24740 + Interview Questions in Mathematics Page 37 InterviewSolution

1801.	If log 2 = 0.3010 and log 3 = 0.4771, find the value of log√24
Answer» If log 2 = 0.3010 and log 3 = 0.4771, find the value of $l o g \sqrt{24}$

Discussion

1802.	Prove that the points (7, 10), (−2, 5) and (3, −4) are the vertices of an isosceles right triangle. [CBSE 2013]
Answer» Prove that the points (7, 10), (−2, 5) and (3, −4) are the vertices of an isosceles right triangle. [CBSE 2013]

Discussion

1803.	P and Q arerespectively the mid-points of sides AB and BC of a triangle ABC andR is the mid-point of AP, show that(i) (ii) (iii)
Answer» P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that (i) (ii) (iii)

1803.

P and Q arerespectively the mid-points of sides AB and BC of a triangle ABC andR is the mid-point of AP, show that(i) (ii) (iii)

Answer»

P and Q are
respectively the mid-points of sides AB and BC of a triangle ABC and
R is the mid-point of AP, show that

(i) (ii)

(iii)

Discussion

1804.	Find area of the triangle whose vertices are:(2, 3), (-1, 0), (2, -4)
Answer» Find area of the triangle whose vertices are: (2, 3), (-1, 0), (2, -4)

Discussion

1805.	Meaning of linear pair angles
Answer» Meaning of linear pair angles

Discussion

1806.	An incomplete distribution is given as follows:Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70Frequency: 10 20 ? 40 ? 25 15You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
Answer» An incomplete distribution is given as follows: Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequency: 10 20 ? 40 ? 25 15 You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Discussion

1807.	In Q.No. 1, if AD = 6 cm, CF = 10 cm, and AE = 8 cm, find AB.
Answer» In Q.No. 1, if AD = 6 cm, CF = 10 cm, and AE = 8 cm, find AB.

Discussion

1808.	The degree of the polynomial f(x, y, z) =\sqrt2 x^3y^4z+3x^5y^2z^3+4xyz is
Answer» The degree of the polynomial f(x, y, z) =\sqrt2 x^3y^4z+3x^5y^2z^3+4xyz is

Discussion

1809.	If lth, mth and nth terms of an HP are x,y and z respectively, then find the value of yz(m-n) + xz(n-l) + xy(l -m).
Answer» If lth, mth and nth terms of an HP are x,y and z respectively, then find the value of yz(m-n) + xz(n-l) + xy(l -m).

Discussion

1810.	Chennai angle of a parallelogram is two third of its adjacent angle then the smallest angle of the parallelogram is I am not satisfied with the application so please explain me
Answer» Chennai angle of a parallelogram is two third of its adjacent angle then the smallest angle of the parallelogram is I am not satisfied with the application so please explain me

Discussion

1811.	A rational number lying between -3/11+8/11 is (1) 16/10 (2) 15/11 (3) -25/65 (4) 5/1
Answer» A rational number lying between -3/11+8/11 is (1) 16/10 (2) 15/11 (3) -25/65 (4) 5/1

Discussion

1812.	Evaluate ∫x3ln2xdx(where C is constant of integration)
Answer» Evaluate $\int x^{3} {ln}^{2} x d x$ (where $C$ is constant of integration)

Discussion

1813.	Prove that 2+35 is an irrational number, given that 3 is an irrational number.
Answer» Prove that $\frac{2 + \sqrt{3}}{5}$ is an irrational number, given that $\sqrt{3}$ is an irrational number.

Discussion

1814.	Solve the following using laws of exponents and arrange them in ascending order.
Answer» Solve the following using laws of exponents and arrange them in ascending order.

Discussion

1815.	The heights (inAns cm) of 30 students of a class are given below:161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148,153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152, 147, 155, 155, 157.Prepare a frequency table as well as a cumulative frequency table with 160 – 165 (165 not included) as one of the class intervals.
Answer» The heights (inAns cm) of 30 students of a class are given below: 161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148, 153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152, 147, 155, 155, 157. Prepare a frequency table as well as a cumulative frequency table with 160 – 165 (165 not included) as one of the class intervals.

