24740 + Interview Questions in Mathematics Page 59 InterviewSolution

2901.	In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD+∠BED.
Answer» In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of $∠ A C D + ∠ B E D$ .

Discussion

2902.	The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is(a) kX¯(b) X¯k(c) X¯+k(d) X¯-k
Answer» The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is (a) $k \bar{X}$ (b) $\frac{\bar{X}}{k}$ (c) $\bar{X} + k$ (d) $\bar{X} - k$

Discussion

2903.	Question 9 (ii)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 white?
Answer» Question 9 (ii) 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 white?

Discussion

2904.	Find the mean of first five multiples of 3.
Answer» Find the mean of first five multiples of 3.

Discussion

2905.	The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is 30∘ than when it is 60∘. Find the length of the shadow at 30∘.
Answer» The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is $30^{\circ}$ than when it is $60^{\circ}$ . Find the length of the shadow at $30^{\circ}$ .

Discussion

2906.	Question 2ABCD is a rhombus and P, Q, R and S are the mid-points of the sides, AB, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
Answer» Question 2 ABCD is a rhombus and P, Q, R and S are the mid-points of the sides, AB, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Discussion

2907.	The point of intersection of y=6x−9 with the x-axis is ___.
Answer» The point of intersection of $y = 6 x - 9$ with the x-axis is ___.

Discussion

2908.	Factorize x6+y6
Answer» Factorize $x^{6} + y^{6}$

Discussion

2909.	Match the correct decimal form to its fractional form.
Answer» Match the correct decimal form to its fractional form.

Discussion

2910.	Question 3How many sides does a regular polygon have, if the measure of an exterior angle is 24∘?
Answer» Question 3 How many sides does a regular polygon have, if the measure of an exterior angle is $24^{\circ}$ ?

Discussion

2911.	8. Number of lines that can be drawn through the point (4,-5) so that its distance from (-2,3) will be equal to 12 is equal to A 0 B 1 C2 D3
Answer» 8. Number of lines that can be drawn through the point (4,-5) so that its distance from (-2,3) will be equal to 12 is equal to A 0 B 1 C2 D3

Discussion

2912.	Assertion: Area of the triangle whose vertices are A(−32,3),B(6,−2) and C(−3,4) is 0 Reason : The points A, B and C are collinear
Answer» Assertion: Area of the triangle whose vertices are $A (\frac{- 3}{2}, 3), B (6, - 2)$ and $C (- 3, 4)$ is 0 Reason : The points A, B and C are collinear

Discussion

2913.	Question 44If Y-coordinate is 3 times X-coordinate, from a table for it and draw a graph.
Answer» Question 44 If Y-coordinate is 3 times X-coordinate, from a table for it and draw a graph.

Discussion

2914.	One of the zeroes of the polynomial is 2x2+7x – 4 is
Answer» One of the zeroes of the polynomial is $2 x^{2} + 7 x - 4$ is

Discussion

2915.	What is the area(in cm2) of this triangle?___
Answer» What is the area(in ${c m}^{2}$ ) of this triangle? ___

2915.

What is the area(in cm2) of this triangle?___

Answer»

What is the area(in ${c m}^{2}$ ) of this triangle?

___

Discussion

2916.	A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.
Answer» A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.

Discussion

2917.	ntif AD,BE,CF are the altitudes of triangle ABC whose orthocentre is H , then C is the orthocentre ofn nt(1)tri(ABH)n nt(2)tri(BDH)n nt(3)tri(ABD)n nt(4)tri(BEA)n
Answer» ntif AD,BE,CF are the altitudes of triangle ABC whose orthocentre is H , then C is the orthocentre ofn nt(1)tri(ABH)n nt(2)tri(BDH)n nt(3)tri(ABD)n nt(4)tri(BEA)n

Discussion

2918.	Find the value of expression: 2√2+√2=?
Answer» Find the value of expression: $2 \sqrt{2} + \sqrt{2} = ?$

Discussion

2919.	The cost of a pen is rupees 16 taking number of pens as y. Form a linear equation in x and y when the number of pens purchased is 6.
Answer» The cost of a pen is rupees 16 taking number of pens as y. Form a linear equation in x and y when the number of pens purchased is 6.

