24740 + Interview Questions in Mathematics Page 11 InterviewSolution

501.	In the adjoining figure,MNPQ and ABPQ are parallelogram and T is any point on the side BP.Prove that (i) ar(MNPQ)=ar(ABPQ) (ii) ar(△ ATQ)=12ar(MNPQ)
Answer» In the adjoining figure,MNPQ and ABPQ are parallelogram and T is any point on the side BP.Prove that (i) ar(MNPQ)=ar(ABPQ) (ii) $a r (△ A T Q) = \frac{1}{2} a r (M N P Q)$

501.

In the adjoining figure,MNPQ and ABPQ are parallelogram and T is any point on the side BP.Prove that (i) ar(MNPQ)=ar(ABPQ) (ii) ar(△ ATQ)=12ar(MNPQ)

Answer»

In the adjoining figure,MNPQ and ABPQ are parallelogram and T is any point on the side BP.Prove that

(i) ar(MNPQ)=ar(ABPQ)

(ii) $a r (△ A T Q) = \frac{1}{2} a r (M N P Q)$

Discussion

502.	Question 10Both x and y are in direct proportion, then 1x and 1y are(a) In indirect proportion(b) In inverse proportion(c) Neither in direct in inverse proportion(d) Sometimes in direct and sometimes in inverse proportion
Answer» Question 10 Both x and y are in direct proportion, then $\frac{1}{x}$ and $\frac{1}{y}$ are (a) In indirect proportion (b) In inverse proportion (c) Neither in direct in inverse proportion (d) Sometimes in direct and sometimes in inverse proportion

502.

Question 10Both x and y are in direct proportion, then 1x and 1y are(a) In indirect proportion(b) In inverse proportion(c) Neither in direct in inverse proportion(d) Sometimes in direct and sometimes in inverse proportion

Answer»

Question 10

Both x and y are in direct proportion, then $\frac{1}{x}$ and $\frac{1}{y}$ are

(a) In indirect proportion

(b) In inverse proportion

(c) Neither in direct in inverse proportion

(d) Sometimes in direct and sometimes in inverse proportion

Discussion

503.	A vector →a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If with respect to the new system, →a has components (p+1) and 1, then
Answer» A vector $\to a$ has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If with respect to the new system, $\to a$ has components (p+1) and 1, then

Discussion

504.	The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is(a) 2 : 1(b) 4 : 1(c) 8 : 1(d) 1 : 1
Answer» The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is (a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 1 : 1

Discussion

505.	In the given figure, ABCD is a \|\|gm. O is any point on AC. PQ \|\| AB and LM \|\| AD. Prove that ar (\|\|gm DLOP) = ar (\|\|gm BMOQ)
Answer» In the given figure, ABCD is a \|\|^gm. O is any point on AC. PQ \|\| AB and LM \|\| AD. Prove that ar (\|\|^gm DLOP) = ar (\|\|^gm BMOQ)

Discussion

506.	If √(1−x6)+√(1−y6)=a(x3−y3) and dydx=f(x,y)√(1−y61−x6), then
Answer» If $\sqrt{(1 - x^{6})} + \sqrt{(1 - y^{6})} = a (x^{3} - y^{3})$ and $\frac{d y}{d x} = f (x, y) \sqrt{(\frac{1 - y^{6}}{1 - x^{6}})},$ then

Discussion

507.	If x + y + z = 0, show that x3 + y3 + z3 = 3 xyz.
Answer» If x + y + z = 0, show that x³ + y³ + z³ = 3 xyz.

Discussion

508.	Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =(i) 86°(ii) 90°(iii) 94°(iv) 137°
Answer» Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD = (i) 86° (ii) 90° (iii) 94° (iv) 137°

Discussion

509.	P and Q are the mid-points of the opposite sides AB and CD of parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.
Answer» P and Q are the mid-points of the opposite sides AB and CD of parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

Discussion

510.	If vector (â + 2ê) is perpendicular to vector (5â - 4ê), then the angle between â and ê.
Answer» If vector (â + 2ê) is perpendicular to vector (5â - 4ê), then the angle between â and ê.

