24740 + Interview Questions in Mathematics Page 189 InterviewSolution

9401.	In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Answer» In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

Discussion

9402.	In the adjoining figure,BD\|\|CA, E is the midpoint of CA and BD=12CA.Prove that ar(△ ABC)=2ar(△ DBC).
Answer» In the adjoining figure,BD\|\|CA, E is the midpoint of CA and BD= $\frac{1}{2} C A$ .Prove that $a r (△ A B C) = 2 a r (△ D B C)$ .

Discussion

9403.	Simplify: (3√3+2√2)(2√3+3√2)
Answer» Simplify: $(3 \sqrt{3} + 2 \sqrt{2})$ $(2 \sqrt{3} + 3 \sqrt{2})$

Discussion

9404.	The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. The area of the triangle is
Answer» The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. The area of the triangle is

Discussion

9405.	28.How orthocentre of obtused triangle is outside triangle?
Answer» 28.How orthocentre of obtused triangle is outside triangle?

Discussion

9406.	Match the polynomials with their respective factors.
Answer» Match the polynomials with their respective factors.

Discussion

9407.	61.Water rises in a capillary up to a height of 8.0cm .if the capillary is inclined at an angle of45^° with the vertical height of water .how much lenght of the capillary will be occupied by water? If the lenght of the capillary is reduced to 4.0cm and it is held vertically in water ,then what wulk be the position of water?
Answer» 61.Water rises in a capillary up to a height of 8.0cm .if the capillary is inclined at an angle of45^° with the vertical height of water .how much lenght of the capillary will be occupied by water? If the lenght of the capillary is reduced to 4.0cm and it is held vertically in water ,then what wulk be the position of water?

Discussion

9408.	The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of ₹ 50 per m.
Answer» The area of a circular playground is $22176 m^{2}$ . Find the cost of fencing this ground at the rate of ₹ 50 per m.

Discussion

9409.	Write the rationalising factor of root 12
Answer» Write the rationalising factor of root 12

Discussion

9410.	In the given figure, AB is parallel to DC and the area of rectangle PQRS is 42 cm2. Also, AD = BC = 17 cm. What is the length of DC?
Answer» In the given figure, AB is parallel to DC and the area of rectangle PQRS is 42 cm2. Also, AD = BC = 17 cm. What is the length of DC?

9410.

In the given figure, AB is parallel to DC and the area of rectangle PQRS is 42 cm2. Also, AD = BC = 17 cm. What is the length of DC?

Answer»

In the given figure, AB is parallel to DC and the area of rectangle PQRS is 42 cm2. Also, AD = BC = 17 cm.

What is the length of DC?

Discussion

9411.	A father tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Select the algebraic equations that represent this situation.
Answer» A father tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Select the algebraic equations that represent this situation.

Discussion

9412.	If ABC is a triangle , AB = AC,and AB = BC then ΔABC
Answer» If ABC is a triangle , AB = AC,and AB = BC then ΔABC

Discussion

9413.	Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is(a) 1 : 2(b) 2:1(c) 1 : 2(d) 1 : 4(d)
Answer» Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is (a) $1 : \sqrt{2}$ (b) $\sqrt{2} : 1$ (c) 1 : 2 (d) 1 : 4 (d)

Discussion

9414.	Factorise the following using suitable identities: (x+3)+p^2+2p(x+3)
Answer» Factorise the following using suitable identities: (x+3)+p^2+2p(x+3)

9414.

Factorise the following using suitable identities: (x+3)+p^2+2p(x+3)

Answer»

Factorise the following using suitable identities:

(x+3)+p^2+2p(x+3)

Discussion

9415.	(i) Solve 12x2−9y+12−16x2(ii) Find the sum of 9my+10my2 and −9xy−20my2
Answer» (i) Solve $12 x^{2} - 9 y + 12 - 16 x^{2}$ (ii) Find the sum of $9 m y + 10 m y^{2}$ and $- 9 x y - 20 m y^{2}$

Discussion

9416.

