24740 + Interview Questions in Mathematics Page 2 InterviewSolution

51.	Write the complement of:(i) a(ii) (x+5)o(iii) 13rd of 180o
Answer» Write the complement of: (i) $a$ (ii) $(x + 5)^{o}$ (iii) $\frac{1}{3}$ rd of $180^{o}$

Discussion

52.	Factorize 27y^6 - 28y^3 + 8
Answer» Factorize 27y^6 - 28y^3 + 8

Discussion

53.	In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.
Answer» In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

53.

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

Answer»

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

Discussion

54.	A cylinderical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?
Answer» A cylinderical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Discussion

55.	Find the value of the given expression: (2p+3)×(2p−3)×(4p2+9)
Answer» Find the value of the given expression: $(2 p + 3) \times (2 p - 3) \times (4 p^{2} + 9)$

Discussion

56.	ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD=∠CBD.
Answer» ABC and ADC are two right triangles with common hypotenuse AC. Prove that $∠ CAD = ∠ CBD$ .

56.

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD=∠CBD.

Answer»

ABC and ADC are two right triangles with common hypotenuse AC. Prove that $∠ CAD = ∠ CBD$ .

Discussion

57.	The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.
Answer» The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the diameter and the height of the pillar.

Discussion

58.

Match the following Column-I Column-II (A) a,b,c>0 then ab+c+bc+a+ca+b can't take the value (p) 12181 (B) p and q are positive real numbers and p + q = 1, then (p+1p)2+(q+1q)2 can't take the value (q) 343229 (C) x, y, z are real numbers such that 0 <x, y, z< 1 and x + y + z = 2, then xyz(1−x)(1−y)(1−z) can take the value (r) 13315 (D) x, y, z are positive real numbers such that x + y + z = 1, then \frac{(1+x)(1+y)(1+z)}{(1-x)(1-y)(1-z)} can take the value (s) 41351 (t) 8

Answer» Match the following

	Column-I		Column-II
(A)	$a, b, c > 0$ then $\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b}$ can't take the value	(p)	$\frac{121}{81}$
(B)	p and q are positive real numbers and p + q = 1, then ${(p + \frac{1}{p})}^{2} + {(q + \frac{1}{q})}^{2}$ can't take the value	(q)	$\frac{343}{229}$
(C)	x, y, z are real numbers such that 0 <x, y, z< 1 and x + y + z = 2, then $\frac{x y z}{(1 - x) (1 - y) (1 - z)}$ can take the value	(r)	$\frac{133}{15}$
(D)	x, y, z are positive real numbers such that x + y + z = 1, then \frac{(1+x)(1+y)(1+z)}{(1-x)(1-y)(1-z)} can take the value	(s)	$\frac{413}{51}$
		(t)	8

Discussion

59.	If the height of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.
Answer» If the height of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.

Discussion

60.	When a natural number X is divided by 5 ,the remainder is 2. When a natural number Y is divided by 5,the remainder is 4, the remainder is Z when X+Y is divided by 5.The value of 2z/3-5/3
Answer» When a natural number X is divided by 5 ,the remainder is 2. When a natural number Y is divided by 5,the remainder is 4, the remainder is Z when X+Y is divided by 5.The value of 2z/3-5/3

Discussion

61.	Choose the equivalent rational numbers of 818.
Answer» Choose the equivalent rational numbers of $\frac{8}{18} .$

Discussion

62.	A circus artist is climbing the 20m rope. Which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.
Answer» A circus artist is climbing the 20m rope. Which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

63.	If N is a set of all natural numbers and Q is a set of all rational numbers, then which of the following is a correct representation for these two sets?
Answer» If $N$ is a set of all natural numbers and $Q$ is a set of all rational numbers, then which of the following is a correct representation for these two sets?

Discussion

64.	In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
Answer» In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Discussion

65.	The curved surface area of a sphere of radius 5 cm is ____ sq cm.
Answer» The curved surface area of a sphere of radius 5 cm is ____ sq cm.

