32581 + Interview Questions in Mathematics Page 105 InterviewSolution

5201.	49. A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter L of hemisphere is equal to the edge of cube determine the surface area of remaining solid
Answer» 49. A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter L of hemisphere is equal to the edge of cube determine the surface area of remaining solid

Discussion

5202.	ABC is a triangle and M & N are points on AB and AC such that MN \|\| BC. Find the given ratios if AM:MB = 2:3.1. AN:AC2. AN:NC3. NC:AC
Answer» ABC is a triangle and M & N are points on AB and AC such that MN \|\| BC. Find the given ratios if AM:MB = 2:3. 1. $A N : A C$ 2. $A N : N C$ 3. $N C : A C$

Discussion

5203.	Question 11 (i) By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then. 3x+y+4 = 0, 6x – 2y + 4 = 0
Answer» Question 11 (i) By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then. 3x+y+4 = 0, 6x – 2y + 4 = 0

Discussion

5204.	During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h=−16t2+24t+1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?
Answer» During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h = - 16 t^{2} + 24 t + 1$ , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Discussion

5205.	In the given figure, O is the centre of the circle. Find x.
Answer» In the given figure, O is the centre of the circle. Find $x$ .

5205.

In the given figure, O is the centre of the circle. Find x.

Answer»

In the given figure, O is the centre of the circle. Find $x$ .

Discussion

5206.	If the ratio of sums upto n terms of two AP's is (5n+3) : (3n+4), then what is the ratio of their 17th terms? [3 MARKS]
Answer» If the ratio of sums upto n terms of two AP's is (5n+3) : (3n+4), then what is the ratio of their 17th terms? [3 MARKS]

Discussion

5207.	If (2p-1), 7 and 3p are in AP, find the value of p.
Answer» If $(2 p - 1),$ 7 and 3p are in AP, find the value of p.

Discussion

5208.	Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son's age. Find: (i) The age of the son five years ago. (ii) The present age of the woman. [4 MARKS]
Answer» Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son's age. Find: (i) The age of the son five years ago. (ii) The present age of the woman. [4 MARKS]

Discussion

5209.	What is the sum of the first 20 whole numbers?
Answer» What is the sum of the first 20 whole numbers?

Discussion

5210.	If a triangle has angles 45∘,45∘, and 90∘, what is the ratio of the sides of the triangle opposite to these angles respectively?
Answer» If a triangle has angles $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ , what is the ratio of the sides of the triangle opposite to these angles respectively?

5210.

If a triangle has angles 45∘,45∘, and 90∘, what is the ratio of the sides of the triangle opposite to these angles respectively?

Answer»

If a triangle has angles $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ , what is the ratio of the sides of the triangle opposite to these angles respectively?

Discussion

5211.	In a quadrilateral ABCD, ∠B = 90°. If AD2 = AB2 + BC2 + CD2 then prove that ∠ACD = 90°.
Answer» In a quadrilateral ABCD, ∠B = 90°. If AD² = AB² + BC² + CD² then prove that ∠ACD = 90°.

Discussion

5212.	The dimensions of a room are 14 m × 10 m × 6.5 m. There are two doors and 4 windows in the room. Each door measures 2.5 m × 1.2 m and each window measures 1.5 × 1 m. Find the cost of painting the four walls of the room at Rs 35 per m2.
Answer» The dimensions of a room are 14 m × 10 m × 6.5 m. There are two doors and 4 windows in the room. Each door measures 2.5 m × 1.2 m and each window measures 1.5 × 1 m. Find the cost of painting the four walls of the room at Rs 35 per m².

Discussion

5213.	A washing tub in the shape of a frustum of a cone has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub ? (π=227)
Answer» A washing tub in the shape of a frustum of a cone has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub ? ( $π = \frac{22}{7}$ )

Discussion

5214.	If ′G′ is centroid and ′I′ is incentre of the triangle formed by line 3x+4y=12 with co-ordinate axis and GI=23√λ2−4(λ>0) then [λ]= (where [.] is G.I.F)
Answer» If $^{'} G^{'}$ is centroid and $^{'} I^{'}$ is incentre of the triangle formed by line $3 x + 4 y = 12$ with co-ordinate axis and $G I = \frac{2}{3} \sqrt{λ^{2} - 4} (λ > 0)$ then $[λ] =$ (where $[.]$ is G.I.F)