Discussion

1816.	Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?
Answer» Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Discussion

1817.	In the given figure, BCAC = 2425 .Find the value of cosec2A – cot2A .
Answer» In the given figure, $\frac{B C}{A C}$ = $\frac{24}{25}$ .Find the value of $c o s e c^{2} A$ – $c o t^{2} A$ .

1817.

In the given figure, BCAC = 2425 .Find the value of cosec2A – cot2A .

Answer»

In the given figure, $\frac{B C}{A C}$ = $\frac{24}{25}$ .Find the value of $c o s e c^{2} A$ – $c o t^{2} A$ .

Discussion

1818.	If x=5- root 24, then find the value of 10(x square+1/x square) - 97(x+1/x)-10
Answer» If x=5- root 24, then find the value of 10(x square+1/x square) - 97(x+1/x)-10

Discussion

1819.	The following table shows number of males and females of a locality in different age groups.Age~in~years10−2021−50Above~50Male12164Female8146If one person is selected at random, find the probability that the selected person is male
Answer» The following table shows number of males and females of a locality in different age groups. $\begin{matrix} Age~in~years & 10 - 20 & 21 - 50 & Above~50 Male & 12 & 16 & 4 Female & 8 & 14 & 6 \end{matrix}$ If one person is selected at random, find the probability that the selected person is male

1819.

The following table shows number of males and females of a locality in different age groups.Age~in~years10−2021−50Above~50Male12164Female8146If one person is selected at random, find the probability that the selected person is male

Answer»

The following table shows number of males and females of a locality in different age groups.

$\begin{matrix} Age~in~years & 10 - 20 & 21 - 50 & Above~50 Male & 12 & 16 & 4 Female & 8 & 14 & 6 \end{matrix}$

If one person is selected at random, find the probability that the selected person is male

Discussion

1820.	In a circle, with centre O, a cyclic quadrilateral ABCD is drawn with AB as a diameter of the circle and CD equal to radius of the circle. If AD and BC produced meet at point P; show that ∠ APB = 60o.
Answer» In a circle, with centre O, a cyclic quadrilateral ABCD is drawn with AB as a diameter of the circle and CD equal to radius of the circle. If AD and BC produced meet at point P; show that $∠$ APB = $60^{o}$ .

Discussion

1821.	D is the mid-point of side BC of ΔABC and E is the mid-point BD. If O is the mid point of AE, then prove that ar(ΔBOE) = 18 ar(ΔABC).
Answer» D is the mid-point of side BC of ΔABC and E is the mid-point BD. If O is the mid point of AE, then prove that ar(ΔBOE) = $\frac{1}{8}$ ar(ΔABC).

Discussion

1822.	If the polynomials ax3+4x2+3x−4 and x3−4x+a leave the same remainder when divided by x−3, find the value of a ?
Answer» If the polynomials $a x^{3} + 4 x^{2} + 3 x - 4$ and $x^{3} - 4 x + a$ leave the same remainder when divided by $x - 3$ , find the value of a ?

Discussion

1823.	The number of different words that can be made from the letters of the word INTERMEDIATE, such that two vowels never come together, is __________.
Answer» The number of different words that can be made from the letters of the word INTERMEDIATE, such that two vowels never come together, is __________.

Discussion

1824.	Question 39The sum of angles of a concave quadrilateral isa) More than 360∘b) Less than 360∘c) Equal to 360∘d) Twice of 360∘
Answer» Question 39 The sum of angles of a concave quadrilateral is a) More than $360^{\circ}$ b) Less than $360^{\circ}$ c) Equal to $360^{\circ}$ d) Twice of $360^{\circ}$

Discussion

1825.	In a ∆ABC, if ∠A − ∠B = 42° and ∠B − ∠C = 21° then ∠B = ?(a) 32°(b) 63°(c) 53°(d) 95°Figure
Answer» In a ∆ABC, if ∠A − ∠B = 42° and ∠B − ∠C = 21° then ∠B = ? (a) 32° (b) 63° (c) 53° (d) 95° Figure

Discussion

1826.

Write the number of faces, edges and vertices of each shape in the table. Name Cylinder Cone Pentagonal Pyramid Hexagonal Pyramid Hexagonal prism Pentagonal prism Shape Faces Vertices Edges

Answer» Write the number of faces, edges and vertices of each shape in the table.

Name	Cylinder	Cone	Pentagonal Pyramid	Hexagonal Pyramid	Hexagonal prism	Pentagonal prism
Shape
Faces
Vertices
Edges

Discussion

1827.	Express the given formula in term of y. TTi=1+y−12
Answer» Express the given formula in term of y. $\frac{T}{T_{i}} = 1 + \frac{y - 1}{2}$

1827.

Express the given formula in term of y. TTi=1+y−12

Answer»

Express the given formula in term of y.

$\frac{T}{T_{i}} = 1 + \frac{y - 1}{2}$

Discussion

1828.	A ΔABC is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming ΔPQR, as shown in the adjoining figure, show that BC=12QR.
Answer» A $Δ A B C$ is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming $Δ P Q R$ , as shown in the adjoining figure, show that $B C = \frac{1}{2} Q R$ .

1828.

A ΔABC is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming ΔPQR, as shown in the adjoining figure, show that BC=12QR.

Answer»

A $Δ A B C$ is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming $Δ P Q R$ , as shown in the adjoining figure, show that $B C = \frac{1}{2} Q R$ .

Discussion

1829.	The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then
Answer» The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

1829.

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

Answer»

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

Discussion

1830.	Draw the co-ordinate system on a plane and plot the following points.L (-2, 4), M (5, 6), N (-3, -4), P (2, -3), Q(6, -5), S(7, 0), T(0, -5)
Answer» Draw the co-ordinate system on a plane and plot the following points. L (-2, 4), M (5, 6), N (-3, -4), P (2, -3), Q(6, -5), S(7, 0), T(0, -5)

Discussion

1831.	In Triangle ABC AD is the median. Prove that AB +AC > 2AD.
Answer» In Triangle ABC AD is the median. Prove that AB +AC > 2AD.

Discussion

1832.	Which of the following numbers can be represented as non-terminating, repeating decimals?
Answer» Which of the following numbers can be represented as non-terminating, repeating decimals?

Discussion

1833.	The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 3. Find the volume of the cylinder if its total surface area is 1848 cm2.
Answer» The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 3. Find the volume of the cylinder if its total surface area is 1848 cm².

Discussion

1834.	Determine the measure of each of the equal angles of a right-angled isosceles triangle OR ABC is a right-angled triangle in which ∠A=90∘ and AB=AC. Find ∠B and ∠ C.
Answer» Determine the measure of each of the equal angles of a right-angled isosceles triangle OR ABC is a right-angled triangle in which $∠ A = 90^{\circ} a n d A B = A C . F i n d ∠ B a n d ∠ C .$

1834.

Determine the measure of each of the equal angles of a right-angled isosceles triangle OR ABC is a right-angled triangle in which ∠A=90∘ and AB=AC. Find ∠B and ∠ C.

Answer»

Determine the measure of each of the equal angles of a right-angled isosceles triangle

OR

ABC is a right-angled triangle in which $∠ A = 90^{\circ} a n d A B = A C . F i n d ∠ B a n d ∠ C .$

Discussion

1835.	If A={x:x=3n, n∈N,4≤n≤6} and B = {12, 15, 18}, then A and B are ___________.
Answer» If A={ $x : x = 3 n, n \in N, 4 \leq n \leq 6}$ and B = {12, 15, 18}, then A and B are ___________.

Discussion

1836.	Median of the data 10 21, 5, 6, 4, 12, 14, 3, is(1) 16(3) 4(2) 8(4) None of these
Answer» Median of the data 10 21, 5, 6, 4, 12, 14, 3, is(1) 16(3) 4(2) 8(4) None of these

Discussion

1837.	find the number of solutions of the equation e^x=x^2
Answer» find the number of solutions of the equation e^x=x^2

Discussion

1838.	Find the value of λ, if x = −λ and y = 52 is a solution of the equation x + 4y − 7 = 0.
Answer» Find the value of λ, if x = −λ and y = $\frac{5}{2}$ is a solution of the equation x + 4y − 7 = 0.

Discussion

1839.	In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.
Answer» In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.

Discussion

1840.	If the value of p2+q2=21 and pq=30, then find the value of (p+q)2
Answer» If the value of $p^{2} + q^{2} = 21$ and $p q = 30$ , then find the value of $(p + q)^{2}$

Discussion

1841.	Using factor theorem,factorize the polynomial: 1) x4-2x3-7x2+8x+12
Answer» Using factor theorem,factorize the polynomial: 1) x⁴-2x³-7x²+8x+12

1841.

Using factor theorem,factorize the polynomial: 1) x4-2x3-7x2+8x+12

Answer»

Using factor theorem,factorize the polynomial:

1) x⁴-2x³-7x²+8x+12

Discussion

1842.	x⁴-(x²-b²)⁴
Answer» x⁴-(x²-b²)⁴

Discussion

1843.	Prove that √3+√5 is an irrational number.
Answer» Prove that $\sqrt{3} + \sqrt{5}$ is an irrational number.

Discussion

1844.	Question 2Write all the other trigonometric ratios of ∠A in terms of sec A.
Answer» Question 2 Write all the other trigonometric ratios of $∠$ A in terms of sec A.

Discussion

1845.	Question 3 In the given figure, if AB\|\|DE,∠BAC=35∘ and ∠CDE=53∘, find ∠DCE.
Answer» Question 3 In the given figure, if $A B \| \| D E, ∠ B A C = 35^{\circ} a n d ∠ C D E = 53^{\circ}, f i n d ∠ D C E .$

Discussion

1846.	If (x2−y2) = 18 and (x - y) = 3, find the value of 16x2y2
Answer» If $(x^{2} - y^{2})$ = 18 and (x - y) = 3, find the value of 16 $x^{2} y^{2}$

Discussion

1847.	Explain,how irrational numbers differ from rational number?
Answer» Explain,how irrational numbers differ from rational number?

Discussion

1848.	A goldsmith can choose between 3 metals A, B or C to make an artifact. What is the probability that he chooses C?
Answer» A goldsmith can choose between 3 metals A, B or C to make an artifact. What is the probability that he chooses C?

Discussion

1849.	What is the trigonometry eq of 2 sinA+tanA=0
Answer» What is the trigonometry eq of 2 sinA+tanA=0

Discussion

1850.	In a quadrilateral ABCD AO and bo are the bisector of angle A and Angle B respectively prove that angle aob is equals to half of angle C plus half of angle d
Answer» In a quadrilateral ABCD AO and bo are the bisector of angle A and Angle B respectively prove that angle aob is equals to half of angle C plus half of angle d

Discussion

Explore topic-wise InterviewSolutions in .

If log 2 = 0.3010 and log 3 = 0.4771, find the value of log√24

Prove that the points (7, 10), (−2, 5) and (3, −4) are the vertices of an isosceles right triangle. [CBSE 2013]

P and Q arerespectively the mid-points of sides AB and BC of a triangle ABC andR is the mid-point of AP, show that(i) (ii) (iii)

Find area of the triangle whose vertices are:(2, 3), (-1, 0), (2, -4)

Meaning of linear pair angles

An incomplete distribution is given as follows:Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70Frequency: 10 20 ? 40 ? 25 15You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

In Q.No. 1, if AD = 6 cm, CF = 10 cm, and AE = 8 cm, find AB.

The degree of the polynomial f(x, y, z) =\sqrt2 x^3y^4z+3x^5y^2z^3+4xyz is

If lth, mth and nth terms of an HP are x,y and z respectively, then find the value of yz(m-n) + xz(n-l) + xy(l -m).

Chennai angle of a parallelogram is two third of its adjacent angle then the smallest angle of the parallelogram is I am not satisfied with the application so please explain me

A rational number lying between -3/11+8/11 is (1) 16/10 (2) 15/11 (3) -25/65 (4) 5/1

Evaluate ∫x3ln2xdx(where C is constant of integration)

Prove that 2+35 is an irrational number, given that 3 is an irrational number.