Discussion

66.	In each of the following two polynomials, find the value of a, if x − a is factor:(i) x6 − ax5 + x4 − ax3 + 3x − a + 2(ii x5 − a2x3 + 2x + a + 1)
Answer» In each of the following two polynomials, find the value of a, if x − a is factor: (i) x⁶ − ax⁵ + x⁴ − ax³ + 3x − a + 2 (ii x⁵ − a²x³ + 2x + a + 1)

Discussion

67.	△ABC is an isosceles triangle and LO is perpendicular to MN. Show that ∠M = ∠N.
Answer» $△$ ABC is an isosceles triangle and LO is perpendicular to MN. Show that $∠ M$ = $∠ N$ .

Discussion

68.	Prove that 3+2√5 is irrational number.
Answer» Prove that $3 + 2 \sqrt{5}$ is irrational number.

Discussion

69.	In the following figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC).Can you answer the question that you have left in the ’Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?[Remark: Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide ΔABC into n triangles of equal areas.]
Answer» In the following figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you answer the question that you have left in the ’Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area? [Remark: Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide ΔABC into n triangles of equal areas.]

69.

In the following figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC).Can you answer the question that you have left in the ’Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?[Remark: Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide ΔABC into n triangles of equal areas.]

Answer»

In the following figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC).

Can you answer the question that you have left in the ’Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?

[Remark: Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide ΔABC into n triangles of equal areas.]

Discussion

70.	If A is an acute angle and cosA=(5/13), then the value of cosec A is .........................
Answer» If A is an acute angle and cosA=(5/13), then the value of cosec A is .........................

Discussion

71.	Verify that x 3 + y3 + z3 -3xyz = 1/2 (x+y+z) [(x-y) 2 + (y-z) 2 +(z-x) 2]
Answer» Verify that x ³+ y³ + z³ -3xyz = 1/2 (x+y+z) [(x-y) ²+ (y-z) ²+(z-x) ²]

Discussion

72.	Write actual division, find which of the following rational numbers are terminating decimals.(i) 1380(ii) 724(iii) 512(iv) 31375(v) 16125
Answer» Write actual division, find which of the following rational numbers are terminating decimals. (i) $\frac{13}{80}$ (ii) $\frac{7}{24}$ (iii) $\frac{5}{12}$ (iv) $\frac{31}{375}$ (v) $\frac{16}{125}$

Discussion

73.	In a triangle ABC,∠A>π2,AA1 and AA2 are median and altitude, respectively. If ∠BAA1=∠A1AA2=∠A2AC, then value of sin3A3⋅cosA3 is:
Answer» In a triangle $A B C, ∠ A > \frac{π}{2}, A A_{1}$ and $A A_{2}$ are median and altitude, respectively. If $∠ B A A_{1} = ∠ A_{1} A A_{2} = ∠ A_{2} A C,$ then value of ${sin}^{3} \frac{A}{3} \cdot cos \frac{A}{3}$ is:

Discussion

74.	In the graph there is 4 quadrant . The line of hyperbola is passing from 1st and 4th quadrant then why the equation of the hyperbola is positive? Why not it is negative ?
Answer» In the graph there is 4 quadrant . The line of hyperbola is passing from 1st and 4th quadrant then why the equation of the hyperbola is positive? Why not it is negative ?

Discussion

75.	24. The area defined by \|x-2\| + \|y+1\| is greater than and equal to 1 and less than and equal to 2 is
Answer» 24. The area defined by \|x-2\| + \|y+1\| is greater than and equal to 1 and less than and equal to 2 is

Discussion

76.	Some measures are given in the adjacent figure, find the area of ABCD
Answer» Some measures are given in the adjacent figure, find the area of ABCD

Discussion

77.	The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is(a) 25 cm2(b) 28 cm2(c) 30 cm2(d) 40 cm2
Answer» The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is (a) 25 cm² (b) 28 cm² (c) 30 cm² (d) 40 cm²

Discussion

78.	45∘ can be obtained by drawing the angles of measure
Answer» $45^{\circ}$ can be obtained by drawing the angles of measure

Discussion

79.	If the bisectors ofopposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing ot at the points P&Q. Prove that PQ is the diameter of the circle.
Answer» If the bisectors ofopposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing ot at the points P&Q. Prove that PQ is the diameter of the circle.

Discussion

80.	Question 54The class size of the interval 80 - 85 is ___,
Answer» Question 54 The class size of the interval 80 - 85 is ___,

80.

