator of 222+√3+√5. We get
Answer» After rationalising the denominator of $\frac{22}{2 + \sqrt{3} + \sqrt{5}} .$ We get

Discussion

7021.	Using any one construction method, divide a line segment AB=12 cm in the ratio 4:3. [2 MARKS]
Answer» Using any one construction method, divide a line segment AB=12 cm in the ratio 4:3. [2 MARKS]

Discussion

7022.	Factorise:21x2 + 5x – 6
Answer» Factorise: 21x²+ 5x – 6

Discussion

7023.	Write the equation of a line passing through the point (3, 5) and parallel to x-axis.
Answer» Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

Discussion

7024.	Pair the inverse equations.(Multiplication and division equation).
Answer» Pair the inverse equations. (Multiplication and division equation).

Discussion

7025.	Fill In The Blanks If AB and AC are equal chords of a circle, then the biesector of ∠BAC passes through the ___________.
Answer» Fill In The Blanks If AB and AC are equal chords of a circle, then the biesector of ∠BAC passes through the ___________.

Discussion

7026.	Question 47State whether the following statement is True or False.Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.
Answer» Question 47 State whether the following statement is True or False. Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.

Discussion

7027.	Maximum number of points that can lie on a line are:-
Answer» Maximum number of points that can lie on a line are:-

Discussion

7028.	Find the area of a circular sector subtending an angle 120∘ at the centre if the area of the whole circle is 36 cm2.
Answer» Find the area of a circular sector subtending an angle $120^{\circ}$ at the centre if the area of the whole circle is 36 $c m^{2}$ .

Discussion

7029.	1, 2, 3, 4, 5... The given numbers are
Answer» $1, 2, 3, 4, 5...$ The given numbers are

Discussion

7030.	The probability of getting a composite number in a throw of an unbiased dice is___
Answer» The probability of getting a composite number in a throw of an unbiased dice is___

Discussion

7031.	The value of (0.6)0−(0.1)−1(323)−1(32)3+(−13)−1 is _____________.
Answer» The value of $\frac{(0.6)^{0} - (0.1)^{- 1}}{(\frac{3}{2^{3}})^{- 1} (\frac{3}{2})^{3} + (- \frac{1}{3})^{- 1}}$ is _____________.

Discussion

7032.	Factorize: 3a2−9ab
Answer» Factorize: $3 a^{2} - 9 a b$

Discussion

7033.	Show howcan be represented on the number line.
Answer» Show howcan be represented on the number line.

Discussion

7034.	cos A1+sin A+tan A=
Answer» $\frac{c o s A}{1 + s i n A} + t a n A =$

Discussion

7035.	△ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of ∠BCD?
Answer» $△ A B C$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of $∠ B C D$ ?

7035.

△ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of ∠BCD?

Answer»

$△ A B C$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of $∠ B C D$ ?

Discussion

7036.	Question 2(b):Is every chord of a circle also a diameter?
Answer» Question 2(b): Is every chord of a circle also a diameter?

7036.

Question 2(b):Is every chord of a circle also a diameter?

Answer»

Question 2(b):

Is every chord of a circle also a diameter?

Discussion

7037.	Solve the following pair of equations:2x+y=73x+2y=12Choose the correct answer from the given options.
Answer» Solve the following pair of equations: $2 x + y = 7$ $3 x + 2 y = 12$ Choose the correct answer from the given options.

Discussion

7038.	Question 4For which of the following, diagonals are perpendicular to each other?a) Parallelogramb) Kitec) Trapeziumd) Rectangle
Answer» Question 4 For which of the following, diagonals are perpendicular to each other? a) Parallelogram b) Kite c) Trapezium d) Rectangle

Discussion

7039.	"If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent." Is the statement true? Why?
Answer» "If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent." Is the statement true? Why?

