32581 + Interview Questions in Mathematics

1.	Which of the following CANNOT be the exponents of the variables in a polynomial?
Answer» Which of the following CANNOT be the exponents of the variables in a polynomial?

Discussion

2.	If f : R→ R is a function defined by f(x)={2x if x⩾0−3x if x<0 Find the value of f(-10).f(2) + f(-1) – f(3).
Answer» If f : R $\to$ R is a function defined by $f (x) = {\begin{matrix} 2 x if x ⩾ 0 - 3 x if x < 0 \end{matrix}$ Find the value of f(-10).f(2) + f(-1) – f(3).

2.

If f : R→ R is a function defined by f(x)={2x if x⩾0−3x if x<0 Find the value of f(-10).f(2) + f(-1) – f(3).

Answer»

If f : R $\to$ R is a function defined by

$f (x) = {\begin{matrix} 2 x if x ⩾ 0 - 3 x if x < 0 \end{matrix}$

Find the value of f(-10).f(2) + f(-1) – f(3).

Discussion

3.	If 5tanθ=4, then write the value of cosθ-sinθcosθ+sinθ.
Answer» $If 5 \tan θ = 4, then write the value of \frac{(\cos θ - \sin θ)}{(\cos θ + \sin θ)} .$

Discussion

4.	In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:(i) the name of a girl(ii) the name of a boy?
Answer» In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is: (i) the name of a girl (ii) the name of a boy?

Discussion

5.	the sum of a two digit number and the number obtained by reversing the digits is 66 if the digit of the number differ by 2 find the number how many such numbers are there?
Answer» the sum of a two digit number and the number obtained by reversing the digits is 66 if the digit of the number differ by 2 find the number how many such numbers are there?

Discussion

6.	Amit deposited ₹150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?
Answer» Amit deposited ₹150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

Discussion

7.	Choose the correct alternative answer for the following questions.(1) sinθ cosecθ = ?(A) 1(B) 0(C) 12(D) 2(2) cosec 45° =?(A) 12(B) 2(C) 32(D)23 (3) 1 + tan2 θ = ?(A) cot2 θ(B) cosec2 θ(C) sec2 θ(D) tan2 θ (4) When we see at a higher level , from the horizontal line,angle formed is ....... .(A) angle of elevation.(B) angle of depression.(C) 0(D) straight angle.
Answer» Choose the correct alternative answer for the following questions. (1) sin $θ$ cosec $θ$ = ? (A) 1 (B) 0 (C) $\frac{1}{2}$ (D) $\sqrt{2}$ (2) cosec 45^° =? (A) $\frac{1}{2}$ (B) $\sqrt{2}$ (C) $\frac{\sqrt{3}}{2}$ (D) $\frac{2}{\sqrt{3}}$ (3) 1 + tan² $θ$ = ? (A) cot² $θ$ (B) cosec² $θ$ (C) sec² $θ$ (D) tan² $θ$ (4) When we see at a higher level , from the horizontal line,angle formed is ....... . (A) angle of elevation. (B) angle of depression. (C) 0 (D) straight angle.

Discussion

8.	The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
Answer» The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

Discussion

9.	In a cricket match , the player hits a 4 in every 12 balls. What is the probablity of him not hitting a 4 .
Answer» In a cricket match , the player hits a 4 in every 12 balls. What is the probablity of him not hitting a 4 .

Discussion

10.	Find the product:(−103pq3) × (65p3q)
Answer» Find the product: $(- \frac{10}{3} p q^{3}) \times (\frac{6}{5} p^{3} q)$

Discussion

11.	49. Find the foot of the sides of right angle triangle ,if foot of hypotenuse are (-4,1) and (1,3)
Answer» 49. Find the foot of the sides of right angle triangle ,if foot of hypotenuse are (-4,1) and (1,3)

Discussion

12.	The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.
Answer» The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.

12.

The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.

Answer»

The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A.

Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.

Discussion

13.	In the given figure, O is the centre of two concentric circles fo radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm. Find the length of BP.
Answer» In the given figure, O is the centre of two concentric circles fo radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm. Find the length of BP.