Discussion

5215.	A bag contains three green marbles, four blue marbles, and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is
Answer» A bag contains three green marbles, four blue marbles, and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

Discussion

5216.	if x^3/2+1/x^3/2 =2 root 5, x is greater than zero, find x^3-1/x^3
Answer» if x^3/2+1/x^3/2 =2 root 5, x is greater than zero, find x^3-1/x^3

Discussion

5217.	cosec2 57o - tan2 33o = ? (a) 0 (b) 1 (c) -1 (d) 2
Answer» $c o s e c^{2} 57^{o}$ - $t a n^{2} 33^{o}$ = ? (a) 0 (b) 1 (c) -1 (d) 2

5217.

cosec2 57o - tan2 33o = ? (a) 0 (b) 1 (c) -1 (d) 2

Answer»

$c o s e c^{2} 57^{o}$ - $t a n^{2} 33^{o}$ = ?

(a) 0 (b) 1 (c) -1 (d) 2

Discussion

5218.	Find the volume of the figure (in inch3).100
Answer» Find the volume of the figure (in ${inch}^{3}$ ). 100

Discussion

5219.	The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs.
Answer» The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs.

Discussion

5220.	Use Euclid's division algorithm to find the HCF of 196 and 38220.
Answer» Use Euclid's division algorithm to find the HCF of 196 and 38220.

Discussion

5221.	If sinθ + sin2θ = 1 then cos2θ + cos4θ is equal to
Answer» If sinθ + sin²θ = 1 then cos²θ + cos⁴θ is equal to

Discussion

5222.	Question 4 (x)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(x) a, 2a, 3a, 4a …
Answer» Question 4 (x) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (x) a, 2a, 3a, 4a …

Discussion

5223.	Seema Ltd. offered for subscription 10,000 shares of ₹ 25 each, payable ₹ 5 per share on application, ₹ 10 per share on allotment (including ₹ 5 per share as premium), ₹ 5 per share as first call on the shares and the balance in two equal amounts at intervals of three months. All the shares were applied for and allotted. All the money was received except the second call and final call on 200 and 400 shares respectively. Pass the entries in the company's Journal, Cash Book and the ledger. Also show the company's Balance Sheet on completion of the above transactions.
Answer» Seema Ltd. offered for subscription 10,000 shares of ₹ 25 each, payable ₹ 5 per share on application, ₹ 10 per share on allotment (including ₹ 5 per share as premium), ₹ 5 per share as first call on the shares and the balance in two equal amounts at intervals of three months. All the shares were applied for and allotted. All the money was received except the second call and final call on 200 and 400 shares respectively. Pass the entries in the company's Journal, Cash Book and the ledger. Also show the company's Balance Sheet on completion of the above transactions.

Discussion

5224.

The distribution below gives the weight of 30 students in a class. Find the median weight of students: Weight (in kg): 40−45 45−50 50−55 55−60 60−65 65−70 70−75 No. of students: 2 3 8 6 6 3 2

Answer» The distribution below gives the weight of 30 students in a class. Find the median weight of students:

Weight (in kg):	40−45	45−50	50−55	55−60	60−65	65−70	70−75
No. of students:	2	3	8	6	6	3	2

Discussion

5225.	The sum of two natural numbers is 15 and the sum of their reciprocals is 310. Find the numbers. [CBSE 2005]
Answer» The sum of two natural numbers is 15 and the sum of their reciprocals is $\frac{3}{10}$ . Find the numbers. [CBSE 2005]

Discussion

5226.	The following are the marks obtained in Science by students in class X.The mean was calculated to be 63.33.Is this mean an appropriate representation of the average marks obtained?If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?What is the value of this measure of central tendency for the given data?MarksFrequency10−20120−30030−40040−50050−60160−70570−801580−902090−1003
Answer» The following are the marks obtained in Science by students in class X. The mean was calculated to be 63.33. Is this mean an appropriate representation of the average marks obtained? If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution? What is the value of this measure of central tendency for the given data? $\begin{matrix} Marks & Frequency 10 - 20 & 1 20 - 30 & 0 30 - 40 & 0 40 - 50 & 0 50 - 60 & 1 60 - 70 & 5 70 - 80 & 15 80 - 90 & 20 90 - 100 & 3 \end{matrix}$

Discussion

5227.	In the following figure, Show that
Answer» In the following figure, Show that

5227.

In the following figure, Show that

Answer»

In the following figure, Show that

Discussion

5228.	The 5th term of an arithmetic sequence is 9 and its 9th term is 5. What is its common difference? What is the 14th term?
Answer» The 5^th term of an arithmetic sequence is 9 and its 9^th term is 5. What is its common difference? What is the 14^th term?

Discussion

5229.	Ashish and Aakash are partners sharing profit in the ratio of 3 : 2. Their Capital Accounts showed a credit balance of ₹ 5,00,000 and ₹ 6,00,000 respectively as on 31st March, 2019 after debit of drawings during the year of ₹ 1,50,000 and ₹ 1,00,000 respectively. Net profit for the year ended 31st March, 2019 was ₹ 5,00,000. Interest on capital is to be allowed 10% p.a.Pass the Journal entry for interest on capital and prepare Profit and Loss Appropriation Account.
Answer» Ashish and Aakash are partners sharing profit in the ratio of 3 : 2. Their Capital Accounts showed a credit balance of ₹ 5,00,000 and ₹ 6,00,000 respectively as on 31st March, 2019 after debit of drawings during the year of ₹ 1,50,000 and ₹ 1,00,000 respectively. Net profit for the year ended 31st March, 2019 was ₹ 5,00,000. Interest on capital is to be allowed 10% p.a. Pass the Journal entry for interest on capital and prepare Profit and Loss Appropriation Account.

Discussion

5230.	The volume of a cone of radius 7 cm and slant height 14 cm is ______.(use π=227)
Answer» The volume of a cone of radius 7 $c m$ and slant height 14 $c m$ is ______. $(u s e π = \frac{22}{7})$

Discussion

5231.	Question 124 (iv) Evaluate the following, using distributive property. 68×(−17)+(−68)×3
Answer» Question 124 (iv) Evaluate the following, using distributive property. $68 \times (- 17) + (- 68) \times 3$

5231.

Question 124 (iv) Evaluate the following, using distributive property. 68×(−17)+(−68)×3

Answer»

Question 124 (iv)

Evaluate the following, using distributive property.
$68 \times (- 17) + (- 68) \times 3$

Discussion

5232.	A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?10
Answer» A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate? 10

Discussion

5233.	Let U={1,2,3,4,5,6,7,8,9},A={1,2,3,4},B={2,4,6,8} and C={3,4,5,6}.Find (i) A′ (ii) B′ (iii) (A∪C)′(iv) (A∪B)′ (v) (A′)′ (vi) (B−C)′
Answer» Let $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8}$ and $C = {3, 4, 5, 6} .$ Find $(i) A^{'} (i i) B^{'} (i i i) (A \cup C)^{'}$ $(i v) (A \cup B)^{'} (v) (A^{'})^{'} (v i) (B - C)^{'}$

Discussion

5234.	Sin60 degree = 2tan30 degree/1+tan square30 degree
Answer» Sin60 degree = 2tan30 degree/1+tan square30 degree

Discussion

5235.	The angles of depression of the top and bottom of a tower as seen from the top of a 603 m high cliff are 45° and 60° respectively. Find the height of the tower.
Answer» The angles of depression of the top and bottom of a tower as seen from the top of a $60 \sqrt{3}$ m high cliff are 45° and 60° respectively. Find the height of the tower.

Discussion

5236.	A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [4 MARKS]
Answer» A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [4 MARKS]

Discussion

5237.	What is the largest number that must be substracted from 1160 so that the sum of 1160 and the resulting number is completely divisible by 19.
Answer» What is the largest number that must be substracted from 1160 so that the sum of 1160 and the resulting number is completely divisible by 19.

Discussion

5238.	Question 1Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).
Answer» Question 1 Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Discussion

5239.	Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.
Answer» Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

Discussion

5240.	A survey was done in a Housing Society where the number of Vehicles were categorized according to their Mileage.The Graph Given shows the Histogram for the Mileage vs The number of vehicles present.Which of the Following Frequency distribution table is correct for the Graph?
Answer» A survey was done in a Housing Society where the number of Vehicles were categorized according to their Mileage. The Graph Given shows the Histogram for the Mileage vs The number of vehicles present. Which of the Following Frequency distribution table is correct for the Graph?

5240.

A survey was done in a Housing Society where the number of Vehicles were categorized according to their Mileage.The Graph Given shows the Histogram for the Mileage vs The number of vehicles present.Which of the Following Frequency distribution table is correct for the Graph?

Answer»

A survey was done in a Housing Society where the number of Vehicles were categorized according to their Mileage.

The Graph Given shows the Histogram for the Mileage vs The number of vehicles present.

Which of the Following Frequency distribution table is correct for the Graph?

Discussion

5241.	The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in teh ratio 1: 5, find the AP.
Answer» The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in teh ratio 1: 5, find the AP.

Discussion

5242.	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 = 30o then ∠ PTA = ? (a) 60o (b) 30o (c) 15o (d) 45o
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 = $30^{o}$ then $∠$ PTA = ? (a) $60^{o}$ (b) $30^{o}$ (c) $15^{o}$ (d) $45^{o}$

5242.

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 = 30o then ∠ PTA = ? (a) 60o (b) 30o (c) 15o (d) 45o

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 = $30^{o}$ then $∠$ PTA = ?

(a) $60^{o}$ (b) $30^{o}$ (c) $15^{o}$ (d) $45^{o}$

Discussion

5243.	The area of triangle formed by the line passing through (0,1) and having intercepts in the ratio 2: 3 with co-ordinate axes is____ Sq.units.
Answer» The area of triangle formed by the line passing through (0,1) and having intercepts in the ratio 2: 3 with co-ordinate axes is____ Sq.units.

Discussion

5244.	Question 22 (i)(i) Complete the following table:Event: Sum of 2 dice23456789101112Probability136536136
Answer» Question 22 (i) (i) Complete the following table: $\begin{matrix} Event: Sum of 2 dice & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 Probability & \frac{1}{36} & \frac{5}{36} & \frac{1}{36} \end{matrix}$

Discussion

5245.	The angle of elevation of the top of a tree from a point A on the ground is 60∘ . On walking 20 m away from point A, to a point B, the angle of elevation changes to 30∘. Find the height of the tree.
Answer» The angle of elevation of the top of a tree from a point A on the ground is $60^{\circ}$ . On walking 20 m away from point A, to a point B, the angle of elevation changes to $30^{\circ}$ . Find the height of the tree.

Discussion

5246.	If a square matrix A is such that det(A)=5 and det(2A)=320, then the order of A is
Answer» If a square matrix $A$ is such that $det (A) = 5$ and $det (2 A) = 320$ , then the order of $A$ is

Discussion

5247.	Ayush starts walking from his house to office . Instead of going to the office directly , he goes to a bank first , from there to his daughter 's school and then reaches the office. what is the extra distance travelled by Ayush in reaching the office ? ( Assume that all distances covered are in straight lines) . If the house is situated at (2,4) , bank at (5,8) , school at (13,14) and office at ( 13,26) and coordinates are in kilometers .
Answer» Ayush starts walking from his house to office . Instead of going to the office directly , he goes to a bank first , from there to his daughter 's school and then reaches the office. what is the extra distance travelled by Ayush in reaching the office ? ( Assume that all distances covered are in straight lines) . If the house is situated at (2,4) , bank at (5,8) , school at (13,14) and office at ( 13,26) and coordinates are in kilometers .

Discussion

5248.	Question 5 (x)Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (1+tan2A1+cot2A)=(1−tanA1−cotA)2=tan2A
Answer» Question 5 (x) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. $(\frac{1 + t a n^{2} A}{1 + c o t^{2} A}) = (\frac{1 - t a n A}{1 - c o t A})^{2} = t a n^{2} A$

Discussion

5249.	Question 12On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?
Answer» Question 12 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?

Discussion

5250.	the value of k for which the system of equations kx+(k+4)y-7=0 and (k+4)x+9ky-10=0 has no solution, can be
Answer» the value of k for which the system of equations kx+(k+4)y-7=0 and (k+4)x+9ky-10=0 has no solution, can be

Discussion

Explore topic-wise InterviewSolutions in .

49. A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter L of hemisphere is equal to the edge of cube determine the surface area of remaining solid

ABC is a triangle and M & N are points on AB and AC such that MN || BC. Find the given ratios if AM:MB = 2:3.1. AN:AC2. AN:NC3. NC:AC

Question 11 (i) By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then. 3x+y+4 = 0, 6x – 2y + 4 = 0

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h=−16t2+24t+1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

In the given figure, O is the centre of the circle. Find x.