Discussion

511.	State whether the statements are True or False. Question 28The distance of any point from the X-axis is called the X-coordinates.
Answer» State whether the statements are True or False. Question 28 The distance of any point from the X-axis is called the X-coordinates.

Discussion

512.	Mention the type of polynomial based on the degreea) −5x4+5x3+9x+6b) 2x2+9x+6
Answer» Mention the type of polynomial based on the degree a) $- 5 x^{4} + 5 x^{3} + 9 x + 6$ b) $2 x^{2} + 9 x + 6$

Discussion

513.	If h, S, and V denote respectively the height, curved surface area, and volume of a right circular cone, then 9πVh3−S2h2−9V2 is equal to _____. (Given: r=h)
Answer» If $h$ , $S$ , and $V$ denote respectively the height, curved surface area, and volume of a right circular cone, then $9 π V h^{3} - S^{2} h^{2} - 9 V^{2}$ is equal to _____. (Given: $r = h$ )

Discussion

514.	How to locate √2√3 on same number line?
Answer» How to locate $\sqrt{2} \sqrt{3}$ on same number line?

Discussion

515.	26. If x is a positive imteger such that distance between the points P(x,2) and Q(3,-6) is 10 units then x is equal to ?
Answer» 26. If x is a positive imteger such that distance between the points P(x,2) and Q(3,-6) is 10 units then x is equal to ?

Discussion

516.	Let p(x) be any polynomial. When it is divided by (x-19) and (x-91) then the remainders are 91 and 19 respectively. Find The remainder when p(x)is divided by (x-19)(x-91)
Answer» Let p(x) be any polynomial. When it is divided by (x-19) and (x-91) then the remainders are 91 and 19 respectively. Find The remainder when p(x)is divided by (x-19)(x-91)

Discussion

517.	Which of these numbers is not a natural number?
Answer» Which of these numbers is not a natural number?

Discussion

518.	Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45∘. Find the circumradius of the triangle measures.
Answer» Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45 $^{\circ}$ . Find the circumradius of the triangle measures.

Discussion

519.	The sum of two numbers is 31.26. If one of them is 11.76, what is the other number in fractional form?
Answer» The sum of two numbers is 31.26. If one of them is 11.76, what is the other number in fractional form?

Discussion

520.	Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
Answer» Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm², find the cost of cardboard required for supplying 250 boxes of each kind.

Discussion

521.	In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:(i) 5, 7, 9(ii) 2, 10, 15(iii) 3, 4, 5
Answer» In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle: (i) 5, 7, 9 (ii) 2, 10, 15 (iii) 3, 4, 5

Discussion

522.	Prove that (20-(3)^1/2-1÷2(2)^1/2×8(6)^1/2)^1/2 = (2)^1/2[(3)^1/2+1]
Answer» Prove that (20-(3)^1/2-1÷2(2)^1/2×8(6)^1/2)^1/2 = (2)^1/2[(3)^1/2+1]

522.

Prove that (20-(3)^1/2-1÷2(2)^1/2×8(6)^1/2)^1/2 = (2)^1/2[(3)^1/2+1]

Answer»

Prove that

(20-(3)^1/2-1÷2(2)^1/2×8(6)^1/2)^1/2 = (2)^1/2[(3)^1/2+1]

Discussion

523.	The simple interest on a certain sum of money for 3 years at 6% per annum is ₹432. Find the principal.
Answer» The simple interest on a certain sum of money for 3 years at $6 %$ per annum is ₹432. Find the principal.

Discussion

524.	Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.(i) 2x−y5+6=0(ii)x5−y6=1 (iii) √2x+√3y=5
Answer» Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case. (i) $2 x - \frac{y}{5} + 6 = 0$ (ii) $\frac{x}{5} - \frac{y}{6} = 1$ (iii) $\sqrt{2} x + \sqrt{3} y = 5$

524.

Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.(i) 2x−y5+6=0(ii)x5−y6=1 (iii) √2x+√3y=5

Answer» Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.

(i)

2 x - \frac{y}{5} + 6 = 0

(ii) $\frac{x}{5} - \frac{y}{6} = 1$

(iii) $\sqrt{2} x + \sqrt{3} y = 5$

Discussion

525.	The value of 2+7/5. Is ?
Answer» The value of 2+7/5. Is ?

Discussion

526.	Volume of water that can be stored in a spherical tank of diameter 42 cm is.[ use π=227 ]
Answer» Volume of water that can be stored in a spherical tank of diameter $42 c m$ is. [ use $π = \frac{22}{7}$ ]

Discussion

527.	Question 50 If a diagonal of a quadrilateral bisects both the angles, then it is a a) Kite b) Parallelogram c) Rhombus d) Rectangle
Answer» Question 50 If a diagonal of a quadrilateral bisects both the angles, then it is a a) Kite b) Parallelogram c) Rhombus d) Rectangle

Discussion

528.	In the given figure, D is a point on side BC of a ΔABC and E is a point such that CD = DE. Prove that AB + AC > BE.
Answer» In the given figure, D is a point on side BC of a ΔABC and E is a point such that CD = DE. Prove that AB + AC > BE.

Discussion

529.	Find the quantity of concrete required to make 70 cylindrical pillars of radius 5 cm and height 10 m.
Answer» Find the quantity of concrete required to make 70 cylindrical pillars of radius $5 c m$ and height $10 m$ .

Discussion

530.	Question 97 The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?
Answer» Question 97 The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?

Discussion

531.	The polynomials ax^3+3x^2-13 and 2x^2-5x+a leaves the same remainder in each case when divided by (x-2)
Answer» The polynomials ax^3+3x^2-13 and 2x^2-5x+a leaves the same remainder in each case when divided by (x-2)

Discussion

532.	If a quadrilateral ABCD is a parallelogram then
Answer» If a quadrilateral ABCD is a parallelogram then

Discussion

533.	If {((x)5)2×(2)−1}13=x3, then find the value of x.
Answer» If ${{({(x)}^{5})}^{2} \times {(2)}^{- 1}}^{\frac{1}{3}} = x^{3},$ then find the value of $x$ .

Discussion

534.	One angle of a pentagon is 140o. If the remaining angles are in the ration 1:2:3:4, find the size of the greatest angle
Answer» One angle of a pentagon is 140^o. If the remaining angles are in the ration 1:2:3:4, find the size of the greatest angle

Discussion

535.	If r1=9 cm and r2=5 cm, then find the area of the shaded region. (Use π=227)176
Answer» If $r_{1} = 9 c m$ and $r_{2} = 5 c m$ , then find the area of the shaded region. (Use $π = \frac{22}{7}$ ) 176

Discussion

536.	If the cube root of 27343 is equal to 3afind the value of "a".7
Answer» $If the cube root of \frac{27}{343} is equal to$ $\frac{3}{a}$ find the value of "a". 7

Discussion

537.	The figure formed by joining the mid-points of the adjacent sides of a rhombus is a(a) square(b) rectangle(c) trapezium(d) none of these
Answer» The figure formed by joining the mid-points of the adjacent sides of a rhombus is a (a) square (b) rectangle (c) trapezium (d) none of these

Discussion

538.	Question 1 (v)Solve the following pair of linear equations by the substitution method.√2x+√3y=0;√3x−√8y=0
Answer» Question 1 (v) Solve the following pair of linear equations by the substitution method. $\sqrt{2} x + \sqrt{3} y = 0; \sqrt{3} x - \sqrt{8} y = 0$

Discussion

539.	Let S1 and S2 be the two slits in a Young's double slit experiment. If central maxima is observed at P and ∠ S1PS2=θ (θ is small), find the y−coordinate of the third minima assuming the origin to be at the central maxima, λ is the wavelength of light used.
Answer» Let $S_{1}$ and $S_{2}$ be the two slits in a Young's double slit experiment. If central maxima is observed at $P$ and $∠ S_{1} P S_{2} = θ (θ is small)$ , find the $y -$ coordinate of the third minima assuming the origin to be at the central maxima, $λ$ is the wavelength of light used.