Discussion

14.	A, B and C are partners sharing profits and losses in the ratio of A 1/2, B 3/10, C 1/5 after providing for interest 5% on their respective capitals, viz., A ₹ 50,000; B ₹ 30,000 and C ₹ 20,000 and allowing B and C a salary of ₹ 5,000 each per annum. During the year ended 31st March, 2019, A has drawn ₹ 10,000 and B and C in addition to their salaries have drawn ₹ 2,500 and ₹ 1,000 respectively. Profit and Loss Account for the year ended 31st March, 2019 showed a net profit of ₹ 45,000. On 1st April, 2018, the balances in the Current Accounts of the partners were A (Cr.) ₹ 4,500; B (Cr.) ₹ 1,500 and C (Cr.) ₹ 1,000. Interest is not charged on Drawings or Current Account balances. Show Partners' Capital and Current Accounts as at 31st March, 2019 after division of profits in accordance with the partnership agreement.
Answer» A, B and C are partners sharing profits and losses in the ratio of A 1/2, B 3/10, C 1/5 after providing for interest 5% on their respective capitals, viz., A ₹ 50,000; B ₹ 30,000 and C ₹ 20,000 and allowing B and C a salary of ₹ 5,000 each per annum. During the year ended 31st March, 2019, A has drawn ₹ 10,000 and B and C in addition to their salaries have drawn ₹ 2,500 and ₹ 1,000 respectively. Profit and Loss Account for the year ended 31st March, 2019 showed a net profit of ₹ 45,000. On 1st April, 2018, the balances in the Current Accounts of the partners were A (Cr.) ₹ 4,500; B (Cr.) ₹ 1,500 and C (Cr.) ₹ 1,000. Interest is not charged on Drawings or Current Account balances. Show Partners' Capital and Current Accounts as at 31st March, 2019 after division of profits in accordance with the partnership agreement.

Discussion

15.	Question 6 To draw a pair of tangents to a circle which are inclined to each other at an angle of 60∘, it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be (A) 135∘ (B) 90∘ (C) 60∘ (D) 120∘
Answer» Question 6 To draw a pair of tangents to a circle which are inclined to each other at an angle of $60^{\circ}$ , it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be (A) $135^{\circ}$ (B) $90^{\circ}$ (C) $60^{\circ}$ (D) $120^{\circ}$

Discussion

16.	Question 1(iv)Find the roots of the following quadratic equations by factorisation:(iv) 2x2−x+18=0
Answer» Question 1(iv) Find the roots of the following quadratic equations by factorisation: (iv) $2 x^{2} - x + \frac{1}{8} = 0$

Discussion

17.	Choose the correct answer of the following question:The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30°. The distance of the car from the tower is(a) 503 m (b) 1503 m (c) 1502 m (d) 75 m [CBSE 2014]
Answer» Choose the correct answer of the following question: The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30°. The distance of the car from the tower is (a) $50 \sqrt{3}$ m (b) $150 \sqrt{3}$ m (c) $150 \sqrt{2}$ m (d) 75 m [CBSE 2014]

Discussion

18.	From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse. 3=1.73
Answer» From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse. $(\sqrt{3} = 1.73)$

Discussion

19.	A Triangle ABC with AB=3cm BC=6cm AC=4cm is enlarged to a triangle DEF with longest side = 9cm. Find the scale factor and hence the lengths of other sides of triangle DEF.
Answer» A Triangle ABC with AB=3cm BC=6cm AC=4cm is enlarged to a triangle DEF with longest side = 9cm. Find the scale factor and hence the lengths of other sides of triangle DEF.

19.

A Triangle ABC with AB=3cm BC=6cm AC=4cm is enlarged to a triangle DEF with longest side = 9cm. Find the scale factor and hence the lengths of other sides of triangle DEF.

Answer»

A Triangle ABC with AB=3cm BC=6cm AC=4cm is enlarged to a triangle DEF with longest side = 9cm.

Find the scale factor and hence the lengths of other sides of triangle DEF.

Discussion

20.	If α and β are the zeros of the quadratic polynomial f(x)=x2−1, find a quadratic polynomial whose zeros are 2αβ and 2βα
Answer» If $α a n d β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - 1$ , find a quadratic polynomial whose zeros are $\frac{2 α}{β} a n d \frac{2 β}{α}$

Discussion

21.	Find the area of the smaller part of the circle x 2 + y 2 = a 2 cut off by the line
Answer» Find the area of the smaller part of the circle x 2 + y 2 = a 2 cut off by the line

Discussion

22.	If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer» If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Discussion

23.	Q. There are two vessels - A, and B. A contains water and milk in the ratio 3:2 and vessel B contains milk and honey in the ratio 5:4. If one takes equal quantities of solutions from vessels A and B, and pours it into vessel C, what will be the concentration of milk in the new solution?
Answer» Q. There are two vessels - A, and B. A contains water and milk in the ratio $3 : 2$ and vessel B contains milk and honey in the ratio $5 : 4$ . If one takes equal quantities of solutions from vessels A and B, and pours it into vessel C, what will be the concentration of milk in the new solution?

Discussion

24.	A quadratic equation x2+kx+2=0 has one of its roots as 2. What is the value of k ?
Answer» A quadratic equation $x^{2} + k x + 2 = 0$ has one of its roots as $2$ . What is the value of $k$ ?

Discussion

25.	Q77. Select the missing number/letters from the given responses
Answer» Q77. Select the missing number/letters from the given responses

25.

Q77. Select the missing number/letters from the given responses

Answer»

Q77. Select the missing number/letters from the given responses

Discussion

26.	Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides.the length of each perpendicular is equal to a units.The distance between their feet being equal to b units.Find the area of the rhombus
Answer» Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides.the length of each perpendicular is equal to a units.The distance between their feet being equal to b units.Find the area of the rhombus

Discussion

27.	What are the coordinates of the point which divides the line segment joining (- 1, 7) and (4, - 3) in the ratio 2:3?
Answer» What are the coordinates of the point which divides the line segment joining (- 1, 7) and (4, - 3) in the ratio 2:3?

Discussion

28.	Factorise 12a2b+15ab2.
Answer» Factorise 12a²b+15ab².

Discussion

29.	Surds and irrational numbers are same?
Answer» Surds and irrational numbers are same?

Discussion

30.	The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.
Answer» The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.

Discussion

31.	In the given figure, Δ ABC is circumscribing a circle. Find the length of BC.
Answer» In the given figure, Δ ABC is circumscribing a circle. Find the length of BC.

Discussion

32.	In ΔABC given below, AB = 10 cm, AC = 8 cm and ∠A=45∘. The find the area of ΔABC.
Answer» In $Δ A B C$ given below, AB = 10 cm, AC = 8 cm and $∠ A = 45^{\circ}$ . The find the area of $Δ A B C$ .

32.

In ΔABC given below, AB = 10 cm, AC = 8 cm and ∠A=45∘. The find the area of ΔABC.

Answer»

In $Δ A B C$ given below, AB = 10 cm, AC = 8 cm and $∠ A = 45^{\circ}$ . The find the area of $Δ A B C$ .

Discussion

33.	If a cone is cut into two parts by a horizontal plane passing through the midpoint of its axis, the ratio of the volumes of upper and lower part is (a) 1:2 (6) 2:1 (c) 1:7(d) 1:8
Answer» If a cone is cut into two parts by a horizontal plane passing through the midpoint of its axis, the ratio of the volumes of upper and lower part is (a) 1:2 (6) 2:1 (c) 1:7 (d) 1:8

Discussion

34.	Question 4How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?
Answer» Question 4 How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?

Discussion

35.	Joshma is playing hide-and-seek with Sheeba and Shradha. If Sheeba is hiding 5 meters south of Joshma and the straight distance between Sheeba and Shradha is 13 meters, then how many meters towards the east of Joshma is Shradha?
Answer» Joshma is playing hide-and-seek with Sheeba and Shradha. If Sheeba is hiding 5 meters south of Joshma and the straight distance between Sheeba and Shradha is 13 meters, then how many meters towards the east of Joshma is Shradha?

Discussion

36.	Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(−3, −1).
Answer» Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(−3, −1).

Discussion

37.	If the circumference of a circle is equal to the perimeter of a square then the ratio their areas is:(a) 22 : 7(b) 14 :11(c) 7 :22(d) 7 :11
Answer» If the circumference of a circle is equal to the perimeter of a square then the ratio their areas is: (a) 22 : 7 (b) 14 :11 (c) 7 :22 (d) 7 :11

Discussion

38.	A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass. [CBSE 2012)
Answer» A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass. [CBSE 2012)

Discussion

39.	The square of a number when decreased by 15 is equal to twice the original number. Which of the following are true about the numbers?
Answer» The square of a number when decreased by 15 is equal to twice the original number. Which of the following are true about the numbers?

Discussion

40.	There is (are) ________ value(s) of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 have infinitely many solutions.
Answer» There is (are) ________ value(s) of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 have infinitely many solutions.