If the ratio of sums upto n terms of two AP's is (5n+3) : (3n+4), then what is the ratio of their 17th terms? [3 MARKS]

If (2p-1), 7 and 3p are in AP, find the value of p.

Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son's age. Find: (i) The age of the son five years ago. (ii) The present age of the woman. [4 MARKS]

What is the sum of the first 20 whole numbers?

If a triangle has angles 45∘,45∘, and 90∘, what is the ratio of the sides of the triangle opposite to these angles respectively?

In a quadrilateral ABCD, ∠B = 90°. If AD2 = AB2 + BC2 + CD2 then prove that ∠ACD = 90°.

The dimensions of a room are 14 m × 10 m × 6.5 m. There are two doors and 4 windows in the room. Each door measures 2.5 m × 1.2 m and each window measures 1.5 × 1 m. Find the cost of painting the four walls of the room at Rs 35 per m2.

A washing tub in the shape of a frustum of a cone has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub ? (π=227)

If ′G′ is centroid and ′I′ is incentre of the triangle formed by line 3x+4y=12 with co-ordinate axis and GI=23√λ2−4(λ&gt;0) then [λ]= (where [.] is G.I.F)

A bag contains three green marbles, four blue marbles, and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

if x^3/2+1/x^3/2 =2 root 5, x is greater than zero, find x^3-1/x^3

cosec2 57o - tan2 33o = ? (a) 0 (b) 1 (c) -1 (d) 2

Find the volume of the figure (in inch3).100

The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs.

Use Euclid's division algorithm to find the HCF of 196 and 38220.

If sinθ + sin2θ = 1 then cos2θ + cos4θ is equal to

Question 4 (x)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(x) a, 2a, 3a, 4a …

The distribution below gives the weight of 30 students in a class. Find the median weight of students: Weight (in kg): 40−45 45−50 50−55 55−60 60−65 65−70 70−75 No. of students: 2 3 8 6 6 3 2

The sum of two natural numbers is 15 and the sum of their reciprocals is 310. Find the numbers. [CBSE 2005]

In the following figure, Show that

The 5th term of an arithmetic sequence is 9 and its 9th term is 5. What is its common difference? What is the 14th term?

The volume of a cone of radius 7 cm and slant height 14 cm is ______.(use π=227)

Question 124 (iv) Evaluate the following, using distributive property. 68×(−17)+(−68)×3

A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?10

Let U={1,2,3,4,5,6,7,8,9},A={1,2,3,4},B={2,4,6,8} and C={3,4,5,6}.Find (i) A′ (ii) B′ (iii) (A∪C)′(iv) (A∪B)′ (v) (A′)′ (vi) (B−C)′

Sin60 degree = 2tan30 degree/1+tan square30 degree

The angles of depression of the top and bottom of a tower as seen from the top of a 603 m high cliff are 45° and 60° respectively. Find the height of the tower.

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [4 MARKS]

What is the largest number that must be substracted from 1160 so that the sum of 1160 and the resulting number is completely divisible by 19.

Question 1Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

A survey was done in a Housing Society where the number of Vehicles were categorized according to their Mileage.The Graph Given shows the Histogram for the Mileage vs The number of vehicles present.Which of the Following Frequency distribution table is correct for the Graph?

The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in teh ratio 1: 5, find the AP.

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 = 30o then ∠ PTA = ? (a) 60o (b) 30o (c) 15o (d) 45o

The area of triangle formed by the line passing through (0,1) and having intercepts in the ratio 2: 3 with co-ordinate axes is____ Sq.units.

Question 22 (i)(i) Complete the following table:Event: Sum of 2 dice23456789101112Probability136536136

The angle of elevation of the top of a tree from a point A on the ground is 60∘ . On walking 20 m away from point A, to a point B, the angle of elevation changes to 30∘. Find the height of the tree.

If a square matrix A is such that det(A)=5 and det(2A)=320, then the order of A is

Question 5 (x)Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (1+tan2A1+cot2A)=(1−tanA1−cotA)2=tan2A

Question 12On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?

the value of k for which the system of equations kx+(k+4)y-7=0 and (k+4)x+9ky-10=0 has no solution, can be

If ′G′ is centroid and ′I′ is incentre of the triangle formed by line 3x+4y=12 with co-ordinate axis and GI=23√λ2−4(λ>0) then [λ]= (where [.] is G.I.F)