The following table gives the lifetimes of 400 neon lamps: Lifetime (in hr) 300−400 400−500 500−600 600−700 700−800 800−900 900−1000 Number of lamps 14 56 60 86 74 62 48 (i) Represent the given information with the help of a histogram.(ii) How many lamps have a lifetime of more than 700 hours?

Answer» The following table gives the lifetimes of 400 neon lamps:

Lifetime (in hr)	300−400	400−500	500−600	600−700	700−800	800−900	900−1000
Number of lamps	14	56	60	86	74	62	48

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

Discussion

9417.	2y3 + y2 − 2y − 1
Answer» 2y³ + y² − 2y − 1

Discussion

9418.	Evaluate: 53 - 23 - 33
Answer» Evaluate: 5³- 2³- 3³

Discussion

9419.	Question 3 (iv) Simplify: 712.812
Answer» Question 3 (iv) Simplify: $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

9419.

Question 3 (iv) Simplify: 712.812

Answer»

Question 3 (iv)
Simplify:

$7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

Discussion

9420.	What is zeroes of a polynomial?
Answer» What is zeroes of a polynomial?

Discussion

9421.	Which of the following is the correct increasing order for a given number α, α>0?
Answer» Which of the following is the correct increasing order for a given number $α$ , $α > 0$ ?

Discussion

9422.	A cuboid is 25 cm long, 15 cm broad and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?
Answer» A cuboid is 25 cm long, 15 cm broad and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?

Discussion

9423.	The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is __________.
Answer» The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is __________.

Discussion

9424.	If the bisectors of the base angles of a triangle enclose an angle of 135∘. Prove that the triangle is a right triangle.
Answer» If the bisectors of the base angles of a triangle enclose an angle of $135^{\circ}$ . Prove that the triangle is a right triangle.

Discussion

9425.	How many linear equations are satisfied by x = 2 and y = -3?
Answer» How many linear equations are satisfied by x = 2 and y = -3?

Discussion

9426.	The area of a square piece of land is 900 sq.m Find its length.
Answer» The area of a square piece of land is 900 sq.m Find its length.

Discussion

9427.	Complete the following cumulative frequency table Cumulative frequency cumulative frequency Class. Frequency. ( Less than type ) ( more than type) 100-500 45 500-1000 19. 1000-1500. 16. 1500-2000. 2. 2000-2500. 5 Sir, complete the following table where the numbers are not written and send me as soon as possible because tomorrow is my algebra paper
Answer» Complete the following cumulative frequency table Cumulative frequency cumulative frequency Class. Frequency. ( Less than type ) ( more than type) 100-500 45 500-1000 19. 1000-1500. 16. 1500-2000. 2. 2000-2500. 5 Sir, complete the following table where the numbers are not written and send me as soon as possible because tomorrow is my algebra paper

Discussion

9428.	The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be(a) 27π cm3(b) 36π cm3(c) 108π cm3(d) 12π cm3
Answer» The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be (a) 27 $π$ cm³ (b) 36 $π$ cm³ (c) 108 $π$ cm³ (d) 12 $π$ cm³

Discussion

9429.	Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Answer» Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Discussion

9430.	The marks obtained by 17 students in a mathematics test (out of 100) are given below:90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68.Find the range of the above data.
Answer» The marks obtained by 17 students in a mathematics test (out of 100) are given below: 90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68. Find the range of the above data.

Discussion

9431.	If the Secondary Education cess is ₹500, and there is no rebatable component of Income tax declared, find the annual income if the person is 65 years old?
Answer» If the Secondary Education cess is ₹500, and there is no rebatable component of Income tax declared, find the annual income if the person is 65 years old?

Discussion

9432.	Question 172ABCD is a parallelogram. Find the values of x, y and z.
Answer» Question 172 ABCD is a parallelogram. Find the values of x, y and z.

Discussion

9433.	In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Prove that:(i) distance between the chords, if both the chords are on the opposite sides of the centre, is 23 cm, and(ii) distance between the chords, if both the chords are on the same side of the centre is 7 cm.
Answer» In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Prove that: (i) distance between the chords, if both the chords are on the opposite sides of the centre, is 23 cm, and (ii) distance between the chords, if both the chords are on the same side of the centre is 7 cm.

