32581 + Interview Questions in Mathematics

1.	What is the reason behind taking b =6 in the Question: Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. [3 MARKS]
Answer» What is the reason behind taking b =6 in the Question: Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. [3 MARKS]

Discussion

2.	The money required to buy 50 of ₹ 40 shares at a discount of ₹ 10 will be
Answer» The money required to buy 50 of ₹ 40 shares at a discount of ₹ 10 will be

Discussion

3.	The radius of a circle is 20 cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is(a) 105 cm(b) 103 cm(c) 105 cm(d) 102 cm
Answer» The radius of a circle is 20 cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is (a) 10 $\sqrt{5}$ cm (b) 10 $\sqrt{3}$ cm (c) 10 $\sqrt{5}$ cm (d) 10 $\sqrt{2}$ cm

Discussion

4.	80. Points A (4,3) B, (x,4) , C (5,- 6) and D(3,y) in order are vertices of a parallelogram. Find the distance between AB and CD .
Answer» 80. Points A (4,3) B, (x,4) , C (5,- 6) and D(3,y) in order are vertices of a parallelogram. Find the distance between AB and CD .

Discussion

5.

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution: Monthly consumption (in units) 140−160 160−180 180−200 200−220 220−240 240−260 260−280 Number of families 3 8 15 40 50 30 10 Prepare a 'more than type' ogive for the following frequency distribution. [CBSE 2014]

Answer» The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly consumption (in units)	140−160	160−180	180−200	200−220	220−240	240−260	260−280
Number of families	3	8	15	40	50	30	10

Prepare a 'more than type' ogive for the following frequency distribution. [CBSE 2014]

Discussion

6.	Question 1 (v) Solve the following pairs of equations by reducing them to a pair of linear equations: 7x−2yxy=5 8x+7yxy=15
Answer» Question 1 (v) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{7 x - 2 y}{x y} = 5$ $\frac{8 x + 7 y}{x y} = 15$

Discussion

7.	A bag contains cards numbers from 1 to 49. A card is drawn from the bag at random, after mixing the cards thoroughly. Find the probability that the number on the drawn card is: (1) An odd number (2) A multiple of 5 (3) A perfect Square (4) An even prime number
Answer» A bag contains cards numbers from 1 to 49. A card is drawn from the bag at random, after mixing the cards thoroughly. Find the probability that the number on the drawn card is: (1) An odd number (2) A multiple of 5 (3) A perfect Square (4) An even prime number

Discussion

8.	Question 92 (xxiii)Factorise the following using the identity a2−b2=(a+b)(a−b).x4−y4
Answer» Question 92 (xxiii) Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$ $x^{4} - y^{4}$

8.

Question 92 (xxiii)Factorise the following using the identity a2−b2=(a+b)(a−b).x4−y4

Answer»

Question 92 (xxiii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$x^{4} - y^{4}$

Discussion

9.	Two equal circles touch each other externally at C and AB is a common tangent to the circles . Then, ∠ACB =(a) 60°(b) 45°(c) 30°(d) 90°
Answer» Two equal circles touch each other externally at C and AB is a common tangent to the circles . Then, ∠ACB = (a) 60° (b) 45° (c) 30° (d) 90°

Discussion

10.	Prove that the points (2,3), (−4, −6) and (1, 3/2) do not form a triangle.
Answer» Prove that the points (2,3), (−4, −6) and (1, 3/2) do not form a triangle.

Discussion

11.	For every pair of a and b there exist p and r such that a=bq+r give example of a and b satisfying r > b
Answer» For every pair of a and b there exist p and r such that a=bq+r give example of a and b satisfying r > b

Discussion

12.	Question 8A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.
Answer» Question 8 A random survey of the number of children of various age groups playing in park was found as follows: $\begin{matrix} Age (in years) & Number of children 1 - 2 & 5 2 - 3 & 3 3 - 5 & 6 5 - 7 & 12 7 - 10 & 9 10 - 15 & 10 15 - 17 & 4 \end{matrix}$ Draw a histogram to represent the data above.