Discussion

41.	An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: Firm AFirm BNo. of wage earners586648Mean of monthly wagesRs.5253Rs.5253Variance of the distribution of wages100121 (i)Which firm spends larger amount as monthly wages? (ii)Which firm shows greater variability in individual wages?
Answer» An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: $\begin{matrix} F i r m A & F i r m B N o . o f w a g e e a r n e r s & 586 & 648 M e a n o f m o n t h l y w a g e s & R s . 5253 & R s . 5253 V a r i a n c e o f t h e d i s t r i b u t i o n o f w a g e s & 100 & 121 \end{matrix}$ (i)Which firm spends larger amount as monthly wages? (ii)Which firm shows greater variability in individual wages?

41.

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: Firm AFirm BNo. of wage earners586648Mean of monthly wagesRs.5253Rs.5253Variance of the distribution of wages100121 (i)Which firm spends larger amount as monthly wages? (ii)Which firm shows greater variability in individual wages?

Answer»

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

$\begin{matrix} F i r m A & F i r m B N o . o f w a g e e a r n e r s & 586 & 648 M e a n o f m o n t h l y w a g e s & R s . 5253 & R s . 5253 V a r i a n c e o f t h e d i s t r i b u t i o n o f w a g e s & 100 & 121 \end{matrix}$

(i)Which firm spends larger amount as monthly wages?

(ii)Which firm shows greater variability in individual wages?

Discussion

42.	Point A (-4, 1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x = 2 is the perpendicular bisector of AB?
Answer» Point A (-4, 1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x = 2 is the perpendicular bisector of AB?

Discussion

43.	A ladder makes an angle of 60º with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is(a) 43 (b) 43 (c) 22 (d) 4 [CBSE 2014]
Answer» A ladder makes an angle of 60º with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is (a) $\frac{4}{\sqrt{3}}$ (b) $4 \sqrt{3}$ (c) $2 \sqrt{2}$ (d) $4$ [CBSE 2014]

Discussion

44.	Form the pair of linear equations in the following problems, and find their solution graphically:(i) 10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.(iii) Champa went to a 'sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of skirts is two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased." Help her friends to find how many pants and skirts Champa bought.
Answer» Form the pair of linear equations in the following problems, and find their solution graphically: (i) 10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. (ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen. (iii) Champa went to a 'sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of skirts is two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased." Help her friends to find how many pants and skirts Champa bought.

Discussion

45.	The area of a sector of a circle of radius 5 cm is 5 π cm2 . Find the angle contained by the sector.
Answer» The area of a sector of a circle of radius 5 cm is 5 π cm² . Find the angle contained by the sector.

Discussion

46.	Prove the following trigonometric identities: tan2A+cot2A=sec2 A cosec2A−2
Answer» Prove the following trigonometric identities: $t a n^{2} A + c o t^{2} A = s e c^{2} A c o s e c^{2} A - 2$

46.

Prove the following trigonometric identities: tan2A+cot2A=sec2 A cosec2A−2

Answer»

Prove the following trigonometric identities:

$t a n^{2} A + c o t^{2} A = s e c^{2} A c o s e c^{2} A - 2$

Discussion

47.	If he area of a sector of a circle is 720 of the area of the circle, then the sector angle is equal to(a) 110°(b) 130°(c) 100°(d) 126°
Answer» If he area of a sector of a circle is $\frac{7}{20}$ of the area of the circle, then the sector angle is equal to (a) 110° (b) 130° (c) 100° (d) 126°

Discussion

48.	The locus of the point( acoscubetheta,asincubetheta)is
Answer» The locus of the point( acoscubetheta,asincubetheta)is

Discussion

49.	(4)10/2 mthrown horizontally from a tower45. A body is100 m high, at t= 0 with a velocity 10 m/sThe velocity of the body is directed at an angle 45with the horizontal at a time equal to (g 10 m/s2(1) 1 s(er2 s(3) 3 s(4) 4 sSpace
Answer» (4)10/2 mthrown horizontally from a tower45. A body is100 m high, at t= 0 with a velocity 10 m/sThe velocity of the body is directed at an angle 45with the horizontal at a time equal to (g 10 m/s2(1) 1 s(er2 s(3) 3 s(4) 4 sSpace

Discussion

50.	An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same tiles would have been needed to pave the same area. Find the size of the larger tiles.
Answer» An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same tiles would have been needed to pave the same area. Find the size of the larger tiles.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Which of the following CANNOT be the exponents of the variables in a polynomial?

If f : R→ R is a function defined by f(x)={2x if x⩾0−3x if x&lt;0 Find the value of f(-10).f(2) + f(-1) – f(3).

If 5tanθ=4, then write the value of cosθ-sinθcosθ+sinθ.

the sum of a two digit number and the number obtained by reversing the digits is 66 if the digit of the number differ by 2 find the number how many such numbers are there?

Amit deposited ₹150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

In a cricket match , the player hits a 4 in every 12 balls. What is the probablity of him not hitting a 4 .

Find the product:(−103pq3) × (65p3q)

49. Find the foot of the sides of right angle triangle ,if foot of hypotenuse are (-4,1) and (1,3)

The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.

In the given figure, O is the centre of two concentric circles fo radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm. Find the length of BP.

Question 6 To draw a pair of tangents to a circle which are inclined to each other at an angle of 60∘, it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be (A) 135∘ (B) 90∘ (C) 60∘ (D) 120∘

Question 1(iv)Find the roots of the following quadratic equations by factorisation:(iv) 2x2−x+18=0

Choose the correct answer of the following question:The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30°. The distance of the car from the tower is(a) 503 m (b) 1503 m (c) 1502 m (d) 75 m [CBSE 2014]

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse. 3=1.73

A Triangle ABC with AB=3cm BC=6cm AC=4cm is enlarged to a triangle DEF with longest side = 9cm. Find the scale factor and hence the lengths of other sides of triangle DEF.

If α and β are the zeros of the quadratic polynomial f(x)=x2−1, find a quadratic polynomial whose zeros are 2αβ and 2βα

Find the area of the smaller part of the circle x 2 + y 2 = a 2 cut off by the line

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Q. There are two vessels - A, and B. A contains water and milk in the ratio 3:2 and vessel B contains milk and honey in the ratio 5:4. If one takes equal quantities of solutions from vessels A and B, and pours it into vessel C, what will be the concentration of milk in the new solution?

A quadratic equation x2+kx+2=0 has one of its roots as 2. What is the value of k ?

Q77. Select the missing number/letters from the given responses

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides.the length of each perpendicular is equal to a units.The distance between their feet being equal to b units.Find the area of the rhombus

What are the coordinates of the point which divides the line segment joining (- 1, 7) and (4, - 3) in the ratio 2:3?

Factorise 12a2b+15ab2.

Surds and irrational numbers are same?

The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.

In the given figure, Δ ABC is circumscribing a circle. Find the length of BC.

In ΔABC given below, AB = 10 cm, AC = 8 cm and ∠A=45∘. The find the area of ΔABC.

If a cone is cut into two parts by a horizontal plane passing through the midpoint of its axis, the ratio of the volumes of upper and lower part is (a) 1:2 (6) 2:1 (c) 1:7(d) 1:8

Question 4How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?

Joshma is playing hide-and-seek with Sheeba and Shradha. If Sheeba is hiding 5 meters south of Joshma and the straight distance between Sheeba and Shradha is 13 meters, then how many meters towards the east of Joshma is Shradha?

Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(−3, −1).

If the circumference of a circle is equal to the perimeter of a square then the ratio their areas is:(a) 22 : 7(b) 14 :11(c) 7 :22(d) 7 :11

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass. [CBSE 2012)

The square of a number when decreased by 15 is equal to twice the original number. Which of the following are true about the numbers?

There is (are) ________ value(s) of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 have infinitely many solutions.

Point A (-4, 1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x = 2 is the perpendicular bisector of AB?

A ladder makes an angle of 60º with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is(a) 43 (b) 43 (c) 22 (d) 4 [CBSE 2014]

The area of a sector of a circle of radius 5 cm is 5 π cm2 . Find the angle contained by the sector.

Prove the following trigonometric identities: tan2A+cot2A=sec2 A cosec2A−2

If he area of a sector of a circle is 720 of the area of the circle, then the sector angle is equal to(a) 110°(b) 130°(c) 100°(d) 126°

The locus of the point( acoscubetheta,asincubetheta)is

(4)10/2 mthrown horizontally from a tower45. A body is100 m high, at t= 0 with a velocity 10 m/sThe velocity of the body is directed at an angle 45with the horizontal at a time equal to (g 10 m/s2(1) 1 s(er2 s(3) 3 s(4) 4 sSpace

An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same tiles would have been needed to pave the same area. Find the size of the larger tiles.

If f : R→ R is a function defined by f(x)={2x if x⩾0−3x if x<0 Find the value of f(-10).f(2) + f(-1) – f(3).