24740 + Interview Questions in Mathematics Page 120 InterviewSolution

5951.	If ∫(x+√1+x2)ndx=1a(n+1){x+√1+x2}n+1+1b(n−1){x+√1+x2}n−1+C;(n>1) then a+b=
Answer» If $\int (x + \sqrt{1 + x^{2}})^{n} d x = \frac{1}{a (n + 1)} {x + \sqrt{1 + x^{2}}}^{n + 1} + \frac{1}{b (n - 1)} {x + \sqrt{1 + x^{2}}}^{n - 1} + C; (n > 1)$ then $a + b =$

Discussion

5952.	How many planes can be made to pass through two points?
Answer» How many planes can be made to pass through two points?

Discussion

5953.	Which of the following rational numbers is a non-terminating and repeating decimal?
Answer» Which of the following rational numbers is a non-terminating and repeating decimal?

Discussion

5954.	Question 176ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
Answer» Question 176 ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.

Discussion

5955.	The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1l)
Answer» The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1l)

Discussion

5956.	If 6n = 1296, then 6n–3 = _________.
Answer» If 6ⁿ = 1296, then 6^n–3 = _________.

Discussion

5957.	Question 7 The lateral surface area of a cube is 256 m2. The volume of the cube is: A) 512 m3 B) 64 m3 C) 216 m3 D) 256 m3
Answer» Question 7 The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is: A) $512 m^{3}$ B) $64 m^{3}$ C) $216 m^{3}$ D) $256 m^{3}$

Discussion

5958.	Seg AD and seg BE are medians of ∆ ABC and point G is the centroid. If l (AG) = 5 cm, find l (GD). IF l (GE) = 2 cm, find l (BE).
Answer» Seg AD and seg BE are medians of ∆ ABC and point G is the centroid. If l (AG) = 5 cm, find l (GD). IF l (GE) = 2 cm, find l (BE).

Discussion

5959.	How to factorize x3 +2x2 +3x + 2
Answer» How to factorize x³+2x²+3x + 2

Discussion

5960.	A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.
Answer» A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.

Discussion

5961.	Identify which of the following is a trinomial.
Answer» Identify which of the following is a trinomial.

Discussion

5962.	In the given figure, ∠CAE=84∘. If ∠B:∠C=3 : 4, then find the value of ∠B and ∠C.
Answer» In the given figure, $∠ C A E = 84^{\circ}$ . If $∠ B : ∠ C = 3 : 4,$ then find the value of $∠ B$ and $∠ C$ .

Discussion

5963.

Find the mean of the following distribution: x: 10 12 20 25 35 f: 3 10 15 7 5

Answer» Find the mean of the following distribution:

x:	10	12	20	25	35
f:	3	10	15	7	5

Discussion

5964.	Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).
Answer» Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).

Discussion

5965.	Question 6A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass.
Answer» Question 6 A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $c m^{3}$ of iron has approximately 8 g mass.

Discussion

5966.	Which of the following rational numbers lies between −23 and −12?
Answer» Which of the following rational numbers lies between $- \frac{2}{3}$ and $- \frac{1}{2}$ ?

Discussion

5967.	The power set of {1,2} is
Answer» The power set of ${1, 2}$ is

Discussion

5968.	What is the length of an arc which subtends angle θ (degrees) at the centre in a circle of radius r?
Answer» What is the length of an arc which subtends angle $θ$ (degrees) at the centre in a circle of radius r?

Discussion

5969.	In the given figure , two circles with centres O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles.
Answer» In the given figure , two circles with centres O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles.

Discussion

5970.	What does the c in the equation y = mx + c, stand for? __
Answer» What does the c in the equation y = mx + c, stand for? __

Discussion

5971.	If one of the angles of a parallelogram is 80°, its opposite angle is ___ degrees.
Answer» If one of the angles of a parallelogram is 80°, its opposite angle is ___ degrees.

Discussion

5972.	lengtj of the common chord of the circle x^2+ y^2+2x + 3y +1 =0 and x^2+ y^2 4x+ 3y +4
Answer» lengtj of the common chord of the circle x^2+ y^2+2x + 3y +1 =0 and x^2+ y^2 4x+ 3y +4

Discussion

5973.	Give three rational numbers equivalent to −34.
Answer» Give three rational numbers equivalent to $\frac{- 3}{4}$ .

Discussion

5974.	40. Prove that area of a triangle is 1/2.base.height
Answer» 40. Prove that area of a triangle is 1/2.base.height

Discussion

5975.	ΔABC∼ΔPQR Find the values of y and z.
Answer» $Δ A B C \sim Δ P Q R$ Find the values of y and z.

5975.

ΔABC∼ΔPQR Find the values of y and z.

Answer»

$Δ A B C \sim Δ P Q R$

Find the values of y and z.

Discussion

5976.	Evaluate:(-12)³+7³+5³
Answer» Evaluate:(-12)³+7³+5³

Discussion

5977.	Simplify 3x(4x-5)+3 and find its values for (i) x=3 (ii) x=1/2
Answer» Simplify 3x(4x-5)+3 and find its values for (i) x=3 (ii) x=¹^/₂

Discussion

5978.	In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD > BC.
Answer» In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD > BC.

Discussion

5979.	If the sides of a triangle is a,b and c.Then what is the semi perimeter of the triangle?
Answer» If the sides of a triangle is a,b and c.Then what is the semi perimeter of the triangle?

Discussion

5980.	The figure shows an equilateral ΔABC of side 10 cm and a right angle ΔBDC whose side BD = 8 cm and ∠D=90∘.The area of the shaded portion is ___ cm2.
Answer» The figure shows an equilateral $Δ A B C$ of side 10 cm and a right angle $Δ B D C$ whose side BD = 8 cm and $∠ D = 90^{\circ}$ . The area of the shaded portion is ___ $c m^{2}$ .

5980.

The figure shows an equilateral ΔABC of side 10 cm and a right angle ΔBDC whose side BD = 8 cm and ∠D=90∘.The area of the shaded portion is ___ cm2.

Answer»

The figure shows an equilateral $Δ A B C$ of side 10 cm and a right angle $Δ B D C$ whose side BD = 8 cm and $∠ D = 90^{\circ}$ .

The area of the shaded portion is ___ $c m^{2}$ .

Discussion

5981.	A coin is tossed 60 times and the tail appears 35 times. In a random throw of a coin, what is the probability of getting a head? (a) 712 (b) 127 (c) 512 (d) 125
Answer» A coin is tossed 60 times and the tail appears 35 times. In a random throw of a coin, what is the probability of getting a head? (a) $\frac{7}{12}$ (b) $\frac{12}{7}$ (c) $\frac{5}{12}$ (d) $\frac{1}{25}$

5981.

A coin is tossed 60 times and the tail appears 35 times. In a random throw of a coin, what is the probability of getting a head? (a) 712 (b) 127 (c) 512 (d) 125

Answer»

A coin is tossed 60 times and the tail appears 35 times. In a random throw of a coin, what is the probability of getting a head?

(a) $\frac{7}{12}$

(b) $\frac{12}{7}$

(c) $\frac{5}{12}$

(d) $\frac{1}{25}$

Discussion

5982.	ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.
Answer» ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.

Discussion

5983.	If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.
Answer» If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

Discussion

5984.	A linear equation in two variables
Answer» A linear equation in two variables

Discussion

5985.	Two parallel lines m and n are intersected by another pair of parallel lines p and q as shown in the figure. Which of the following criterion is true for ∆ ABC ≅ ∆CDA?
Answer» Two parallel lines m and n are intersected by another pair of parallel lines p and q as shown in the figure. Which of the following criterion is true for ∆ ABC ≅ ∆CDA?

5985.

Two parallel lines m and n are intersected by another pair of parallel lines p and q as shown in the figure. Which of the following criterion is true for ∆ ABC ≅ ∆CDA?

