32581 + Interview Questions in Mathematics Page 99 InterviewSolution

4901.	A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio(a) 9 : 1(b) 1 : 9(c) 3 : 1(d) 1 : 3
Answer» A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio (a) 9 : 1 (b) 1 : 9 (c) 3 : 1 (d) 1 : 3

Discussion

4902.	look at the series and find the next term 0, 6, 24, 60, 120, 210, ?
Answer» look at the series and find the next term 0, 6, 24, 60, 120, 210, ?

4902.

look at the series and find the next term 0, 6, 24, 60, 120, 210, ?

Answer»

look at the series and find the next term

0, 6, 24, 60, 120, 210, ?

Discussion

4903.	27yrs hence sanjay's age will be square of what it was 29yrs ago find his present age
Answer» 27yrs hence sanjay's age will be square of what it was 29yrs ago find his present age

Discussion

4904.	In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region.
Answer» In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region.

Discussion

4905.	Question 19Find the sum of the two middle most terms of the AP −43,−1,−23,⋯,413
Answer» Question 19 Find the sum of the two middle most terms of the AP $- \frac{4}{3}, - 1, - \frac{2}{3}, \dots, 4 \frac{1}{3}$

Discussion

4906.	Find a rational number between 5 and 7
Answer» Find a rational number between 5 and 7

Discussion

4907.	A hemispherical bowl is made up of stones whose thickness is 7 cm. If the inner radius is 35 cm, find the total surface area of the bowl.
Answer» A hemispherical bowl is made up of stones whose thickness is 7 cm. If the inner radius is 35 cm, find the total surface area of the bowl.

Discussion

4908.	If A=⎡⎢⎣11−12033−12⎤⎥⎦,B=⎡⎢⎣1302−14⎤⎥⎦ and C=[123−420−21], find A(BC),(AB)C and show that (AB)C=A(BC).
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & - 1 2 & 0 & 3 3 & - 1 & 2 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 3 0 & 2 - 1 & 4 \end{matrix} ⎤ ⎥ ⎦$ and $C = [\begin{matrix} 1 & 2 & 3 & - 4 2 & 0 & - 2 & 1 \end{matrix}]$ , find $A (B C), (A B) C$ and show that $(A B) C = A (B C) .$

Discussion

4909.	Question 4 Write ‘True’ or ‘False’ and justify your answer in each of the following: √(1−cos2θ)sec2θ=tanθ
Answer» Question 4 Write ‘True’ or ‘False’ and justify your answer in each of the following: $\sqrt{(1 - c o s^{2} θ) s e c^{2} θ} = t a n θ$

Discussion

4910.	Two identical cubes each of volume 216 cm3 are joined together end to end. What is the surface area of the resulting cuboid?
Answer» Two identical cubes each of volume $216 c m^{3}$ are joined together end to end. What is the surface area of the resulting cuboid?

Discussion

4911.	Question 6In figure AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.
Answer» Question 6 In figure AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.

Discussion

4912.	If f(x)=ax+b, where a and b are integers, f(–1)=–5 and f(3)=3, then a and b are equal to , respectively.
Answer» If $f (x) = a x + b$ , where $a$ and $b$ are integers, $f (- 1) = - 5$ and $f (3) = 3$ , then $a$ and $b$ are equal to , respectively.

Discussion

4913.	If dividend = 3x3−2x2+4x−3 and divisor = x2+3x+3,then find the remainder and quotient.
Answer» If dividend = $3 x^{3} - 2 x^{2} + 4 x - 3$ and divisor = $x^{2} + 3 x + 3$ ,then find the remainder and quotient.

Discussion

4914.	Prove the following trigonometric identities: Prove that: (i) √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ (ii) √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 cosec θ (iii) √1+cos θ1−cos θ+√1−cos θ1+cos θ=2 cosec θ (iv) sec θ−1sec θ+1=(sin θ1+cos θ)2
Answer» Prove the following trigonometric identities: Prove that: (i) $\sqrt{\frac{s e c θ - 1}{s e c θ + 1}} + \sqrt{\frac{s e c θ + 1}{s e c θ - 1}} = 2 c o s e c θ$ (ii) $\sqrt{\frac{1 + s i n θ}{1 - s i n θ}} + \sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = 2 c o s e c θ$ (iii) $\sqrt{\frac{1 + c o s θ}{1 - c o s θ}} + \sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = 2 c o s e c θ$ (iv) $\frac{s e c θ - 1}{s e c θ + 1} = {(\frac{s i n θ}{1 + c o s θ})}^{2}$

4914.

Prove the following trigonometric identities: Prove that: (i) √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ (ii) √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 cosec θ (iii) √1+cos θ1−cos θ+√1−cos θ1+cos θ=2 cosec θ (iv) sec θ−1sec θ+1=(sin θ1+cos θ)2

Answer»

Prove the following trigonometric identities:

Prove that:

(i) $\sqrt{\frac{s e c θ - 1}{s e c θ + 1}} + \sqrt{\frac{s e c θ + 1}{s e c θ - 1}} = 2 c o s e c θ$

(ii) $\sqrt{\frac{1 + s i n θ}{1 - s i n θ}} + \sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = 2 c o s e c θ$

(iii) $\sqrt{\frac{1 + c o s θ}{1 - c o s θ}} + \sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = 2 c o s e c θ$

(iv) $\frac{s e c θ - 1}{s e c θ + 1} = {(\frac{s i n θ}{1 + c o s θ})}^{2}$

Discussion

4915.	Which of the following is a composite number?1) 2×2×3+1×2×3+112) 2×5×7+13) 2×3×3×5+14) 2×2×2×2×2×3+1
Answer» Which of the following is a composite number? 1) 2×2×3+1×2×3+11 2) 2×5×7+1 3) 2×3×3×5+1 4) 2×2×2×2×2×3+1

Discussion

4916.	S1: If two triangles are similar, sides are proportional.S2: If two triangles are similar, angles are equal.
Answer» S1: If two triangles are similar, sides are proportional. S2: If two triangles are similar, angles are equal.

Discussion

4917.	Question 20Find the difference of the areas of a sector of angle 120∘ and its corresponding major sector of a circle of radius 21 cm.
Answer» Question 20 Find the difference of the areas of a sector of angle $120^{\circ}$ and its corresponding major sector of a circle of radius 21 cm.

Discussion

4918.	Draw the graphs of the lines x = -2, and y = 3. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the ara of the figure.
Answer» Draw the graphs of the lines x = -2, and y = 3. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the ara of the figure.

Discussion

4919.	Show that any number which is divisible by 3 is of the form n+1,n-1,n+2 where n is any positive integer.
Answer» Show that any number which is divisible by 3 is of the form n+1,n-1,n+2 where n is any positive integer.

Discussion

4920.	For any two sets A and B, if n(A) =15, n(B) = 12, A ∩ B ≠ ϕ and B ⊄ A, then the maximum and and minimum possible values of n(A ∆ B) are _______ and ___________ respectively.
Answer» For any two sets A and B, if n(A) =15, n(B) = 12, A ∩ B ≠ ϕ and B ⊄ A, then the maximum and and minimum possible values of n(A ∆ B) are _______ and ___________ respectively.

Discussion

4921.	The area of the trapezium REMN, in the above given figure is ______.
Answer» The area of the trapezium REMN, in the above given figure is ______.

Discussion

4922.	Solve the following inequation:2x+12+2(3−x)≥7,xϵR
Answer» Solve the following inequation: $\frac{2 x + 1}{2} + 2 (3 - x) \geq 7, x ϵ R$

Discussion

4923.	On 1st January, 2018, Mr. X sold goods to Mr. Y for ₹45,000 plus CGST and SGST 9% each on credit. Mr. Y paid the amount of GST immediately in cash. Mr. X drew 3 bills on him: first bill for ₹10,000 for 1 month, second bill for ₹15,000 for 2 months and third bill for ₹20,000 for 3 months. Mr. Y accepted and returned all the bills to Mr. X.
Answer» On 1st January, 2018, Mr. X sold goods to Mr. Y for ₹45,000 plus CGST and SGST 9% each on credit. Mr. Y paid the amount of GST immediately in cash. Mr. X drew 3 bills on him: first bill for ₹10,000 for 1 month, second bill for ₹15,000 for 2 months and third bill for ₹20,000 for 3 months. Mr. Y accepted and returned all the bills to Mr. X.

Discussion

4924.	On selling a tea set at 5% loss and a lemon set at 15 % gain,a crockery seller gains Rs.7.If he sells the tea set at 5% gain and the lemon set at 10 % gain, he gains Rs.13.Find the actual price of each of the tea set and the lemon set.
Answer» On selling a tea set at 5% loss and a lemon set at 15 % gain,a crockery seller gains Rs.7.If he sells the tea set at 5% gain and the lemon set at 10 % gain, he gains Rs.13.Find the actual price of each of the tea set and the lemon set.

Discussion

4925.	The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm2. The area of the triangle is(a) 49 cm2(b) 4934cm2(c) 734cm2(d) 77 cm2
Answer» The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm². The area of the triangle is (a) 49 cm² (b) $\frac{49 \sqrt{3}}{4} {cm}^{2}$ (c) $\frac{7 \sqrt{3}}{4} {cm}^{2}$ (d) 77 cm²

Discussion

4926.	Solve for x and y:13x+y+13x-y=34123x+y-123x-y=-18
Answer» Solve for x and y: $\frac{1}{(3 x + y)} + \frac{1}{(3 x - y)} = \frac{3}{4} \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}$

Discussion

4927.	A pole 10 m high cast a shadow 10 m long on the ground,then the sun's elevation is?
Answer» A pole 10 m high cast a shadow 10 m long on the ground,then the sun's elevation is?

Discussion

4928.	ABCD is a parallelogram. A circle passes through A,B and C. The circle intersects the line CD produced at E. Prove that AE = AD. [3 MARKS]
Answer» ABCD is a parallelogram. A circle passes through A,B and C. The circle intersects the line CD produced at E. Prove that AE = AD. [3 MARKS]

Discussion

4929.	Using Euclid’s division algorithm, find the HCF of 504 and 1188
Answer» Using Euclid’s division algorithm, find the HCF of 504 and 1188

Discussion

4930.	A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).
Answer» A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).

Discussion

4931.	Given PQ = 4 cm, with PQ as diameter draw a circle. Draw two tangents to the circle at ‘P’ and ‘Q’.
Answer» Given PQ = 4 cm, with PQ as diameter draw a circle. Draw two tangents to the circle at ‘P’ and ‘Q’.

Discussion

4932.	In the adjoining figure, if ∠QPR=60∘ and ∠SPR=70∘, then ∠QRS= ___.
Answer» In the adjoining figure, if $∠ Q P R = 60^{\circ}$ and $∠ S P R = 70^{\circ}$ , then $∠ Q R S$ = ___.

4932.

In the adjoining figure, if ∠QPR=60∘ and ∠SPR=70∘, then ∠QRS= ___.

Answer»

In the adjoining figure, if $∠ Q P R = 60^{\circ}$ and $∠ S P R = 70^{\circ}$ , then $∠ Q R S$ = ___.

Discussion

4933.	15. Let a = 2i + j + 2k and b = i + j. Let c be a vector such that /c a/ = 3, /(ab)c/ = 3 and the angle between c and ab be 30^°. Then a . c is equal to : (1) 25/8 (2) 2 (3) 5 (4) 1/8
Answer» 15. Let a = 2i + j + 2k and b = i + j. Let c be a vector such that /c a/ = 3, /(ab)c/ = 3 and the angle between c and ab be 30^°. Then a . c is equal to : (1) 25/8 (2) 2 (3) 5 (4) 1/8

Discussion

4934.	Aman's age is 3 times his son's age 10 year ago he was 5 times his son's age find their present ages
Answer» Aman's age is 3 times his son's age 10 year ago he was 5 times his son's age find their present ages

Discussion

4935.	A Circumcircle passes through the ___ of a polygon
Answer» A Circumcircle passes through the ___ of a polygon

Discussion

4936.	Question 4 (xii)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(xii) √2,√8,√18,√32……
Answer» Question 4 (xii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xii) $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32} \dots \dots$

Discussion

4937.	A cottage industry produces a certain number of articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced.
Answer» A cottage industry produces a certain number of articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced.

Discussion

4938.	What is the square root of (2x+3)2–24x?
Answer» What is the square root of $(2 x + 3)^{2} - 24 x$ ?

Discussion

4939.	The ratio of the radius of the base of a cylinder to its height is 7 : 6. If the volume of the cylinder is 294π cm³, then it's base diameter is
Answer» The ratio of the radius of the base of a cylinder to its height is 7 : 6. If the volume of the cylinder is 294π cm³, then it's base diameter is

Discussion

4940.	Solve t'2-2t+300=0
Answer» Solve t'2-2t+300=0

Discussion

4941.	Let ABC be an isosceles triangle with AB=AC and let D,E,F be the mid points of BC,CA and AB respectively . Show that AD perpendicular to EF and bisected by EF. AD is bisected by EF.
Answer» Let ABC be an isosceles triangle with AB=AC and let D,E,F be the mid points of BC,CA and AB respectively . Show that AD perpendicular to EF and bisected by EF. AD is bisected by EF.

Discussion

4942.	Choose the correct option and justify Sin 2A = 2 Sin A is true when A = 0 degree 30 degree 45 degree 60 degree
Answer» Choose the correct option and justify Sin 2A = 2 Sin A is true when A = 0 degree 30 degree 45 degree 60 degree

4942.

Choose the correct option and justify Sin 2A = 2 Sin A is true when A = 0 degree 30 degree 45 degree 60 degree

Answer»

Choose the correct option and justify

Sin 2A = 2 Sin A is true when A =

0 degree

30 degree

45 degree

60 degree

Discussion

4943.	In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30∘ then ∠PTA = ?(a) 60∘(b) 30∘(c) 15∘(d) 45∘
Answer» In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30^∘ then ∠PTA = ? (a) 60^∘ (b) 30^∘ (c) 15^∘ (d) 45^∘

Discussion

4944.	The quadratic equation x2 – 11(p + q)x + (10p2 + 24pq + 10q2) = 0, where p ≠ ±q has
Answer» The quadratic equation x2 – 11(p + q)x + (10p2 + 24pq + 10q2) = 0, where p ≠ ±q has

Discussion

4945.	The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018Use a graph sheet to draw an ogive for the distribution.Using the graph estimate the Interquartile range
Answer» The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. $\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$ Use a graph sheet to draw an ogive for the distribution. Using the graph estimate the Interquartile range

4945.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018Use a graph sheet to draw an ogive for the distribution.Using the graph estimate the Interquartile range

Answer»

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the Interquartile range

Discussion

4946.	(A) Find the sum of the following finite series(a) 1 + 6 + 11 + 16 + ………+ 96(b) 1 + 4 + 7 + ……..+ 73(B) Find the number of terms in the following series if(a) 3 + 5 + 7 + ……..= 624(b) 15 + 12 + 9 + 6 + ……..−90
Answer» (A) Find the sum of the following finite series (a) 1 + 6 + 11 + 16 + ………+ 96 (b) 1 + 4 + 7 + ……..+ 73 (B) Find the number of terms in the following series if (a) 3 + 5 + 7 + ……..= 624 (b) 15 + 12 + 9 + 6 + ……..−90

4946.

(A) Find the sum of the following finite series(a) 1 + 6 + 11 + 16 + ………+ 96(b) 1 + 4 + 7 + ……..+ 73(B) Find the number of terms in the following series if(a) 3 + 5 + 7 + ……..= 624(b) 15 + 12 + 9 + 6 + ……..−90

Answer»

(A) Find the sum of the following finite series

(a) 1 + 6 + 11 + 16 + ………+ 96

(b) 1 + 4 + 7 + ……..+ 73

(B) Find the number of terms in the following series if

(a) 3 + 5 + 7 + ……..= 624

(b) 15 + 12 + 9 + 6 + ……..−90

Discussion

4947.	The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree whenseen from the top of the second tree is 45∘. If the height of the second tree is 80 m, find the height of the first tree.
Answer» The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree whenseen from the top of the second tree is $45^{\circ}$ . If the height of the second tree is 80 m, find the height of the first tree.

Discussion

4948.	Factorise : a2b2+8ab−9
Answer» Factorise : $a^{2} b^{2} + 8 a b - 9$

4948.

Factorise : a2b2+8ab−9

Answer»

Factorise :

$a^{2} b^{2} + 8 a b - 9$

Discussion

4949.	Question 6For the following distribution,Class0−55−1010−1515−2020−25Frequency101512209the sum of lower limits of the median class and modal class is(a) 15(b) 25(c) 30(d) 35
Answer» Question 6 For the following distribution, $\begin{matrix} C l a s s & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 F r e q u e n c y & 10 & 15 & 12 & 20 & 9 \end{matrix}$ the sum of lower limits of the median class and modal class is (a) 15 (b) 25 (c) 30 (d) 35

Discussion

4950.	For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?
Answer» For the given linear equation $y - 3 x + 1 = 0,$ what are the values of $y$ if $x = [3, - 4, 2]$ ?

Discussion

Explore topic-wise InterviewSolutions in .

A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio(a) 9 : 1(b) 1 : 9(c) 3 : 1(d) 1 : 3

look at the series and find the next term 0, 6, 24, 60, 120, 210, ?

​​​​27yrs hence sanjay's age will be square of what it was 29yrs ago find his present age

In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region.

Question 19Find the sum of the two middle most terms of the AP −43,−1,−23,⋯,413

Find a rational number between 5 and 7

A hemispherical bowl is made up of stones whose thickness is 7 cm. If the inner radius is 35 cm, find the total surface area of the bowl.

If A=⎡⎢⎣11−12033−12⎤⎥⎦,B=⎡⎢⎣1302−14⎤⎥⎦ and C=[123−420−21], find A(BC),(AB)C and show that (AB)C=A(BC).

Question 4 Write ‘True’ or ‘False’ and justify your answer in each of the following:​​​​​​​ √(1−cos2θ)sec2θ=tanθ

Two identical cubes each of volume 216 cm3 are joined together end to end. What is the surface area of the resulting cuboid?

Question 6In figure AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.

If f(x)=ax+b, where a and b are integers, f(–1)=–5 and f(3)=3, then a and b are equal to , respectively.

If dividend = 3x3−2x2+4x−3 and divisor = x2+3x+3,then find the remainder and quotient.

Prove the following trigonometric identities: Prove that: (i) √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ (ii) √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 cosec θ (iii) √1+cos θ1−cos θ+√1−cos θ1+cos θ=2 cosec θ (iv) sec θ−1sec θ+1=(sin θ1+cos θ)2

Which of the following is a composite number?1) 2×2×3+1×2×3+112) 2×5×7+13) 2×3×3×5+14) 2×2×2×2×2×3+1

S1: If two triangles are similar, sides are proportional.S2: If two triangles are similar, angles are equal.

Question 20Find the difference of the areas of a sector of angle 120∘ and its corresponding major sector of a circle of radius 21 cm.

Draw the graphs of the lines x = -2, and y = 3. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the ara of the figure.

Show that any number which is divisible by 3 is of the form n+1,n-1,n+2 where n is any positive integer.

For any two sets A and B, if n(A) =15, n(B) = 12, A ∩ B ≠ ϕ and B ⊄ A, then the maximum and and minimum possible values of n(A ∆ B) are _______ and ___________ respectively.

The area of the trapezium REMN, in the above given figure is ______.

Solve the following inequation:2x+12+2(3−x)≥7,xϵR

On selling a tea set at 5% loss and a lemon set at 15 % gain,a crockery seller gains Rs.7.If he sells the tea set at 5% gain and the lemon set at 10 % gain, he gains Rs.13.Find the actual price of each of the tea set and the lemon set.

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm2. The area of the triangle is(a) 49 cm2(b) 4934cm2(c) 734cm2(d) 77 cm2

Solve for x and y:13x+y+13x-y=34123x+y-123x-y=-18

A pole 10 m high cast a shadow 10 m long on the ground,then the sun's elevation is?

ABCD is a parallelogram. A circle passes through A,B and C. The circle intersects the line CD produced at E. Prove that AE = AD. [3 MARKS]

Using Euclid’s division algorithm, find the HCF of 504 and 1188

A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).

Given PQ = 4 cm, with PQ as diameter draw a circle. Draw two tangents to the circle at ‘P’ and ‘Q’.

In the adjoining figure, if ∠QPR=60∘ and ∠SPR=70∘, then ∠QRS= ___.

15. Let a = 2i + j + 2k and b = i + j. Let c be a vector such that /c a/ = 3, /(ab)c/ = 3 and the angle between c and ab be 30^°. Then a . c is equal to : (1) 25/8 (2) 2 (3) 5 (4) 1/8

Aman's age is 3 times his son's age 10 year ago he was 5 times his son's age find their present ages

A Circumcircle passes through the ___ of a polygon

Question 4 (xii)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(xii) √2,√8,√18,√32……

What is the square root of (2x+3)2–24x?

The ratio of the radius of the base of a cylinder to its height is 7 : 6. If the volume of the cylinder is 294π cm³, then it's base diameter is

Solve t'2-2t+300=0

Let ABC be an isosceles triangle with AB=AC and let D,E,F be the mid points of BC,CA and AB respectively . Show that AD perpendicular to EF and bisected by EF. AD is bisected by EF.

Choose the correct option and justify Sin 2A = 2 Sin A is true when A = 0 degree 30 degree 45 degree 60 degree

In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30∘ then ∠PTA = ?(a) 60∘(b) 30∘(c) 15∘(d) 45∘

The quadratic equation x2 – 11(p + q)x + (10p2 + 24pq + 10q2) = 0, where p ≠ ±q has

(A) Find the sum of the following finite series(a) 1 + 6 + 11 + 16 + ………+ 96(b) 1 + 4 + 7 + ……..+ 73(B) Find the number of terms in the following series if(a) 3 + 5 + 7 + ……..= 624(b) 15 + 12 + 9 + 6 + ……..−90

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree whenseen from the top of the second tree is 45∘. If the height of the second tree is 80 m, find the height of the first tree.

Factorise : a2b2+8ab−9

Question 6For the following distribution,Class0−55−1010−1515−2020−25Frequency101512209the sum of lower limits of the median class and modal class is(a) 15(b) 25(c) 30(d) 35

For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?

27yrs hence sanjay's age will be square of what it was 29yrs ago find his present age

Question 4 Write ‘True’ or ‘False’ and justify your answer in each of the following: √(1−cos2θ)sec2θ=tanθ

For any two sets A and B, if n(A) =15, n(B) = 12, A ∩ B ≠ ϕ and B ⊄ A, then the maximum and and minimum possible values of n(A ∆ B) are _ and _____ respectively.