Question 54The class size of the interval 80 - 85 is ___,

Answer»

Question 54

The class size of the interval 80 - 85 is ___,

Discussion

81.	Question 4Which of the following cannot be the probability of an event?(a) 23(b) -1.5(c) 15%(d) 0.7
Answer» Question 4 Which of the following cannot be the probability of an event? (a) $\frac{2}{3}$ (b) -1.5 (c) 15% (d) 0.7

Discussion

82.	Which of the following is not a criterion for congruence of triangles?(a) SAS(b) SSA(c) ASA(d) SSS
Answer» Which of the following is not a criterion for congruence of triangles? (a) SAS (b) SSA (c) ASA (d) SSS

Discussion

83.	Expand-: (-2a+3b+4c)
Answer» Expand-: (-2a+3b+4c)

Discussion

84.	ABC is a right angle triangle right angled at B with hypotenuse AC=26 cm and perimeter 60 cm calculate the area of the triangle and other two sides.
Answer» ABC is a right angle triangle right angled at B with hypotenuse AC=26 cm and perimeter 60 cm calculate the area of the triangle and other two sides.

Discussion

85.	rationlaise : 1/√7+√6-√13
Answer» rationlaise : 1/√7+√6-√13

Discussion

86.	The area of right triangle is 150 cm square. if its altitude exceeds the base by 5 cm .calculate perimeter of triangle
Answer» The area of right triangle is 150 cm square. if its altitude exceeds the base by 5 cm .calculate perimeter of triangle

Discussion

87.	Find the distance between the following pairs of points:(i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)
Answer» Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)

87.

Find the distance between the following pairs of points:(i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)

Answer»

Find the distance between the following pairs of points:

(i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)

Discussion

88.	Factorize:x2 + y − xy − x
Answer» Factorize: x² + y − xy − x

Discussion

89.	Compute the area of trapezium PQRS in the given figure.
Answer» Compute the area of trapezium PQRS in the given figure.

Discussion

90.	A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?
Answer» A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?

Discussion

91.	12×base×height is the formula for which type of triangles?
Answer» $\frac{1}{2} \times base \times height$ is the formula for which type of triangles?

Discussion

92.	In the given figure, AB is a diameter of the circle such that ∠A = 35° and ∠Q = 25°, find ∠PBR.
Answer» In the given figure, AB is a diameter of the circle such that ∠A = 35° and ∠Q = 25°, find ∠PBR.

Discussion

93.	If the surface area of a sphere is 144π m2, then its volume (in m3) is (a) 288 π(b) 316 π(c) 300 π(d) 188 π
Answer» If the surface area of a sphere is 144π m², then its volume (in m³) is (a) 288 π (b) 316 π (c) 300 π (d) 188 π

Discussion

94.	In the figure, △ABC is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠BAC,then what is the value of BD in cm?3
Answer» $In the figure, △ A B C is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠ B A C, then what is the value of BD in cm?$ 3

Discussion

95.	Which of the following is a terminating decimal?[1 mark]
Answer» Which of the following is a terminating decimal? [1 mark]

Discussion

96.	The radius of a circle is 5.6 cm. Then what will be the length of its longest chord?
Answer» The radius of a circle is 5.6 cm. Then what will be the length of its longest chord?

Discussion

97.	Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.
Answer» Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.

97.

Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.

Answer»

Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.

Discussion

98.	What is the fraction of students who failed in Maths exam if the total number of students who appeared in the exam was 65 and the number of students who passed is 57?
Answer» What is the fraction of students who failed in Maths exam if the total number of students who appeared in the exam was 65 and the number of students who passed is 57?

Discussion

99.	In a trapezium ABCD, O is the point of intersection of AC and BD, AB \|\| CD, and AB=52×CD. The area of AOB=100 cm2. The area of ΔOCD is :[1 mark]
Answer» In a trapezium ABCD, O is the point of intersection of AC and BD, AB \|\| CD, and $A B = \frac{5}{2} \times C D$ . The area of $A O B = 100 c m^{2}$ . The area of $Δ O C D$ is : [1 mark]

Discussion

100.	Find the perimeter and the area of the right angled triangle whose sides are 6 feet, 8 feet and 10 feet?
Answer» Find the perimeter and the area of the right angled triangle whose sides are 6 feet, 8 feet and 10 feet?

Discussion

Explore topic-wise InterviewSolutions in .