Discussion

9434.	(→a.^i)(→a×^i)+(→a.^j)(→a×^j)+(→a.^k)(→a×^k) is always equal to
Answer» $(\to a .^i) (\to a \times^i) + (\to a .^j) (\to a \times^j) + (\to a .^k) (\to a \times^k)$ is always equal to

Discussion

9435.	Which of the following is irrational?(a) 0.15(b) 0.01516(c) 0.1516¯(d) 0.5015001500015.
Answer» Which of the following is irrational? (a) 0.15 (b) 0.01516 (c) $0 . \bar{1516}$ (d) 0.5015001500015.

Discussion

9436.	Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.
Answer» Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Discussion

9437.	The value of 3√212+3√64 is
Answer» The value of $\sqrt[3]{212 + \sqrt[3]{64}}$ is

Discussion

9438.	Find the leftmost and the rightmost number when the following are represented on the number line.−1910 ,−95 ,−85 ,−32 ,−1710
Answer» Find the leftmost and the rightmost number when the following are represented on the number line. $\frac{- 19}{10}, \frac{- 9}{5}, \frac{- 8}{5}, \frac{- 3}{2}, \frac{- 17}{10}$

9438.

Find the leftmost and the rightmost number when the following are represented on the number line.−1910 ,−95 ,−85 ,−32 ,−1710

Answer»

Find the leftmost and the rightmost number when the following are represented on the number line.

$\frac{- 19}{10}, \frac{- 9}{5}, \frac{- 8}{5}, \frac{- 3}{2}, \frac{- 17}{10}$

Discussion

9439.	The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to(a) a6 + b6(b) a6 − b6(c) a3 − b3(d) a3 + b3
Answer» The product (a + b) (a − b) (a² − ab + b²) (a² + ab + b²) is equal to (a) a⁶ + b⁶ (b) a⁶ − b⁶ (c) a³ − b³ (d) a³+ b³

Discussion

9440.	11. Factorise: 12[(x2+7x)2]-8(x2+7x)(2x-1)-15[(2x-1)2]
Answer» 11. Factorise: 12[(x2+7x)2]-8(x2+7x)(2x-1)-15[(2x-1)2]

Discussion

9441.	Factorise: √2x2+3x+√2
Answer» Factorise: $\sqrt{2} x^{2} + 3 x + \sqrt{2}$

Discussion

9442.	Following is the set of observed data for successive 15 minutes period of 90 minutes storm in a catchment Duration (min)153045607590Rainfall (cm/hr)2.02.08.07.01.251.25 If the value of ϕ−index is 3 cm /hr , the value of W-index will be ___2.08
Answer» Following is the set of observed data for successive 15 minutes period of 90 minutes storm in a catchment $\begin{matrix} Duration (min) & 15 & 30 & 45 & 60 & 75 & 90 Rainfall (cm/hr) & 2.0 & 2.0 & 8.0 & 7.0 & 1.25 & 1.25 \end{matrix}$ If the value of $ϕ - i n d e x$ is 3 cm /hr , the value of W-index will be ___ 2.08

Discussion

9443.	Comment upon the nature of roots of the equation x−1x−1=x+42x+2
Answer» Comment upon the nature of roots of the equation $\frac{x - 1}{x - 1} = \frac{x + 4}{2 x + 2}$

Discussion

9444.	If the areas of two given shapes are equal, will their perimeters also be equal?
Answer» If the areas of two given shapes are equal, will their perimeters also be equal?

Discussion

9445.	In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE).
Answer» In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE).

9445.

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE).

Answer»

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE).

Discussion

9446.	Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if 112of steel actually used was wasted in making the closed tank?
Answer» Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if $\frac{1}{12}$ of steel actually used was wasted in making the closed tank?

Discussion

9447.	If A and B are two square matrices such that B=−A−1BA, then (A+B)2 is equal to
Answer» If A and B are two square matrices such that $B = - A^{- 1} B A$ , then $(A + B)^{2}$ is equal to

Discussion

9448.	The point on the y-axis which is equidistant from the point A(6,5) and B(−4,3) is _______________
Answer» The point on the y-axis which is equidistant from the point A $(6, 5)$ and B $(- 4, 3)$ is _______________

Discussion

9449.	ABC is an isosceles triangle with AB = AC. Drawn AP ⊥ BC to show that ∠B = ∠C.
Answer» ABC is an isosceles triangle with AB = AC. Drawn AP ⊥ BC to show that ∠B = ∠C.

Discussion

9450.	Find the quotient obtained when x4+x3−2x2+x−1 is divided by x−1.
Answer» Find the quotient obtained when $x^{4} + x^{3} - 2 x^{2} + x - 1$ is divided by $x - 1$ .

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

In the adjoining figure,BD||CA, E is the midpoint of CA and BD=12CA.Prove that ar(△ ABC)=2ar(△ DBC).

Simplify: (3√3+2√2)(2√3+3√2)

The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. The area of the triangle is

28.How orthocentre of obtused triangle is outside triangle?

Match the polynomials with their respective factors.

The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of ₹ 50 per m.

Write the rationalising factor of root 12

In the given figure, AB is parallel to DC and the area of rectangle PQRS is 42 cm2. Also, AD = BC = 17 cm. What is the length of DC?

A father tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Select the algebraic equations that represent this situation.

If ABC is a triangle , AB = AC,and AB = BC then ΔABC

Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is(a) 1 : 2(b) 2:1(c) 1 : 2(d) 1 : 4(d)

Factorise the following using suitable identities: (x+3)+p^2+2p(x+3)

(i) Solve 12x2−9y+12−16x2(ii) Find the sum of 9my+10my2 and −9xy−20my2

2y3 + y2 − 2y − 1

Evaluate: 53 - 23 - 33

Question 3 (iv) Simplify: 712.812

What is zeroes of a polynomial?

Which of the following is the correct increasing order for a given number α, α&gt;0?

A cuboid is 25 cm long, 15 cm broad and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is __________.

If the bisectors of the base angles of a triangle enclose an angle of 135∘. Prove that the triangle is a right triangle.

How many linear equations are satisfied by x = 2 and y = -3?

The area of a square piece of land is 900 sq.m Find its length.

The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be(a) 27π cm3(b) 36π cm3(c) 108π cm3(d) 12π cm3

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

The marks obtained by 17 students in a mathematics test (out of 100) are given below:90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68.Find the range of the above data.

If the Secondary Education cess is ₹500, and there is no rebatable component of Income tax declared, find the annual income if the person is 65 years old?

Question 172ABCD is a parallelogram. Find the values of x, y and z.

(→a.^i)(→a×^i)+(→a.^j)(→a×^j)+(→a.^k)(→a×^k) is always equal to

Which of the following is irrational?(a) 0.15(b) 0.01516(c) 0.1516¯(d) 0.5015001500015.

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

The value of 3√212+3√64 is

Find the leftmost and the rightmost number when the following are represented on the number line.−1910 ,−95 ,−85 ,−32 ,−1710

The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to(a) a6 + b6(b) a6 − b6(c) a3 − b3(d) a3 + b3

11. Factorise: 12[(x2+7x)2]-8(x2+7x)(2x-1)-15[(2x-1)2]

Factorise: √2x2+3x+√2

Following is the set of observed data for successive 15 minutes period of 90 minutes storm in a catchment Duration (min)153045607590Rainfall (cm/hr)2.02.08.07.01.251.25 If the value of ϕ−index is 3 cm /hr , the value of W-index will be ___2.08

Comment upon the nature of roots of the equation x−1x−1=x+42x+2

If the areas of two given shapes are equal, will their perimeters also be equal?

In the given pentagon ABCDE, prove that 2CD &lt; Perimeter (ABCDE).

Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if 112of steel actually used was wasted in making the closed tank?

If A and B are two square matrices such that B=−A−1BA, then (A+B)2 is equal to

The point on the y-axis which is equidistant from the point A(6,5) and B(−4,3) is _______________

ABC is an isosceles triangle with AB = AC. Drawn AP ⊥ BC to show that ∠B = ∠C.

Find the quotient obtained when x4+x3−2x2+x−1 is divided by x−1.

Which of the following is the correct increasing order for a given number α, α>0?

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE).