32581 + Interview Questions in Mathematics Page 23 InterviewSolution

1101.	Prove that the points A(2, 4), B(2, 6) and C2+3, 5 are the vertices of an equilateral triangle.
Answer» Prove that the points A(2, 4), B(2, 6) and $C (2 + \sqrt{3}, 5)$ are the vertices of an equilateral triangle.

Discussion

1102.	Prove the following trigonometric identities: 1+tan2θ1+cot2θ=(1−tan θ1−cot θ)2=tan2θ
Answer» Prove the following trigonometric identities: $\frac{1 + t a n^{2} θ}{1 + c o t^{2} θ} = {(\frac{1 - t a n θ}{1 - c o t θ})}^{2} = t a n^{2} θ$

1102.

Prove the following trigonometric identities: 1+tan2θ1+cot2θ=(1−tan θ1−cot θ)2=tan2θ

Answer»

Prove the following trigonometric identities:

$\frac{1 + t a n^{2} θ}{1 + c o t^{2} θ} = {(\frac{1 - t a n θ}{1 - c o t θ})}^{2} = t a n^{2} θ$

Discussion

1103.	Find the mean of the data given in the table using step - deviation method.Class IntervalFrequency0−101010−201220−30730−40640−50550−608
Answer» Find the mean of the data given in the table using step - deviation method. $\begin{matrix} Class Interval & Frequency 0 - 10 & 10 10 - 20 & 12 20 - 30 & 7 30 - 40 & 6 40 - 50 & 5 50 - 60 & 8 \end{matrix}$

Discussion

1104.	11. If a+b=10 and ab=16, find the value of asquare+ab+bsquare
Answer» 11. If a+b=10 and ab=16, find the value of asquare+ab+bsquare

Discussion

1105.	When the polynomial x3+2x2−5ax−7 is divided by (x−1), the remainder is A and when the polynomial x3+ax2−12x+16 is divided by (x+2), the remainder is B. Find the value of 'a' if 2A+B=0.
Answer» When the polynomial $x^{3} + 2 x^{2} - 5 a x - 7$ is divided by $(x - 1)$ , the remainder is A and when the polynomial $x^{3} + a x^{2} - 12 x + 16$ is divided by $(x + 2)$ , the remainder is B. Find the value of 'a' if $2 A + B = 0$ .

Discussion

1106.	Find k if the line passing through points P(–12, –3) and Q(4, k) has slope 12.
Answer» Find k if the line passing through points P(–12, –3) and Q(4, k) has slope $\frac{1}{2}$ .

Discussion

1107.	The number of employees in a factory decreases in the ratio 8:7 and the salary of employees increases in the ratio of 5:6. Find whether the total salary of the employees increased or decreased and in what ratio.
Answer» The number of employees in a factory decreases in the ratio 8:7 and the salary of employees increases in the ratio of 5:6. Find whether the total salary of the employees increased or decreased and in what ratio.

Discussion

1108.	O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre, ∠AOB = 110∘, then angle subtended by the arc at any point on the circle say ∠APB is ____, where P is any point on the circle.
Answer» O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre, $∠$ AOB = $110^{\circ}$ , then angle subtended by the arc at any point on the circle say $∠$ APB is ____, where P is any point on the circle.

Discussion

1109.	If the first term of an A.P. is 3 and the sum of its first 25 terms in equal to the sum of its next 15 terms, then the common difference of this A.P. is
Answer» If the first term of an A.P. is $3$ and the sum of its first $25$ terms in equal to the sum of its next $15$ terms, then the common difference of this A.P. is

Discussion

1110.	Ritwik and Richa decide to trim the green and the brown path of their backyard, respectively. If both have the same speed, which one of them can finish trimming earlier? Why?
Answer» Ritwik and Richa decide to trim the green and the brown path of their backyard, respectively. If both have the same speed, which one of them can finish trimming earlier? Why?

Discussion

1111.	How many numbers lie between squares of 25 and 26?
Answer» How many numbers lie between squares of 25 and 26?

Discussion

1112.	The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is [CBSE 2014](a) 3(b) 5(c) 4(d) 6
Answer» The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is [CBSE 2014] (a) 3 (b) 5 (c) 4 (d) 6

Discussion

1113.	If [124−109]+A=[9−114−23], then A is
Answer» If $[\begin{matrix} 1 & 2 & 4 - 1 & 0 & 9 \end{matrix}] + A = [\begin{matrix} 9 & - 1 & 1 4 & - 2 & 3 \end{matrix}],$ then $A$ is

Discussion

1114.	You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.
Answer» You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

1114.

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Answer»

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Discussion

1115.	Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Answer» Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Discussion

1116.	if f(x) =x-1/x+1 then f(2x) is equal to1) f(x)+2/f(x)+32) f(x)+3/f(x)+23) f(x)+3/3f(x)+14)3f(x)+1/f(x)+3
Answer» if f(x) =x-1/x+1 then f(2x) is equal to 1) f(x)+2/f(x)+3 2) f(x)+3/f(x)+2 3) f(x)+3/3f(x)+1 4)3f(x)+1/f(x)+3

Discussion

1117.	Find the values of k for which the following equations have real roots (i) (ii) (iii) x2-4kx+k=0 (iv) kxx-25+10=0(v) kx(x-3)+9=0 (vi) 4x2+kx+3=0
Answer» Find the values of k for which the following equations have real roots (i) (ii) (iii) $x^{2} - 4 k x + k = 0$ (iv) $k x (x - 2 \sqrt{5}) + 10 = 0$ (v) $k x (x - 3) + 9 = 0$ (vi) $4 x^{2} + k x + 3 = 0$

Discussion

1118.	If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is 3:1 then find the angle of elevation of the sun at that time. [CBSE 2017]
Answer» If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is $\sqrt{3} : 1$ then find the angle of elevation of the sun at that time. [CBSE 2017]

Discussion

1119.	Let A={1,2,3},B={3,4} and C={4,5,6}. Find(A) A×(B∩C)(B) (A×B)∩(A×C)(C) A×(B∪C)(D) (A×B)∪(A×C)
Answer» Let $A = {1, 2, 3}, B = {3, 4}$ and $C = {4, 5, 6}$ . Find $(A) A \times (B \cap C)$ $(B) (A \times B) \cap (A \times C)$ $(C) A \times (B \cup C)$ $(D) (A \times B) \cup (A \times C)$

Discussion

1120.	Prove that the points A(2, 4), B(2, 6) and C(2 + √3, 5) are the vertices of an equilateral triangle.
Answer» Prove that the points A(2, 4), B(2, 6) and C(2 + $\sqrt{3}$ , 5) are the vertices of an equilateral triangle.

Discussion

1121.	If 3-13+1=x+y3, find the values of x and y.
Answer» If $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y \sqrt{3},$ find the values of x and y.

Discussion

1122.	The horizontal distance between two towers is 60 metres. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 90 metres, find the height of the first tower.Use 3=1.732
Answer» The horizontal distance between two towers is 60 metres. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 90 metres, find the height of the first tower. $[Use \sqrt{3} = 1.732]$

Discussion

1123.	Question 14Write the correct answer from the given four options. The hypotenuse of a right-angled triangle with its legs of lengths 3x×4x isa) 5xb) 7xc) 16xd) 25x
Answer» Question 14 Write the correct answer from the given four options. The hypotenuse of a right-angled triangle with its legs of lengths $3 x \times 4 x$ is a) 5x b) 7x c) 16x d) 25x

1123.

Question 14Write the correct answer from the given four options. The hypotenuse of a right-angled triangle with its legs of lengths 3x×4x isa) 5xb) 7xc) 16xd) 25x

Answer»

Question 14

Write the correct answer from the given four options.

The hypotenuse of a right-angled triangle with its legs of lengths $3 x \times 4 x$ is

a) 5x

b) 7x

c) 16x

d) 25x

Discussion

1124.	Five cards - the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card si then picked up at random. (a) What is the probability that the drawn card is the queen? (b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.
Answer» Five cards - the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card si then picked up at random. (a) What is the probability that the drawn card is the queen? (b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.

Discussion

1125.	BO and CO are respectively the bisectors of ∠B and ∠C of ΔABC. AO produced meets BC at P. Show that [4 MARKS] (i) ABBP=AOOP (ii) ACCP=AOOP (iii) ABAC=BPPC (iv) AP is the bisector of ∠BAC.
Answer» BO and CO are respectively the bisectors of $∠ B$ and $∠ C$ of $Δ A B C$ . AO produced meets BC at P. Show that [4 MARKS] (i) $\frac{A B}{B P} = \frac{A O}{O P}$ (ii) $\frac{A C}{C P} = \frac{A O}{O P}$ (iii) $\frac{A B}{A C} = \frac{B P}{P C}$ (iv) $A P$ is the bisector of $∠ B A C$ .

1125.

BO and CO are respectively the bisectors of ∠B and ∠C of ΔABC. AO produced meets BC at P. Show that [4 MARKS] (i) ABBP=AOOP (ii) ACCP=AOOP (iii) ABAC=BPPC (iv) AP is the bisector of ∠BAC.

Answer»

BO and CO are respectively the bisectors of $∠ B$ and $∠ C$ of $Δ A B C$ . AO produced meets BC at P.

Show that [4 MARKS]

(i) $\frac{A B}{B P} = \frac{A O}{O P}$

(ii) $\frac{A C}{C P} = \frac{A O}{O P}$

(iii) $\frac{A B}{A C} = \frac{B P}{P C}$

(iv) $A P$ is the bisector of $∠ B A C$ .

Discussion

1126.	In the given figure, O is the centre of a circle PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70∘ then ∠TRQ [CBSE 2015]
Answer» In the given figure, O is the centre of a circle PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70^∘ then ∠TRQ [CBSE 2015]

Discussion

1127.	Find the length of the medians of the triangle with vertices A(0, 0, 6) B(0, 4, 0) and C(6, 0, 0).
Answer» Find the length of the medians of the triangle with vertices $A (0, 0, 6) B (0, 4, 0)$ and $C (6, 0, 0)$ .

Discussion

1128.	Solve the following quadratic equations by factorization:x-2x-3+x-4x-5=103; x≠3, 5
Answer» Solve the following quadratic equations by factorization: $\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5$

Discussion

1129.	What is the sample space when two coins are tossed (H stands for head and T stands for tail)?
Answer» What is the sample space when two coins are tossed (H stands for head and T stands for tail)?

Discussion

1130.	Points P, Q, R and S divide the line segment joining the points A (1, 2) and B(6, 7) into five equal parts. Find the coordinates of the points P, Q and R.
Answer» Points P, Q, R and S divide the line segment joining the points A (1, 2) and B(6, 7) into five equal parts. Find the coordinates of the points P, Q and R.

Discussion

1131.	Question 2Find the area of a quadrant of a circle whose circumference is 22 cm.
Answer» Question 2 Find the area of a quadrant of a circle whose circumference is 22 cm.

Discussion

1132.	If A, B, C are the interior angles of a triangle ABC, prove that(i) tan C+A2=cot B2(ii) sin B+C2=cos A2
Answer» If A, B, C are the interior angles of a triangle ABC, prove that (i) $\tan (\frac{C + A}{2}) = \cot \frac{B}{2}$ (ii) $\sin (\frac{B + C}{2}) = \cos \frac{A}{2}$

Discussion

1133.	A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article (in cm2). __
Answer» A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article (in $c m^{2}$ ). __

1133.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article (in cm2). __

Answer»

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article (in $c m^{2}$ ).

__

Discussion

1134.	Consider the figure where ∠AOB=90∘, and ∠ABC=30∘. Find the value of ∠CAO.
Answer» Consider the figure where $∠ A O B = 90^{\circ},$ and $∠ A B C = 30^{\circ} .$ Find the value of $∠ C A O$ .

Discussion

1135.	Find the mean of the following frequency distribution by step-deviation method.
Answer» Find the mean of the following frequency distribution by step-deviation method.

1135.

Find the mean of the following frequency distribution by step-deviation method.

Answer»

Find the mean of the following frequency distribution by step-deviation method.

Discussion

1136.	Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm2. Also, find its perimeter. [Given: 2 = 1.41]
Answer» Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm². Also, find its perimeter. [Given: $\sqrt{2}$ = 1.41]

Discussion

1137.	If the dividend received from 9% Rs 40 shares is Rs 3240, find the number of shares purchased.
Answer» If the dividend received from $9 %$ Rs 40 shares is Rs 3240, find the number of shares purchased.

Discussion

1138.	The number 0.¯¯¯¯¯¯35 in the form pq, where p and q are integers and q≠0, is
Answer» The number $0. ¯ ¯¯¯¯ ¯ 35$ in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$ , is

Discussion

1139.	Question 5 (v)In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:(v) ar(BFE) = 2ar(FED)
Answer» Question 5 (v) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that: (v) ar(BFE) = 2ar(FED)

Discussion

1140.	Solve the following quadratic equations by factorization:ax-a+bx-b=2cx-c
Answer» Solve the following quadratic equations by factorization: $\frac{a}{x - a} + \frac{b}{x - b} = \frac{2 c}{x - c}$

Discussion

1141.	Find the value of PA in the figure given below.
Answer» Find the value of PA in the figure given below.

Discussion

1142.	A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the hemisphere is equal to the edge of the cube.Determine the volume and total surface area of the remaining block.
Answer» A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the hemisphere is equal to the edge of the cube.Determine the volume and total surface area of the remaining block.

Discussion

1143.	The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are
Answer» The conditions for $a x + b y + c = 0$ to be a linear equation in two variables $(x, y)$ are

Discussion

1144.	The value of k for which the following system of linear equations represent coincident lines is2x + 9y = k; 6x + 27y = 5
Answer» The value of k for which the following system of linear equations represent coincident lines is 2x + 9y = k; 6x + 27y = 5

Discussion

1145.	A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5 cm and heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. The total surface area of the solid is
Answer» A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5 cm and heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. The total surface area of the solid is

Discussion

1146.	In the given figure, if O is the centre of the circle, PQ is a chord. ∠POQ = 90°, area of shaded region is 114 cm2 , find the radius of the circle.(π = 3.14)
Answer» In the given figure, if O is the centre of the circle, PQ is a chord. $∠$ POQ = 90^°, area of shaded region is 114 cm² , find the radius of the circle. ( $π$ = 3.14)

Discussion

1147.	Choose the word which best fills the blank from the four options given. She had her ___ fixed on the horizon.
Answer» Choose the word which best fills the blank from the four options given. She had her ___ fixed on the horizon.

Discussion

1148.	The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?
Answer» The figure given below shows a relation from $P$ to $Q .$ Find the relation, domain and range from the arrow diagram given?

1148.

The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?

Answer»

The figure given below shows a relation from $P$ to $Q .$ Find the relation, domain and range from the arrow diagram given?

Discussion

1149.	Question 96Solve the following:The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.
Answer» Question 96 Solve the following: The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

1149.

Question 96Solve the following:The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

Answer»

Question 96

Solve the following:

The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

Discussion

1150.	A parallelogram with longer side being 20 cm makes an angle of 135∘ with one of the smaller sides. If the area of the parallelogram is 80cm2, then find the length of the smaller side.
Answer» A parallelogram with longer side being 20 cm makes an angle of $135^{\circ}$ with one of the smaller sides. If the area of the parallelogram is $80 c m^{2}$ , then find the length of the smaller side.

1150.

A parallelogram with longer side being 20 cm makes an angle of 135∘ with one of the smaller sides. If the area of the parallelogram is 80cm2, then find the length of the smaller side.

Answer»

A parallelogram with longer side being 20 cm makes an angle of $135^{\circ}$ with one of the smaller sides. If the area of the parallelogram is $80 c m^{2}$ , then find the length of the smaller side.

Discussion

Explore topic-wise InterviewSolutions in .

Prove that the points A(2, 4), B(2, 6) and C2+3, 5 are the vertices of an equilateral triangle.

Prove the following trigonometric identities: 1+tan2θ1+cot2θ=(1−tan θ1−cot θ)2=tan2θ

Find the mean of the data given in the table using step - deviation method.Class IntervalFrequency0−101010−201220−30730−40640−50550−608

11. If a+b=10 and ab=16, find the value of asquare+ab+bsquare

When the polynomial x3+2x2−5ax−7 is divided by (x−1), the remainder is A and when the polynomial x3+ax2−12x+16 is divided by (x+2), the remainder is B. Find the value of 'a' if 2A+B=0.

Find k if the line passing through points P(–12, –3) and Q(4, k) has slope 12.

The number of employees in a factory decreases in the ratio 8:7 and the salary of employees increases in the ratio of 5:6. Find whether the total salary of the employees increased or decreased and in what ratio.

O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre, ∠AOB = 110∘, then angle subtended by the arc at any point on the circle say ∠APB is ____, where P is any point on the circle.

If the first term of an A.P. is 3 and the sum of its first 25 terms in equal to the sum of its next 15 terms, then the common difference of this A.P. is

Ritwik and Richa decide to trim the green and the brown path of their backyard, respectively. If both have the same speed, which one of them can finish trimming earlier? Why?

How many numbers lie between squares of 25 and 26?

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is [CBSE 2014](a) 3(b) 5(c) 4(d) 6

If [124−109]+A=[9−114−23], then A is

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

if f(x) =x-1/x+1 then f(2x) is equal to1) f(x)+2/f(x)+32) f(x)+3/f(x)+23) f(x)+3/3f(x)+14)3f(x)+1/f(x)+3

Find the values of k for which the following equations have real roots (i) (ii) (iii) x2-4kx+k=0 (iv) kxx-25+10=0(v) kx(x-3)+9=0 (vi) 4x2+kx+3=0

If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is 3:1 then find the angle of elevation of the sun at that time. [CBSE 2017]

Let A={1,2,3},B={3,4} and C={4,5,6}. Find(A) A×(B∩C)(B) (A×B)∩(A×C)(C) A×(B∪C)(D) (A×B)∪(A×C)

Prove that the points A(2, 4), B(2, 6) and C(2 + √3, 5) are the vertices of an equilateral triangle.

If 3-13+1=x+y3, find the values of x and y.

The horizontal distance between two towers is 60 metres. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 90 metres, find the height of the first tower.Use 3=1.732

Question 14Write the correct answer from the given four options. The hypotenuse of a right-angled triangle with its legs of lengths 3x×4x isa) 5xb) 7xc) 16xd) 25x

BO and CO are respectively the bisectors of ∠B and ∠C of ΔABC. AO produced meets BC at P. Show that [4 MARKS] (i) ABBP=AOOP (ii) ACCP=AOOP (iii) ABAC=BPPC (iv) AP is the bisector of ∠BAC.

In the given figure, O is the centre of a circle PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70∘ then ∠TRQ [CBSE 2015]

Find the length of the medians of the triangle with vertices A(0, 0, 6) B(0, 4, 0) and C(6, 0, 0).

Solve the following quadratic equations by factorization:x-2x-3+x-4x-5=103; x≠3, 5

What is the sample space when two coins are tossed (H stands for head and T stands for tail)?

Points P, Q, R and S divide the line segment joining the points A (1, 2) and B(6, 7) into five equal parts. Find the coordinates of the points P, Q and R.

Question 2Find the area of a quadrant of a circle whose circumference is 22 cm.

If A, B, C are the interior angles of a triangle ABC, prove that(i) tan C+A2=cot B2(ii) sin B+C2=cos A2

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article (in cm2). __

Consider the figure where ∠AOB=90∘, and ∠ABC=30∘. Find the value of ∠CAO.

Find the mean of the following frequency distribution by step-deviation method.

Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm2. Also, find its perimeter. [Given: 2 = 1.41]

If the dividend received from 9% Rs 40 shares is Rs 3240, find the number of shares purchased.

The number 0.¯¯¯¯¯¯35 in the form pq, where p and q are integers and q≠0, is

Question 5 (v)In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:(v) ar(BFE) = 2ar(FED)

Solve the following quadratic equations by factorization:ax-a+bx-b=2cx-c

Find the value of PA in the figure given below.

A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the hemisphere is equal to the edge of the cube.Determine the volume and total surface area of the remaining block.

The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are

The value of k for which the following system of linear equations represent coincident lines is2x + 9y = k; 6x + 27y = 5

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5 cm and heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. The total surface area of the solid is

In the given figure, if O is the centre of the circle, PQ is a chord. ∠POQ = 90°, area of shaded region is 114 cm2 , find the radius of the circle.(π = 3.14)

Choose the word which best fills the blank from the four options given. She had her ___ fixed on the horizon.

The figure given below shows a relation from P to Q. Find the relation, domain and range from the arrow diagram given?

Question 96Solve the following:The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

A parallelogram with longer side being 20 cm makes an angle of 135∘ with one of the smaller sides. If the area of the parallelogram is 80cm2, then find the length of the smaller side.