Discussion

13.	Nick and Mike were trying to solve the equation 3x2+8x+4=0 by the method of completion of squares. While trying to complete the squares, in one of the steps, Mike subtracted (76)2 whereas Nick subtracted (43)2 and both of them calculated the roots. Their teacher looked at the roots and told them that Nick’s roots are the additive inverses of Mike's roots. Do you agree with the teacher?Justify the reasons.
Answer» Nick and Mike were trying to solve the equation $3 x^{2} + 8 x + 4 = 0$ by the method of completion of squares. While trying to complete the squares, in one of the steps, Mike subtracted $(\frac{7}{6})^{2}$ whereas Nick subtracted $(\frac{4}{3})^{2}$ and both of them calculated the roots. Their teacher looked at the roots and told them that Nick’s roots are the additive inverses of Mike's roots. Do you agree with the teacher?Justify the reasons.

Discussion

14.	If the mode of the data: 64, 60, 48, x, 43, 48, 43, 34 is 43, then x + 3 =(a) 44(b) 45(c) 46(d) 48
Answer» If the mode of the data: 64, 60, 48, x, 43, 48, 43, 34 is 43, then x + 3 = (a) 44 (b) 45 (c) 46 (d) 48

Discussion

15.	Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Answer» Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Discussion

16.	Find the distance between each of the following pairs of points.(1) A(2, 3), B(4, 1)(2) P(–5, 7), Q(–1, 3)(3) R0, –3, S0, 52(4) L(5, –8), M(–7, –3)(5) T(–3, 6), R(9, –10)(6) W –72 , 4, X11, 4
Answer» Find the distance between each of the following pairs of points. (1) A(2, 3), B(4, 1) (2) P(–5, 7), Q(–1, 3) (3) $R (0, - 3), S (0, \frac{5}{2})$ (4) L(5, –8), M(–7, –3) (5) T(–3, 6), R(9, –10) (6) $W (\frac{- 7}{2}, 4), X (11, 4)$

Discussion

17.	Can we write 1-sin theta=cos theta
Answer» Can we write 1-sin theta=cos theta

Discussion

18.	Solve the following systems of equations:23x+2y+33x-2y=17553x+2y+13x-2y=2
Answer» Solve the following systems of equations: $\frac{2}{3 x + 2 y} + \frac{3}{3 x - 2 y} = \frac{17}{5} \frac{5}{3 x + 2 y} + \frac{1}{3 x - 2 y} = 2$

Discussion

19.	A school has 3 sections each from class 1 to 12. Students of this school plant tree in the school campus to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class in which they are studying. How many plants were planted by the students?
Answer» A school has 3 sections each from class 1 to 12. Students of this school plant tree in the school campus to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class in which they are studying. How many plants were planted by the students?

Discussion

20.	The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step deviation Method. Weight (in g)No. of apples80−85585−90890−951095−10012100−1058105−1104110−1153 [4 MARKS]
Answer» The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step deviation Method. $\begin{matrix} W e i g h t (i n g) & N o . o f a p p l e s 80 - 85 & 5 85 - 90 & 8 90 - 95 & 10 95 - 100 & 12 100 - 105 & 8 105 - 110 & 4 110 - 115 & 3 \end{matrix}$ [4 MARKS]

Discussion

21.	Sin theta + cos theta = root 2 then evaluate tan theta +cot theta
Answer» Sin theta + cos theta = root 2 then evaluate tan theta +cot theta

Discussion

22.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data: Number of cars 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 Frequency 7 14 13 12 20 11 15 8

Answer»

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

Number of cars	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 − 60	60 − 70	70 − 80
Frequency	7	14	13	12	20	11	15	8

Discussion

23.	Water flows through a cylindrical pipe , whose inner radius is 1 cm , at the rate of 80 cm /sec in an empty cylindrical tank , the radius of whose base is 40 cm . What is the rise of water level in tank in half an hour ?
Answer» Water flows through a cylindrical pipe , whose inner radius is 1 cm , at the rate of 80 cm /sec in an empty cylindrical tank , the radius of whose base is 40 cm . What is the rise of water level in tank in half an hour ?

Discussion

24.	Question 6The 21st term of an AP whose first two terms are – 3 and 4, isA) 17B) 137C) 143D) -143
Answer» Question 6 The $21^{s t}$ term of an AP whose first two terms are – 3 and 4, is A) 17 B) 137 C) 143 D) -143

Discussion

25.	What will be the remainder when 4x4−3x3+2x2−x is divided by x+1?
Answer» What will be the remainder when $4 x^{4} - 3 x^{3} + 2 x^{2} - x$ is divided by $x + 1$ ?

Discussion

26.	The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.
Answer» The surface area of a solid metallic sphere is $2464 c m^{2}$ . It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.

Discussion

27.	Write down the coordinates of two more points on the line through (1, 3) of slope.
Answer» Write down the coordinates of two more points on the line through (1, 3) of slope.

Discussion

28.	A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in the figure.
Answer» A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $Δ A B C$ , if AB and BC are parallel to the coordinate axes as shown in the figure.

Discussion

29.	Ravi starts for his school at 8:20 am on his bicycle. If he travels at a speed of 10 km/h then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?
Answer» Ravi starts for his school at 8:20 am on his bicycle. If he travels at a speed of 10 km/h then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?

Discussion

30.	In the given figure, PO ⊥ QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisector of each other.
Answer» In the given figure, PO $⊥$ QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisector of each other.

Discussion

31.	Question 4 In the given figure, if PQ\|\|ST,∠PQR=110∘ and ∠RST=130∘ find the ∠QRS. [Hint: Draw a line parallel to ST through point R.]
Answer» Question 4 In the given figure, if $P Q \| \| S T, ∠ P Q R = 110^{\circ}$ and $∠ R S T = 130^{\circ}$ find the $∠ Q R S .$ [Hint: Draw a line parallel to ST through point R.]

Discussion

32.	D and E are points on sides AB and AC respectively of ∆ABC such that ar(∆BCD) = ar(∆BCE). Prove that DE \|\| BC.
Answer» D and E are points on sides AB and AC respectively of ∆ABC such that ar(∆BCD) = ar(∆BCE). Prove that DE \|\| BC.

Discussion

33.	If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cosθ= _____.
Answer» If $θ$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then $c o s θ =$ _____.

Discussion

34.	If O is the centre of the given circle and AB = 10 cm, what could be the length of CD?
Answer» If O is the centre of the given circle and AB = 10 cm, what could be the length of CD?

Discussion

35.	If x = 2pi/7 Then find the value of tan(x)tan(2x) + tan(2x)tan(4x) + tan(4x)tan(x)
Answer» If x = 2pi/7 Then find the value of tan(x)tan(2x) + tan(2x)tan(4x) + tan(4x)tan(x)

Discussion

36.	Find the value of cosec 30∘+cot 45∘.
Answer» Find the value of $c o s e c 30^{\circ} + c o t 45^{\circ}$ .

Discussion

37.	Fill in the blanks to make the statement true:When a number is divided by 8, the result is -3. The number is _______.
Answer» Fill in the blanks to make the statement true: When a number is divided by 8, the result is -3. The number is _______.

37.

Fill in the blanks to make the statement true:When a number is divided by 8, the result is -3. The number is _______.

Answer»

Fill in the blanks to make the statement true:

When a number is divided by 8, the result is -3. The number is _______.

Discussion

38.	(1) If A = 2πr2, then solve for ‘r’ and find the value of ‘r’ when A = 77 and (2) If V = πr2h, then solve for ‘r’ and find the value of ‘r’ when V = 176 and h = 14(3) If r2 = l2 + d2, then solve for ‘d’ and find the value of ‘d’ when r = 5 and l = 4.(4) If c2 = a2 + b2, then solve for ‘b’. If a = 8 and c = 17, find the value of ‘b’.(5) If K = ½ mv2, then solve for ‘v’ and find the value of ‘v’ when K = 100 and m = 2.(6) If v2 = u2 + 2as, solve for ‘v’. If u = 0, a = 2 and s = 100, find the value of v.
Answer» (1) If A = 2πr², then solve for ‘r’ and find the value of ‘r’ when A = 77 and (2) If V = πr²h, then solve for ‘r’ and find the value of ‘r’ when V = 176 and h = 14 (3) If r² = l² + d², then solve for ‘d’ and find the value of ‘d’ when r = 5 and l = 4. (4) If c² = a² + b², then solve for ‘b’. If a = 8 and c = 17, find the value of ‘b’. (5) If K = ½ mv², then solve for ‘v’ and find the value of ‘v’ when K = 100 and m = 2. (6) If v² = u² + 2as, solve for ‘v’. If u = 0, a = 2 and s = 100, find the value of v.

38.

(1) If A = 2πr2, then solve for ‘r’ and find the value of ‘r’ when A = 77 and (2) If V = πr2h, then solve for ‘r’ and find the value of ‘r’ when V = 176 and h = 14(3) If r2 = l2 + d2, then solve for ‘d’ and find the value of ‘d’ when r = 5 and l = 4.(4) If c2 = a2 + b2, then solve for ‘b’. If a = 8 and c = 17, find the value of ‘b’.(5) If K = ½ mv2, then solve for ‘v’ and find the value of ‘v’ when K = 100 and m = 2.(6) If v2 = u2 + 2as, solve for ‘v’. If u = 0, a = 2 and s = 100, find the value of v.

Answer»

(1) If A = 2πr², then solve for ‘r’ and find the value of ‘r’ when A = 77 and

(2) If V = πr²h, then solve for ‘r’ and find the value of ‘r’ when V = 176 and h = 14

(3) If r² = l² + d², then solve for ‘d’ and find the value of ‘d’ when r = 5 and l = 4.

(4) If c² = a² + b², then solve for ‘b’. If a = 8 and c = 17, find the value of ‘b’.

(5) If K = ½ mv², then solve for ‘v’ and find the value of ‘v’ when K = 100 and m = 2.

(6) If v² = u² + 2as, solve for ‘v’. If u = 0, a = 2 and s = 100, find the value of v.

Discussion

39.	Question 1(ii)Do the following pair of linear equations have no solution? Justify your answer.x = 2y and y = 2x
Answer» Question 1(ii) Do the following pair of linear equations have no solution? Justify your answer. x = 2y and y = 2x

Discussion

40.	Question 3If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.
Answer» Question 3 If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

Discussion

41.	A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.
Answer» A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

Discussion

42.	Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student drawn at random passed the exam?
Answer» Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student drawn at random passed the exam?

Discussion

43.	Question 5Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.
Answer» Question 5 Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Discussion

44.	Write the common difference of an A.P. whose nth term is an = 3n + 7.
Answer» Write the common difference of an A.P. whose nth term is a_n = 3n + 7.

Discussion

45.	Obtain all other zeros of (x3+4x3−2x2−20x−15) if two of its zeros are √5 and −√5.
Answer» Obtain all other zeros of $(x^{3} + 4 x^{3} - 2 x^{2} - 20 x - 15)$ if two of its zeros are $\sqrt{5} a n d - \sqrt{5}$ .

Discussion

46.	A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.
Answer» A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

Discussion

47.	A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Answer» A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Discussion

48.	In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B =(a) 35°(b) 65°(c) 75°(d) 85°
Answer» In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B = (a) 35° (b) 65° (c) 75° (d) 85°

Discussion

49.	If α and β are zeroes of polynomial x square - 6x + a. Find value of "a" if 3α + 2β =20
Answer» If α and β are zeroes of polynomial x square - 6x + a. Find value of "a" if 3α + 2β =20

Discussion

50.	If sinθ=45 , Find the value of 4tanθ−5cosθsecθ+4cotθ
Answer» If $s i n θ = \frac{4}{5}$ , Find the value of $\frac{4 t a n θ - 5 c o s θ}{s e c θ + 4 c o t θ}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the reason behind taking b =6 in the Question: Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. [3 MARKS]

The money required to buy 50 of ₹ 40 shares at a discount of ₹ 10 will be

The radius of a circle is 20 cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is(a) 105 cm(b) 103 cm(c) 105 cm(d) 102 cm

80. Points A (4,3) B, (x,4) , C (5,- 6) and D(3,y) in order are vertices of a parallelogram. Find the distance between AB and CD .