Solve the following using laws of exponents and arrange them in ascending order.

Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

In the given figure, BCAC = 2425 .Find the value of cosec2A – cot2A .

If x=5- root 24, then find the value of 10(x square+1/x square) - 97(x+1/x)-10

The following table shows number of males and females of a locality in different age groups.Age~in~years10−2021−50Above~50Male12164Female8146If one person is selected at random, find the probability that the selected person is male

In a circle, with centre O, a cyclic quadrilateral ABCD is drawn with AB as a diameter of the circle and CD equal to radius of the circle. If AD and BC produced meet at point P; show that ∠ APB = 60o.

D is the mid-point of side BC of ΔABC and E is the mid-point BD. If O is the mid point of AE, then prove that ar(ΔBOE) = 18 ar(ΔABC).

If the polynomials ax3+4x2+3x−4 and x3−4x+a leave the same remainder when divided by x−3, find the value of a ?

The number of different words that can be made from the letters of the word INTERMEDIATE, such that two vowels never come together, is __________.

Question 39The sum of angles of a concave quadrilateral isa) More than 360∘b) Less than 360∘c) Equal to 360∘d) Twice of 360∘

In a ∆ABC, if ∠A − ∠B = 42° and ∠B − ∠C = 21° then ∠B = ?(a) 32°(b) 63°(c) 53°(d) 95°Figure

Write the number of faces, edges and vertices of each shape in the table. Name Cylinder Cone Pentagonal Pyramid Hexagonal Pyramid Hexagonal prism Pentagonal prism Shape Faces Vertices Edges ​

Express the given formula in term of y. TTi=1+y−12

A ΔABC is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming ΔPQR, as shown in the adjoining figure, show that BC=12QR.

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

Draw the co-ordinate system on a plane and plot the following points.L (-2, 4), M (5, 6), N (-3, -4), P (2, -3), Q(6, -5), S(7, 0), T(0, -5)

In Triangle ABC AD is the median. Prove that AB +AC > 2AD.

Which of the following numbers can be represented as non-terminating, repeating decimals?

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 3. Find the volume of the cylinder if its total surface area is 1848 cm2.

Determine the measure of each of the equal angles of a right-angled isosceles triangle OR ABC is a right-angled triangle in which ∠A=90∘ and AB=AC. Find ∠B and ∠ C.

If A={x:x=3n, n∈N,4≤n≤6} and B = {12, 15, 18}, then A and B are ___________.

Median of the data 10 21, 5, 6, 4, 12, 14, 3, is(1) 16(3) 4(2) 8(4) None of these

find the number of solutions of the equation e^x=x^2

Find the value of λ, if x = −λ and y = 52 is a solution of the equation x + 4y − 7 = 0.

In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.

If the value of p2+q2=21 and pq=30, then find the value of (p+q)2

Using factor theorem,factorize the polynomial: 1) x4-2x3-7x​2+8x+12

x⁴-(x²-b²)⁴

Prove that √3+√5 is an irrational number.

Question 2Write all the other trigonometric ratios of ∠A in terms of sec A.

Question 3 In the given figure, if AB||DE,∠BAC=35∘ and ∠CDE=53∘, find ∠DCE.

If (x2−y2) = 18 and (x - y) = 3, find the value of 16x2y2

Explain,how irrational numbers differ from rational number?

A goldsmith can choose between 3 metals A, B or C to make an artifact. What is the probability that he chooses C?

What is the trigonometry eq of 2 sinA+tanA=0

In a quadrilateral ABCD AO and bo are the bisector of angle A and Angle B respectively prove that angle aob is equals to half of angle C plus half of angle d

Write the number of faces, edges and vertices of each shape in the table. Name Cylinder Cone Pentagonal Pyramid Hexagonal Pyramid Hexagonal prism Pentagonal prism Shape Faces Vertices Edges

Using factor theorem,factorize the polynomial: 1) x4-2x3-7x2+8x+12