Discussion

540.	If the sides of a triangle are in the ratio 7:8:9 and its smallest side is 14 cm, find the semi perimeter of the triangle. [2 MARKS]
Answer» If the sides of a triangle are in the ratio 7:8:9 and its smallest side is 14 cm, find the semi perimeter of the triangle. [2 MARKS]

Discussion

541.	Question 4 A rectangular plot is given for constructing a house having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m, wide place should be left in the front and back each and 2m wide space on each of other sides. Find the largest area where house can be constructed.
Answer» Question 4 A rectangular plot is given for constructing a house having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m, wide place should be left in the front and back each and 2m wide space on each of other sides. Find the largest area where house can be constructed.

Discussion

542.	38 A rectangle PQRS has it's side PQ parallel to the line y=mx and certices P,Q and S on line y=a, x=b and x=-b respectively.Find the locus if the vertex R
Answer» 38 A rectangle PQRS has it's side PQ parallel to the line y=mx and certices P,Q and S on line y=a, x=b and x=-b respectively.Find the locus if the vertex R

Discussion

543.	A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is
Answer» A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is

543.

A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is

Answer»

A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random.

The probability that the number on the coin is not a prime number, is

Discussion

544.	42. aFe2O3+ bH2 gives cFe+dH20 a,b,c and d are respectively 1123 1111 1323 1223
Answer» 42. aFe2O3+ bH2 gives cFe+dH20 a,b,c and d are respectively 1123 1111 1323 1223

Discussion

545.	Find four rational numbers between 37 and 57
Answer» Find four rational numbers between $\frac{3}{7} a n d \frac{5}{7}$

Discussion

546.	Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.
Answer» Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.

Discussion

547.	34. An equilateral triangle has area A\sqrt{}3. Three circles are drawn with their centres at the vertices of the triangle . Diameter of each circle is equal to the length of each side of the triangle. The area of the triangle not include in any of the three circles is
Answer» 34. An equilateral triangle has area A\sqrt{}3. Three circles are drawn with their centres at the vertices of the triangle . Diameter of each circle is equal to the length of each side of the triangle. The area of the triangle not include in any of the three circles is

Discussion

548.

Find the mean of daily wages of 40 workers in a factory as per data given below: Daily wages (in ₹) (xi) 250 300 350 400 450 Number of workers (fi) 8 11 6 10 5

Answer» Find the mean of daily wages of 40 workers in a factory as per data given below:

Daily wages (in ₹) (x_i)	250	300	350	400	450
Number of workers (f_i)	8	11	6	10	5

Discussion

549.	Identify the rule applied to obtain 25 in the number tower and complete it.
Answer» Identify the rule applied to obtain 25 in the number tower and complete it.

Discussion

550.

In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ΔDEF by the criterion

Answer»

In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ΔDEF by the criterion

Discussion

Explore topic-wise InterviewSolutions in .

In the adjoining figure,MNPQ and ABPQ are parallelogram and T is any point on the side BP.Prove that (i) ar(MNPQ)=ar(ABPQ) (ii) ar(△ ATQ)=12ar(MNPQ)

Question 10Both x and y are in direct proportion, then 1x and 1y are(a) In indirect proportion(b) In inverse proportion(c) Neither in direct in inverse proportion(d) Sometimes in direct and sometimes in inverse proportion

A vector →a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If with respect to the new system, →a has components (p+1) and 1, then

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is(a) 2 : 1(b) 4 : 1(c) 8 : 1(d) 1 : 1

In the given figure, ABCD is a ||gm. O is any point on AC. PQ || AB and LM || AD. Prove that ar (||gm DLOP) = ar (||gm BMOQ)

If √(1−x6)+√(1−y6)=a(x3−y3) and dydx=f(x,y)√(1−y61−x6), then

If x + y + z = 0, show that x3 + y3 + z3 = 3 xyz.

Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =(i) 86°(ii) 90°(iii) 94°(iv) 137°

P and Q are the mid-points of the opposite sides AB and CD of parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

If vector (â + 2ê) is perpendicular to vector (5â - 4ê), then the angle between â and ê.

State whether the statements are True or False. Question 28The distance of any point from the X-axis is called the X-coordinates.

Mention the type of polynomial based on the degreea) −5x4+5x3+9x+6b) 2x2+9x+6

If h, S, and V denote respectively the height, curved surface area, and volume of a right circular cone, then 9πVh3−S2h2−9V2 is equal to _____. (Given: r=h)

How to locate √2√3 on same number line?

26. If x is a positive imteger such that distance between the points P(x,2) and Q(3,-6) is 10 units then x is equal to ?

Let p(x) be any polynomial. When it is divided by (x-19) and (x-91) then the remainders are 91 and 19 respectively. Find The remainder when p(x)is divided by (x-19)(x-91)

Which of these numbers is not a natural number?

Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45∘. Find the circumradius of the triangle measures.

The sum of two numbers is 31.26. If one of them is 11.76, what is the other number in fractional form?

In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:(i) 5, 7, 9(ii) 2, 10, 15(iii) 3, 4, 5

Prove that (20-(3)^1/2-1÷2(2)^1/2×8(6)^1/2)^1/2 = (2)^1/2[(3)^1/2+1]

The simple interest on a certain sum of money for 3 years at 6% per annum is ₹432. Find the principal.

Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.(i) 2x−y5+6=0(ii)x5−y6=1 (iii) √2x+√3y=5

The value of 2+7/5. Is ?

Volume of water that can be stored in a spherical tank of diameter 42 cm is.[ use π=227 ]

Question 50 If a diagonal of a quadrilateral bisects both the angles, then it is a a) Kite b) Parallelogram c) Rhombus d) Rectangle

In the given figure, D is a point on side BC of a ΔABC and E is a point such that CD = DE. Prove that AB + AC > BE.

Find the quantity of concrete required to make 70 cylindrical pillars of radius 5 cm and height 10 m.

Question 97 The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?

The polynomials ax^3+3x^2-13 and 2x^2-5x+a leaves the same remainder in each case when divided by (x-2)

If a quadrilateral ABCD is a parallelogram then

If {((x)5)2×(2)−1}13=x3, then find the value of x.

One angle of a pentagon is 140o. If the remaining angles are in the ration 1:2:3:4, find the size of the greatest angle

If r1=9 cm and r2=5 cm, then find the area of the shaded region. (Use π=227)176

If the cube root of 27343 is equal to 3afind the value of "a".7

The figure formed by joining the mid-points of the adjacent sides of a rhombus is a(a) square(b) rectangle(c) trapezium(d) none of these

Question 1 (v)Solve the following pair of linear equations by the substitution method.√2x+√3y=0;√3x−√8y=0

Let S1 and S2 be the two slits in a Young's double slit experiment. If central maxima is observed at P and ∠ S1PS2=θ (θ is small), find the y−coordinate of the third minima assuming the origin to be at the central maxima, λ is the wavelength of light used.

If the sides of a triangle are in the ratio 7:8:9 and its smallest side is 14 cm, find the semi perimeter of the triangle. [2 MARKS]

38 A rectangle PQRS has it's side PQ parallel to the line y=mx and certices P,Q and S on line y=a, x=b and x=-b respectively.Find the locus if the vertex R

A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is

42. aFe2O3+ bH2 gives cFe+dH20 a,b,c and d are respectively 1123 1111 1323 1223

Find four rational numbers between 37 and 57

Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.

34. An equilateral triangle has area A\sqrt{}3. Three circles are drawn with their centres at the vertices of the triangle . Diameter of each circle is equal to the length of each side of the triangle. The area of the triangle not include in any of the three circles is

Find the mean of daily wages of 40 workers in a factory as per data given below: Daily wages (in ₹) (xi) 250 300 350 400 450 Number of workers (fi) 8 11 6 10 5

Identify the rule applied to obtain 25 in the number tower and complete it.

In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ΔDEF by the criterion