Answer»

Two parallel lines m and n are intersected by another pair of parallel lines p and q as shown in the figure. Which of the following criterion is true for ∆ ABC ≅ ∆CDA?

Discussion

5986.	The angles of a polygon are in the ratio of 3: 4: 5: 6. Find the highest value of angle of the polygon in degree.
Answer» The angles of a polygon are in the ratio of 3: 4: 5: 6. Find the highest value of angle of the polygon in degree.

Discussion

5987.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

5988.	ABCD is a square, X and Y are the points on sides AD and BC respectively such that AY = BX, then
Answer» ABCD is a square, X and Y are the points on sides AD and BC respectively such that AY = BX, then

5988.

ABCD is a square, X and Y are the points on sides AD and BC respectively such that AY = BX, then

Answer»

ABCD is a square, X and Y are the points on sides AD and BC respectively such that AY = BX, then

Discussion

5989.	Identify constant, linear, quadratic, cubic and quartic polynomials from the following.(i) x−x3+x4(ii) −6x2(iii) −p
Answer» Identify constant, linear, quadratic, cubic and quartic polynomials from the following. (i) $x - x^{3} + x^{4}$ (ii) $- 6 x^{2}$ (iii) $- p$

Discussion

5990.	TO prove:--Surface area of a sphere is 4(pie)r^2 .ONLY BY ''INTEGRATION''
Answer» TO prove:-- Surface area of a sphere is 4(pie)r^2 . ONLY BY ''INTEGRATION''

Discussion

5991.	When simplified (x-1+y-1)-1 is equal to(a) xy(b) x+y(c) xyx+y(d) x+yxy
Answer» When simplified $(x^{- 1} + y^{- 1})^{- 1}$ is equal to (a) xy (b) x+y (c) $\frac{x y}{x + y}$ (d) $\frac{x + y}{x y}$

Discussion

5992.	Question 1 In the given figure, E is any point on the median AD of a ΔABC. Show that ar(ABE) = ar(ACE).
Answer» Question 1 In the given figure, E is any point on the median AD of a $Δ A B C$ . Show that ar(ABE) = ar(ACE).

Discussion

5993.	The runs scored by a batsman in 10 matches are 34, 65, 23, 11, 28, 56, 87, 54, 98 and 12 respectively. What is the median of the runs scored in these 10 matches?
Answer» The runs scored by a batsman in 10 matches are 34, 65, 23, 11, 28, 56, 87, 54, 98 and 12 respectively. What is the median of the runs scored in these 10 matches?

Discussion

5994.	Draw a graph using these points A(3,4), B(3,2), C(5,2), D(5,4). Also identify the shape that is made by joining the points ABCD.
Answer» Draw a graph using these points A(3,4), B(3,2), C(5,2), D(5,4). Also identify the shape that is made by joining the points ABCD.

Discussion

5995.	Verify the property x×y=y×x of rational numbers by usingx=−57 and y=1415
Answer» Verify the property $x \times y = y \times x$ of rational numbers by using $x = \frac{- 5}{7}$ and $y = \frac{14}{15}$

Discussion

5996.	Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
Answer» Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Discussion

5997.	Find the value of x and y for the pair of equations 7x−2yxy=5 and 8x−6yxy=15
Answer» Find the value of x and y for the pair of equations $\frac{7 x - 2 y}{x y} = 5$ and $\frac{8 x - 6 y}{x y} = 15$

Discussion

5998.	in triangle pqr angle qpr =angle pqr and m, n are points on sides qr and pr respectively such that qm= pn prove that op = o
Answer» in triangle pqr angle qpr =angle pqr and m, n are points on sides qr and pr respectively such that qm= pn prove that op = o

Discussion

5999.	Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
Answer» Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

Discussion

6000.	A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Answer» A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Discussion

Explore topic-wise InterviewSolutions in .

If ∫(x+√1+x2)ndx=1a(n+1){x+√1+x2}n+1+1b(n−1){x+√1+x2}n−1+C;(n&gt;1) then a+b=

How many planes can be made to pass through two points?

Which of the following rational numbers is a non-terminating and repeating decimal?