Question 1 (v) Solve the following pairs of equations by reducing them to a pair of linear equations: 7x−2yxy=5 8x+7yxy=15

A bag contains cards numbers from 1 to 49. A card is drawn from the bag at random, after mixing the cards thoroughly. Find the probability that the number on the drawn card is: (1) An odd number (2) A multiple of 5 (3) A perfect Square (4) An even prime number

Question 92 (xxiii)Factorise the following using the identity a2−b2=(a+b)(a−b).x4−y4

Two equal circles touch each other externally at C and AB is a common tangent to the circles . Then, ∠ACB =(a) 60°(b) 45°(c) 30°(d) 90°

Prove that the points (2,3), (−4, −6) and (1, 3/2) do not form a triangle.

For every pair of a and b there exist p and r such that a=bq+r give example of a and b satisfying r &gt; b

Question 8A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.

If the mode of the data: 64, 60, 48, x, 43, 48, 43, 34 is 43, then x + 3 =(a) 44(b) 45(c) 46(d) 48

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Find the distance between each of the following pairs of points.(1) A(2, 3), B(4, 1)(2) P(–5, 7), Q(–1, 3)(3) R0, –3, S0, 52(4) L(5, –8), M(–7, –3)(5) T(–3, 6), R(9, –10)(6) W –72 , 4, X11, 4

Can we write 1-sin theta=cos theta

Solve the following systems of equations:23x+2y+33x-2y=17553x+2y+13x-2y=2

The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step deviation Method. Weight (in g)No. of apples80−85585−90890−951095−10012100−1058105−1104110−1153 [4 MARKS]

Sin theta + cos theta = root 2 then evaluate tan theta +cot theta

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data: Number of cars 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 Frequency 7 14 13 12 20 11 15 8

Water flows through a cylindrical pipe , whose inner radius is 1 cm , at the rate of 80 cm /sec in an empty cylindrical tank , the radius of whose base is 40 cm . What is the rise of water level in tank in half an hour ?

Question 6The 21st term of an AP whose first two terms are – 3 and 4, isA) 17B) 137C) 143D) -143

What will be the remainder when 4x4−3x3+2x2−x is divided by x+1?

The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.

Write down the coordinates of two more points on the line through (1, 3) of slope.

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in the figure.

Ravi starts for his school at 8:20 am on his bicycle. If he travels at a speed of 10 km/h then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?

In the given figure, PO ⊥ QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisector of each other.

Question 4 In the given figure, if PQ||ST,∠PQR=110∘ and ∠RST=130∘ find the ∠QRS. [Hint: Draw a line parallel to ST through point R.]

D and E are points on sides AB and AC respectively of ∆ABC such that ar(∆BCD) = ar(∆BCE). Prove that DE || BC.

If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cosθ= _____.

If O is the centre of the given circle and AB = 10 cm, what could be the length of CD?

If x = 2pi/7 Then find the value of tan(x)tan(2x) + tan(2x)tan(4x) + tan(4x)tan(x)

Find the value of cosec 30∘+cot 45∘.

Fill in the blanks to make the statement true:When a number is divided by 8, the result is -3. The number is _______.

Question 1(ii)Do the following pair of linear equations have no solution? Justify your answer.x = 2y and y = 2x

Question 3If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student drawn at random passed the exam?

Question 5Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Write the common difference of an A.P. whose nth term is an = 3n + 7.

Obtain all other zeros of (x3+4x3−2x2−20x−15) if two of its zeros are √5 and −√5.

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B =(a) 35°(b) 65°(c) 75°(d) 85°

If α and β are zeroes of polynomial x square - 6x + a. Find value of "a" if 3α + 2β =20

If sinθ=45 , Find the value of 4tanθ−5cosθsecθ+4cotθ

For every pair of a and b there exist p and r such that a=bq+r give example of a and b satisfying r > b