Discussion

7040.	If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =(a) 9(b) 9.5(c) 10(d) 10.5
Answer» If the arithmetic mean, 7, 8, x, 11, 14 is x, then x = (a) 9 (b) 9.5 (c) 10 (d) 10.5

Discussion

7041.	The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm, then find the length of the chord MN.
Answer» The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm, then find the length of the chord MN.

Discussion

7042.	The height and radius of a cone is 6 cm and 3 cm respectively .The volume of cone is equal to___πcm3.
Answer» The height and radius of a cone is 6 cm and 3 cm respectively .The volume of cone is equal to___ $π {c m}^{3}$ .

Discussion

7043.	Two concentric circles are of diameters 30 cm and 18 cm. Find the length of the chord of the larger circle which touches the smaller circle. [CBSE 2014]
Answer» Two concentric circles are of diameters 30 cm and 18 cm. Find the length of the chord of the larger circle which touches the smaller circle. [CBSE 2014]

Discussion

7044.	Let √3 i + j, √ i + 3 j and β i+ (1-β)j − respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of theacute angle between OA and OB is 3/√2 , then the sum of all possible values of β is (2019 Main)(a) 1 (b) 3(c) 4 (d) 2
Answer» Let √3 i + j, √ i + 3 j and β i+ (1-β)j − respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3/√2 , then the sum of all possible values of β is (2019 Main) (a) 1 (b) 3 (c) 4 (d) 2

Discussion

7045.	Question 1 (vi)Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.
Answer» Question 1 (vi) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Discussion

7046.	30. how should we choose two numbers,each greater than or equal to -2,whose sum is 1/2 so that the sum of the first and the cube of the second is minimum
Answer» 30. how should we choose two numbers,each greater than or equal to -2,whose sum is 1/2 so that the sum of the first and the cube of the second is minimum

Discussion

7047.	If the two chords in a circle are equal, then prove that the angle it subtends at the centre is the same.
Answer» If the two chords in a circle are equal, then prove that the angle it subtends at the centre is the same.

Discussion

7048.	Question 7 It is given that ΔABC≅ΔFDE and AB =5 cm, ∠B=40∘and∠A=80∘, then which of the following is true?(A) DF = 5 cm. ∠F=60∘(B) DF = 5 cm. ∠E=60∘(C) DE = 5 cm. ∠E=60∘(D) DE = 5 cm. ∠D=60∘
Answer» Question 7 It is given that $Δ A B C ≅ Δ F D E$ and AB =5 cm, $∠ B = 40^{\circ} a n d ∠ A = 80^{\circ}$ , then which of the following is true? (A) DF = 5 cm. $∠ F = 60^{\circ}$ (B) DF = 5 cm. $∠ E = 60^{\circ}$ (C) DE = 5 cm. $∠ E = 60^{\circ}$ (D) DE = 5 cm. $∠ D = 60^{\circ}$

Discussion

7049.	If a + b = 10 and ab = 24, then find the value ofa3 + b3
Answer» If a + b = 10 and ab = 24, then find the value of a3 + b3

Discussion

7050.	The mean of 10 numbers is 55. If one number is excluded, their mean becomes 50, the excluded number is:
Answer» The mean of 10 numbers is 55. If one number is excluded, their mean becomes 50, the excluded number is:

Discussion

Explore topic-wise InterviewSolutions in .

State whether the given statement is true or false. Justify your answer The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that AB=29AC.

Let 3a=4, 4b=5, 5c=6, 6d=7, 7e=8 and 8f=9. What is the value of the product abcdef?

If the sum of the lengths of the hypotenuse and a side of a right triangle is constant, the area of the triangle is maximum, when the angle between them is -

Prove that: If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

In parallelogram ABCD, ∠A is 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram of AB = 5x -7 and CD = 3x + 1; find the length of CD.

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12cm × 8cm, how many bricks would be required.

If X¯ is the mean of x1,x2,.......,xn , then for a≠0, the mean of ax1,ax2,......,axn, x1a,x2a,...,xnn is (a) a+1aX¯(b) 12a+1aX¯(c) a+1nX¯n(d) a+1aX¯2n

62. how to draw graph for |2|x|-1|=9

When p(x)=4x3−12x3+11x−5 is divided by (2x - 1), the remainder is

The rational number between 14 and 13 is .

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean X.

What is log?

12x – 7x2 + 4 – 2x3 is called a ___________ polynomial.

Parallelogram ABCD and Rectangle EBCF are between the same parallels. If the area of the parallelogram ABCD is 24 cm2, then the area of the rectangle EBCF is

The component of a vector A=2\overset⇀ i+3\overset⇀ j along the vector B=\overset⇀ i+\overset⇀ j is a.5/\sqrt2 b.4\sqrt2 c.\sqrt2/3 d. None of these

Rim and SIM have the same weights. If each of them gains weight by 3kg then how will their new weights be compared ?

Woody buys 19 boxes of pencil and one of thestudents buys 13 boxes of pencil.What is the total number of boxes of pencil they have?

The height of two buildings is 50 cm and 40 cm respectively. If the distance between their base is 24 cm, then find the distance between their top.

If we take a circle and a sphere of the same radius, then the surface area of the sphere is ___ times the area of the circle.

After rationalising the denominator of 222+√3+√5. We get

Using any one construction method, divide a line segment AB=12 cm in the ratio 4:3. [2 MARKS]

Factorise:21x2 + 5x – 6

Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

Pair the inverse equations.(Multiplication and division equation).

Fill In The Blanks If AB and AC are equal chords of a circle, then the biesector of ∠BAC passes through the ___________.

Question 47State whether the following statement is True or False.Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.

Maximum number of points that can lie on a line are:-

Find the area of a circular sector subtending an angle 120∘ at the centre if the area of the whole circle is 36 cm2.

1, 2, 3, 4, 5... The given numbers are

The probability of getting a composite number in a throw of an unbiased dice is___

The value of (0.6)0−(0.1)−1(323)−1(32)3+(−13)−1 is _____________.

Factorize: 3a2−9ab

Show howcan be represented on the number line.

cos A1+sin A+tan A=

△ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of ∠BCD?

Question 2(b):Is every chord of a circle also a diameter?

Solve the following pair of equations:2x+y=73x+2y=12Choose the correct answer from the given options.

Question 4For which of the following, diagonals are perpendicular to each other?a) Parallelogramb) Kitec) Trapeziumd) Rectangle

"If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent." Is the statement true? Why?

If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =(a) 9(b) 9.5(c) 10(d) 10.5

The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm, then find the length of the chord MN.

The height and radius of a cone is 6 cm and 3 cm respectively .The volume of cone is equal to___πcm3.

Two concentric circles are of diameters 30 cm and 18 cm. Find the length of the chord of the larger circle which touches the smaller circle. [CBSE 2014]

Question 1 (vi)Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

30. how should we choose two numbers,each greater than or equal to -2,whose sum is 1/2 so that the sum of the first and the cube of the second is minimum

If the two chords in a circle are equal, then prove that the angle it subtends at the centre is the same.

Question 7 It is given that ΔABC≅ΔFDE and AB =5 cm, ∠B=40∘and∠A=80∘, then which of the following is true?(A) DF = 5 cm. ∠F=60∘(B) DF = 5 cm. ∠E=60∘(C) DE = 5 cm. ∠E=60∘​​​​​​​(D) DE = 5 cm. ∠D=60∘​​​​​​​

If a + b = 10 and ab = 24, then find the value ofa3 + b3

The mean of 10 numbers is 55. If one number is excluded, their mean becomes 50, the excluded number is:

Question 7 It is given that ΔABC≅ΔFDE and AB =5 cm, ∠B=40∘and∠A=80∘, then which of the following is true?(A) DF = 5 cm. ∠F=60∘(B) DF = 5 cm. ∠E=60∘(C) DE = 5 cm. ∠E=60∘(D) DE = 5 cm. ∠D=60∘