Question 176ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.

The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1l)

If 6n = 1296, then 6n–3 = _________.

Question 7 The lateral surface area of a cube is 256 m2. The volume of the cube is: A) 512 m3 B) 64 m3 C) 216 m3 D) 256 m3​​​​​​​

Seg AD and seg BE are medians of ∆ ABC and point G is the centroid. If l (AG) = 5 cm, find l (GD). IF l (GE) = 2 cm, find l (BE).

How to factorize x​​​​​​3 +2x2 +3x + 2

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed.

Identify which of the following is a trinomial.

In the given figure, ∠CAE=84∘. If ∠B:∠C=3 : 4, then find the value of ∠B and ∠C.

Find the mean of the following distribution: x: 10 12 20 25 35 f: 3 10 15 7 5

Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).

Question 6A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass.

Which of the following rational numbers lies between −23 and −12?

The power set of {1,2} is

What is the length of an arc which subtends angle θ (degrees) at the centre in a circle of radius r?

In the given figure , two circles with centres O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles.

What does the c in the equation y = mx + c, stand for? __

If one of the angles of a parallelogram is 80°, its opposite angle is ___ degrees.

lengtj of the common chord of the circle x^2+ y^2+2x + 3y +1 =0 and x^2+ y^2 4x+ 3y +4

Give three rational numbers equivalent to −34.

40. Prove that area of a triangle is 1/2.base.height

ΔABC∼ΔPQR Find the values of y and z.

Evaluate:(-12)³+7³+5³

Simplify 3x(4x-5)+3 and find its values for (i) x=3 (ii) x=1/2

In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD > BC.

If the sides of a triangle is a,b and c.Then what is the semi perimeter of the triangle?

The figure shows an equilateral ΔABC of side 10 cm and a right angle ΔBDC whose side BD = 8 cm and ∠D=90∘.The area of the shaded portion is ___ cm2.

A coin is tossed 60 times and the tail appears 35 times. In a random throw of a coin, what is the probability of getting a head? (a) 712 (b) 127 (c) 512 (d) 125

ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

A linear equation in two variables

Two parallel lines m and n are intersected by another pair of parallel lines p and q as shown in the figure. Which of the following criterion is true for ∆ ABC ≅ ∆CDA?

The angles of a polygon are in the ratio of 3: 4: 5: 6. Find the highest value of angle of the polygon in degree.

How many irrational numbers exist between two rational numbers?

ABCD is a square, X and Y are the points on sides AD and BC respectively such that AY = BX, then

Identify constant, linear, quadratic, cubic and quartic polynomials from the following.(i) x−x3+x4(ii) −6x2(iii) −p

TO prove:--Surface area of a sphere is 4(pie)r^2 .ONLY BY ''INTEGRATION''

When simplified (x-1+y-1)-1 is equal to(a) xy(b) x+y(c) xyx+y(d) x+yxy

Question 1 In the given figure, E is any point on the median AD of a ΔABC. Show that ar(ABE) = ar(ACE).

The runs scored by a batsman in 10 matches are 34, 65, 23, 11, 28, 56, 87, 54, 98 and 12 respectively. What is the median of the runs scored in these 10 matches?

Draw a graph using these points A(3,4), B(3,2), C(5,2), D(5,4). Also identify the shape that is made by joining the points ABCD.

Verify the property x×y=y×x of rational numbers by usingx=−57 and y=1415

Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Find the value of x and y for the pair of equations 7x−2yxy=5 and 8x−6yxy=15

in triangle pqr angle qpr =angle pqr and m, n are points on sides qr and pr respectively such that qm= pn prove that op = o

Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

If ∫(x+√1+x2)ndx=1a(n+1){x+√1+x2}n+1+1b(n−1){x+√1+x2}n−1+C;(n>1) then a+b=

Question 7 The lateral surface area of a cube is 256 m2. The volume of the cube is: A) 512 m3 B) 64 m3 C) 216 m3 D) 256 m3

How to factorize x3 +2x2 +3x + 2