Discussion

2920.	If point P corresponding to complex number (6 + 4 i ) is rotated about origin with an angle 120° in anticlockwise direction to obtain point Q. Then the complex number corresponding to point Q is
Answer» If point P corresponding to complex number (6 + 4 i ) is rotated about origin with an angle 120° in anticlockwise direction to obtain point Q. Then the complex number corresponding to point Q is

Discussion

2921.	Find the zeros of the quadratic polynomial, whose product, and the sum of zeros are 23 and 10 respectively and also find the polynomial.
Answer» Find the zeros of the quadratic polynomial, whose product, and the sum of zeros are 23 and 10 respectively and also find the polynomial.

Discussion

2922.	Find the total cost of fencing and ploughing a rectangular field (16 m×8 m) at the rate of ₹. 10/m and ₹. 10/m2 respectively.
Answer» Find the total cost of fencing and ploughing a rectangular field $(16 m \times 8 m)$ at the rate of ₹. 10/m and $₹ . 10 / m^{2}$ respectively.

2922.

Find the total cost of fencing and ploughing a rectangular field (16 m×8 m) at the rate of ₹. 10/m and ₹. 10/m2 respectively.

Answer»

Find the total cost of fencing and ploughing a rectangular field $(16 m \times 8 m)$ at the rate of ₹. 10/m and $₹ . 10 / m^{2}$ respectively.

Discussion

2923.	Match the following: QuadrilateralProperties1. TrapeziumA) A parallelogram, where diagonals bisect at right angles, all sides are equal and none of the angles are equal to 90∘2. SquareB) A quadrilateral, where only one pair of opposite sides is parallel and unequal3. RectangleC) A parallelogram, where diagonals are equal, all sides equal and all the angles are 90∘4. RhombusD) A parallelogram, where diagonals and opposite sides are equal, and all the angles are 90∘
Answer» Match the following: $\begin{matrix} Quadrilateral & Properties 1. Trapezium & A) A parallelogram, where diagonals bisect at right angles, all sides are equal and none of the angles are equal to 90^{\circ} 2. Square & B) A quadrilateral, where only one pair of opposite sides is parallel and unequal 3. Rectangle & C) A parallelogram, where diagonals are equal, all sides equal and all the angles are 90^{\circ} 4. Rhombus & D) A parallelogram, where diagonals and opposite sides are equal, and all the angles are 90^{\circ} \end{matrix}$

Discussion

2924.	Which of the following represent(s) a vector
Answer» Which of the following represent(s) a vector

Discussion

2925.	Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC.
Answer» Draw an angle and label it as $∠$ BAC. Construct another angle, equal to $∠$ BAC.

Discussion

2926.	Express 121 as the sum of 11 odd numbers.
Answer» Express 121 as the sum of 11 odd numbers.

Discussion

2927.	Question 2(ii)Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following products:(4x+5)(4x+1)
Answer» Question 2(ii) Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products: $(4 x + 5) (4 x + 1)$

Discussion

2928.	Prove that a cyclic parallelogram is a rectangle.
Answer» Prove that a cyclic parallelogram is a rectangle.

Discussion

2929.	The value of 33√5×73√10×53√20 is
Answer» The value of $3 \sqrt[3]{5} \times 7 \sqrt[3]{10} \times 5 \sqrt[3]{20}$ is

Discussion

2930.	A sphere, a cube and a thin circular plate have the same mass and are made of the same material all of them are heated to same temperature. The maximum rate of cooling is for:
Answer» A sphere, a cube and a thin circular plate have the same mass and are made of the same material all of them are heated to same temperature. The maximum rate of cooling is for:

Discussion

2931.	Match the following based on degree.
Answer» Match the following based on degree.

Discussion

2932.	In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.
Answer» In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

2932.

In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

Answer»

In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

Discussion

2933.	In Fig. 61, the value of xis(a) 72(b) 50(c) 58(d) 48
Answer» In Fig. 61, the value of xis (a) 72 (b) 50 (c) 58 (d) 48

Discussion

2934.	Question 9 (ii)A right circular cylinder just encloses a sphere of radius r (see figure). Find:(ii) curved surface area of the cylinder.
Answer» Question 9 (ii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (ii) curved surface area of the cylinder.

2934.

Question 9 (ii)A right circular cylinder just encloses a sphere of radius r (see figure). Find:(ii) curved surface area of the cylinder.

Answer»

Question 9 (ii)

A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(ii) curved surface area of the cylinder.

Discussion

2935.	The value of 3.¯¯¯¯¯¯42+8.¯¯¯¯¯¯¯¯053 is equal to
Answer» The value of $3. ¯ ¯¯¯¯ ¯ 42 + 8. ¯ ¯¯¯¯¯¯ ¯ 053$ is equal to

Discussion

2936.	Question 7 Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way. Class intervalFrequency(km/h)30−40340−50650−602560−706570−805080−902890−10014 Draw a histogram and frequency polygon representing the data above.
Answer» Question 7 Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y (k m / h) 30 - 40 & 3 40 - 50 & 6 50 - 60 & 25 60 - 70 & 65 70 - 80 & 50 80 - 90 & 28 90 - 100 & 14 \end{matrix}$ Draw a histogram and frequency polygon representing the data above.

Discussion

2937.	If A={x:x is a natural number}, B={x:x is an even natural number}, C={x:x is an odd natural number} and D={x:x is a prime number}, find(i) A∩B(ii) A∩C(iii) A∩D (iv) B∩C(v) B∩D(vi) C∩D
Answer» If $A = {x : x is a natural number}$ , $B = {x : x is an even natural number}$ , $C = {x : x is an odd natural number}$ and $D = {x : x is a prime number}$ , find $(i) A \cap B$ $(i i) A \cap C$ $(i i i) A \cap D$ $(i v) B \cap C$ $(v) B \cap D$ $(v i) C \cap D$

Discussion

2938.	How to do operations on irrational no.
Answer» How to do operations on irrational no.

Discussion

2939.	Question 86 (xi)Using suitable identities, evaluate the following:101×103
Answer» Question 86 (xi) Using suitable identities, evaluate the following: $101 \times 103$

2939.

Question 86 (xi)Using suitable identities, evaluate the following:101×103

Answer»

Question 86 (xi)

Using suitable identities, evaluate the following:

$101 \times 103$

Discussion

2940.	In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE\|\|BP , then AE is
Answer» In the given figure, D is the mid-point of AB and $P C = \frac{1}{2} A P = 3$ cm. If $A D = D B = 4$ cm and $D E \| \| B P$ , then AE is

Discussion

2941.	If 3^(p/q) = 2 than proof that 3^p = 2^q
Answer» If 3^(p/q) = 2 than proof that 3^p = 2^q

Discussion

2942.	Sin( 90 - theta ) = cos theta prove this using coordinate axes
Answer» Sin( 90 - theta ) = cos theta prove this using coordinate axes

Discussion

2943.	The rational number lying between 7 and 8 is.
Answer» The rational number lying between 7 and 8 is.

Discussion

2944.	Two parallel chords of a circle of radius 2 are at a distnace √3+1 apart. If the chords sutend at the center, angles of πk and 2πk, where k>0, then the value of [k] is[Note: [k] denotes the largest integer less than or equal to k]
Answer» Two parallel chords of a circle of radius $2$ are at a distnace $\sqrt{3} + 1$ apart. If the chords sutend at the center, angles of $\frac{π}{k}$ and $\frac{2 π}{k}$ , where $k > 0$ , then the value of $[k]$ is $[$ Note: $[k]$ denotes the largest integer less than or equal to $k]$

Discussion

2945.	Write the number 0.¯¯¯¯¯¯35 in the form pq, where p and q are integers and q≠0, is
Answer» Write the number $0. ¯ ¯¯¯¯ ¯ 35$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ , is

Discussion

2946.	Mark the correct alternative in each of the following:1. Which one of the following is a correct statement?(a) Decimal expansion of a rational number is terminating(b) Decimal expansion of a rational number is non-terminating(c) Decimal expansion of an irrational number is terminating(d) Decimal expansion of an irrational number is non-terminating and non-repeating
Answer» Mark the correct alternative in each of the following: 1. Which one of the following is a correct statement? (a) Decimal expansion of a rational number is terminating (b) Decimal expansion of a rational number is non-terminating (c) Decimal expansion of an irrational number is terminating (d) Decimal expansion of an irrational number is non-terminating and non-repeating

Discussion

2947.	Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60° and 45°.
Answer» Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60° and 45°.

Discussion

2948.	is an irrational number.
Answer» is an irrational number.

Discussion

2949.	Solve by factorization : x-a/x-b + x-b/x-a = a/b + b/a
Answer» Solve by factorization : x-a/x-b + x-b/x-a = a/b + b/a

Discussion

2950.	Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.
Answer» Construct the quadrilateral GOLD where OL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

2950.

Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

Answer»

Construct the quadrilateral GOLD where

OL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

Discussion

Explore topic-wise InterviewSolutions in .

In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD+∠BED.

The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is(a) kX¯(b) X¯k(c) X¯+k(d) X¯-k

Question 9 (ii)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 white?

Find the mean of first five multiples of 3.

The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is 30∘ than when it is 60∘. Find the length of the shadow at 30∘.

Question 2ABCD is a rhombus and P, Q, R and S are the mid-points of the sides, AB, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

The point of intersection of y=6x−9 with the x-axis is ___.

Factorize x6+y6

Match the correct decimal form to its fractional form.

Question 3How many sides does a regular polygon have, if the measure of an exterior angle is 24∘?

8. Number of lines that can be drawn through the point (4,-5) so that its distance from (-2,3) will be equal to 12 is equal to A 0 B 1 C2 D3

Assertion: Area of the triangle whose vertices are A(−32,3),B(6,−2) and C(−3,4) is 0 Reason : The points A, B and C are collinear

Question 44If Y-coordinate is 3 times X-coordinate, from a table for it and draw a graph.

One of the zeroes of the polynomial is 2x2+7x – 4 is

What is the area(in cm2) of this triangle?___

A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.

ntif AD,BE,CF are the altitudes of triangle ABC whose orthocentre is H , then C is the orthocentre ofn nt(1)tri(ABH)n nt(2)tri(BDH)n nt(3)tri(ABD)n nt(4)tri(BEA)n

Find the value of expression: 2√2+√2=?

The cost of a pen is rupees 16 taking number of pens as y. Form a linear equation in x and y when the number of pens purchased is 6.

If point P corresponding to complex number (6 + 4 i ) is rotated about origin with an angle 120° in anticlockwise direction to obtain point Q. Then the complex number corresponding to point Q is

Find the zeros of the quadratic polynomial, whose product, and the sum of zeros are 23 and 10 respectively and also find the polynomial.

Find the total cost of fencing and ploughing a rectangular field (16 m×8 m) at the rate of ₹. 10/m and ₹. 10/m2 respectively.

Which of the following represent(s) a vector

Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC.

Express 121 as the sum of 11 odd numbers.

Question 2(ii)Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following products:(4x+5)(4x+1)

Prove that a cyclic parallelogram is a rectangle.

The value of 33√5×73√10×53√20 is

A sphere, a cube and a thin circular plate have the same mass and are made of the same material all of them are heated to same temperature. The maximum rate of cooling is for:

Match the following based on degree.

In the given figure, PR &gt; PQ and PS bisects ∠QPR. Prove that ∠PSR &gt;∠PSQ.

In Fig. 61, the value of xis(a) 72(b) 50(c) 58(d) 48

Question 9 (ii)A right circular cylinder just encloses a sphere of radius r (see figure). Find:(ii) curved surface area of the cylinder.

The value of 3.¯¯¯¯¯¯42+8.¯¯¯¯¯¯¯¯053 is equal to

Question 7 Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way. Class intervalFrequency(km/h)30−40340−50650−602560−706570−805080−902890−10014 Draw a histogram and frequency polygon representing the data above.

If A={x:x is a natural number}, B={x:x is an even natural number}, C={x:x is an odd natural number} and D={x:x is a prime number}, find(i) A∩B(ii) A∩C(iii) A∩D (iv) B∩C(v) B∩D(vi) C∩D

How to do operations on irrational no.

Question 86 (xi)Using suitable identities, evaluate the following:101×103

In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE||BP , then AE is

If 3^(p/q) = 2 than proof that 3^p = 2^q

Sin( 90 - theta ) = cos theta prove this using coordinate axes

The rational number lying between 7 and 8 is.

Two parallel chords of a circle of radius 2 are at a distnace √3+1 apart. If the chords sutend at the center, angles of πk and 2πk, where k&gt;0, then the value of [k] is[Note: [k] denotes the largest integer less than or equal to k]

Write the number 0.¯¯¯¯¯¯35 in the form pq, where p and q are integers and q≠0, is

Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60° and 45°.

is an irrational number.

Solve by factorization : x-a/x-b + x-b/x-a = a/b + b/a

Construct the quadrilateral GOLD whereOL = 7.5 cm, GL = 6 cm, LD = 5 cm, OD = 10 cm and GD = 6 cm.

In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

Two parallel chords of a circle of radius 2 are at a distnace √3+1 apart. If the chords sutend at the center, angles of πk and 2πk, where k>0, then the value of [k] is[Note: [k] denotes the largest integer less than or equal to k]