Write the complement of:(i) a(ii) (x+5)o(iii) 13rd of 180o

Factorize 27y^6 - 28y^3 + 8

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

A cylinderical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Find the value of the given expression: (2p+3)×(2p−3)×(4p2+9)

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD=∠CBD.

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.

If the height of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.

When a natural number X is divided by 5 ,the remainder is 2. When a natural number Y is divided by 5,the remainder is 4, the remainder is Z when X+Y is divided by 5.The value of 2z/3-5/3

Choose the equivalent rational numbers of 818.

A circus artist is climbing the 20m rope. Which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.

If N is a set of all natural numbers and Q is a set of all rational numbers, then which of the following is a correct representation for these two sets?

In the given figure, ar(DRC)=ar(DPC) and ar(BDP)=ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

The curved surface area of a sphere of radius 5 cm is ____ sq cm.

In each of the following two polynomials, find the value of a, if x − a is factor:(i) x6 − ax5 + x4 − ax3 + 3x − a + 2(ii x5 − a2x3 + 2x + a + 1)

△ABC is an isosceles triangle and LO is perpendicular to MN. Show that ∠M = ∠N.

Prove that 3+2√5 is irrational number.

If A is an acute angle and cosA=(5/13), then the value of cosec A is .........................

Verify that x 3 + y3 + z3 -3xyz = 1/2 (x+y+z) [(x-y) 2 + (y-z) 2 +(z-x) 2]

Write actual division, find which of the following rational numbers are terminating decimals.(i) 1380(ii) 724(iii) 512(iv) 31375(v) 16125

In a triangle ABC,∠A&gt;π2,AA1 and AA2 are median and altitude, respectively. If ∠BAA1=∠A1AA2=∠A2AC, then value of sin3A3⋅cosA3 is:

In the graph there is 4 quadrant . The line of hyperbola is passing from 1st and 4th quadrant then why the equation of the hyperbola is positive? Why not it is negative ?

24. The area defined by |x-2| + |y+1| is greater than and equal to 1 and less than and equal to 2 is

Some measures are given in the adjacent figure, find the area of ABCD

The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is(a) 25 cm2(b) 28 cm2(c) 30 cm2(d) 40 cm2

45∘ can be obtained by drawing the angles of measure

If the bisectors ofopposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing ot at the points P&Q. Prove that PQ is the diameter of the circle.

Question 54The class size of the interval 80 - 85 is ___,

Question 4Which of the following cannot be the probability of an event?(a) 23(b) -1.5(c) 15%(d) 0.7

Which of the following is not a criterion for congruence of triangles?(a) SAS(b) SSA(c) ASA(d) SSS

Expand-: (-2a+3b+4c)

ABC is a right angle triangle right angled at B with hypotenuse AC=26 cm and perimeter 60 cm calculate the area of the triangle and other two sides.

rationlaise : 1/√7+√6-√13

The area of right triangle is 150 cm square. if its altitude exceeds the base by 5 cm .calculate perimeter of triangle

Find the distance between the following pairs of points:(i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)

Factorize:x2 + y − xy − x

Compute the area of trapezium PQRS in the given figure.

A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?

12×base×height is the formula for which type of triangles?

In the given figure, AB is a diameter of the circle such that ∠A = 35° and ∠Q = 25°, find ∠PBR.

If the surface area of a sphere is 144π m2, then its volume (in m3) is (a) 288 π(b) 316 π(c) 300 π(d) 188 π

In the figure, △ABC is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠BAC,then what is the value of BD in cm?3

Which of the following is a terminating decimal?[1 mark]

The radius of a circle is 5.6 cm. Then what will be the length of its longest chord?

Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.

What is the fraction of students who failed in Maths exam if the total number of students who appeared in the exam was 65 and the number of students who passed is 57?

In a trapezium ABCD, O is the point of intersection of AC and BD, AB || CD, and AB=52×CD. The area of AOB=100 cm2. The area of ΔOCD is :[1 mark]

Find the perimeter and the area of the right angled triangle whose sides are 6 feet, 8 feet and 10 feet?

In a triangle ABC,∠A>π2,AA1 and AA2 are median and altitude, respectively. If ∠BAA1=∠A1AA2=∠A2AC, then value of sin3A3⋅cosA3 is: