32581 + Interview Questions in Mathematics Page 33 InterviewSolution

1601.	What is the solution of the pair of linear equations: 2x−3y=2, x+2y=8?
Answer» What is the solution of the pair of linear equations: $2 x - 3 y = 2, x + 2 y = 8$ ?

Discussion

1602.	Is x − 1 a factor of x100 − 1? What about x + 1?
Answer» Is x − 1 a factor of x¹⁰⁰ − 1? What about x + 1?

Discussion

1603.	ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=80∘,∠BAC is 40∘, find ∠BCD.
Answer» ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 80^{\circ}, ∠ B A C$ is $40^{\circ},$ find $∠ B C D$ .

Discussion

1604.	Question 103In a hypothetical sample of 20 people, the amount of money (in Rs thousands) with each was found to be as follows :114, 108, 100, 98, 101, 109, 117, 119, 126, 131,136, 143, 156, 169, 182, 195, 207, 219, 235, 118Draw a histogram of the frequency distribution, taking one of the class intervals as 50-100.
Answer» Question 103 In a hypothetical sample of 20 people, the amount of money (in Rs thousands) with each was found to be as follows : 114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118 Draw a histogram of the frequency distribution, taking one of the class intervals as 50-100.

1604.

Question 103In a hypothetical sample of 20 people, the amount of money (in Rs thousands) with each was found to be as follows :114, 108, 100, 98, 101, 109, 117, 119, 126, 131,136, 143, 156, 169, 182, 195, 207, 219, 235, 118Draw a histogram of the frequency distribution, taking one of the class intervals as 50-100.

Answer»

Question 103

In a hypothetical sample of 20 people, the amount of money (in Rs thousands) with each was found to be as follows :

114, 108, 100, 98, 101, 109, 117, 119, 126, 131,

136, 143, 156, 169, 182, 195, 207, 219, 235, 118

Draw a histogram of the frequency distribution, taking one of the class intervals as 50-100.

Discussion

1605.	A(6, 1), B(8, 2) and C(9, 4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ∆ADE. [CBSE 2015]
Answer» A(6, 1), B(8, 2) and C(9, 4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of $∆ A D E$ . [CBSE 2015]

Discussion

1606.	2^{2x}+2^{x+3}+2^7-2^{x+5}=0 What isThe sum of roots of this equation
Answer» 2^{2x}+2^{x+3}+2^7-2^{x+5}=0 What isThe sum of roots of this equation

Discussion

1607.	If the angle of elevation of a tower from a distance of 100 metres from its foot is 60o, then the height of the tower is
Answer» If the angle of elevation of a tower from a distance of 100 metres from its foot is 60^o, then the height of the tower is

Discussion

1608.	Question 81 The normal body temperature is 98.6∘ F. When Savitri was ill, her temperature rose to 103.1∘ F. How many degrees above normal was that?
Answer» Question 81 The normal body temperature is ${98.6}^{\circ}$ F. When Savitri was ill, her temperature rose to ${103.1}^{\circ}$ F. How many degrees above normal was that?

1608.

Question 81 The normal body temperature is 98.6∘ F. When Savitri was ill, her temperature rose to 103.1∘ F. How many degrees above normal was that?

Answer»

Question 81

The normal body temperature is ${98.6}^{\circ}$ F. When Savitri was ill, her temperature rose to ${103.1}^{\circ}$ F. How many degrees above normal was that?

Discussion

1609.	If (h,k) is the midpoint of (x-y, a - b) and (y-x, b-a), find the value of h+k.
Answer» If (h,k) is the midpoint of (x-y, a - b) and (y-x, b-a), find the value of h+k.

Discussion

1610.	Evaluate ∫(4x+3)√x2+10x+27dx(where C is constant of integration)
Answer» Evaluate $\int (4 x + 3) \sqrt{x^{2} + 10 x + 27} d x$ (where $C$ is constant of integration)

Discussion

1611.	A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.
Answer» A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.

Discussion

1612.	Find the L.C.M. of the following expressions by division method.x3 − 3x2y − 18xy2 + 40y3 and x3 − 4x2y − 11xy2 + 30y3
Answer» Find the L.C.M. of the following expressions by division method. x³ − 3x²y − 18xy² + 40y³ and x³ − 4x²y − 11xy² + 30y³

1612.

Find the L.C.M. of the following expressions by division method.x3 − 3x2y − 18xy2 + 40y3 and x3 − 4x2y − 11xy2 + 30y3

Answer»

Find the L.C.M. of the following expressions by division method.

x³ − 3x²y − 18xy² + 40y³ and x³ − 4x²y − 11xy² + 30y³

Discussion

1613.	An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of two trains.
Answer» An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of two trains.

Discussion

1614.	The value of a22−a13, in the matrix A=⎡⎢⎣120−23432−1⎤⎥⎦, (where aij is the representation of element in the matrix A) is
Answer» The value of $a_{22} - a_{13},$ in the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 0 - 2 & 3 & 4 3 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦,$ $($ where $a_{i j}$ is the representation of element in the matrix $A)$ is

Discussion

1615.	The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A. P.
Answer» The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A. P.

Discussion

1616.	When x3+3x2−mx+4 is divided by x- 2, the remainder is m + 3 find the value of m.
Answer» When $x^{3} + 3 x^{2} - m x + 4$ is divided by x- 2, the remainder is m + 3 find the value of m.

Discussion

1617.	A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Answer» A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

1617.

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

Answer»

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

Discussion

1618.	If A and B are square matrices of the same order and AB = BA = A, then B is called ________ matrix.
Answer» If A and B are square matrices of the same order and AB = BA = A, then B is called ________ matrix.

Discussion

1619.	∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is(a) 7.5 cm(b) 15 cm(c) 22.5 cm(d) 30 cm
Answer» ∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is (a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm

Discussion

1620.	A pair of dice is rolled 5 times. f getting a sum 8 is considered to be success.What is the probability of getting failure?
Answer» A pair of dice is rolled 5 times. f getting a sum 8 is considered to be success.What is the probability of getting failure?

Discussion

1621.	45. What is the ratio of 99/225
Answer» 45. What is the ratio of 99/225

Discussion

1622.	Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22.
Answer» Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22.

Discussion

1623.	In equation y=x2 cos2 2πbita,* gama/t alpha units of x,alpha,beta are m,s^-1,(ms^-1)-1 respectively .the unit of y and gama are
Answer» In equation y=x2 cos2 2πbita,* gama/t alpha units of x,alpha,beta are m,s^-1,(ms^-1)-1 respectively .the unit of y and gama are

Discussion

1624.	The equation 3x−5y=15+3x has
Answer» The equation $3 x - 5 y = 15 + 3 x$ has

Discussion

1625.	The number of cars parked in different parking areas is visually represented as follows:What is the outlier and the mode without outlier of this data?
Answer» The number of cars parked in different parking areas is visually represented as follows: What is the outlier and the mode without outlier of this data?

Discussion

1626.	Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below:What should be dimensions of the rectangles?
Answer» Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below: What should be dimensions of the rectangles?

1626.

Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below:What should be dimensions of the rectangles?

Answer»

Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below:

What should be dimensions of the rectangles?

Discussion

1627.	Examine, whether the following numbers are rational or irrational:(i) 7(ii) 4(iii) 2 + 3(iv) 3 + 2(v) 3 + 5(vi) (2-2)2(vii) (2-2) (2+2) (viii) (2+ 3)2(ix) 5-2(x) 23(xi) 225(xii) 0.3796(xiii) 7.478478(xiv) 1.101001000100001
Answer» Examine, whether the following numbers are rational or irrational: (i) $\sqrt{7}$ (ii) $\sqrt{4}$ (iii) 2 + $\sqrt{3}$ (iv) $\sqrt{3} + \sqrt{2}$ (v) $\sqrt{3} + \sqrt{5}$ (vi) ( $\sqrt{2} - 2)^{2}$ (vii) $(2 - \sqrt{2}) (2 + \sqrt{2})$ (viii) $(\sqrt{2} + \sqrt{3})^{2}$ (ix) $\sqrt{5} - 2$ (x) $\sqrt{23}$ (xi) $\sqrt{225}$ (xii) 0.3796 (xiii) 7.478478 (xiv) 1.101001000100001

Discussion

1628.	108. The line x+y =1 meets the lines represented by the equation y^3+6xy^2 +11x^2y- 6x^3 =0 at the points, P,Q,and R.IF O is the origin, then (OP)^2 +(OQ)^2+ (OR)^{} isequal to
Answer» 108. The line x+y =1 meets the lines represented by the equation y^3+6xy^2 +11x^2y- 6x^3 =0 at the points, P,Q,and R.IF O is the origin, then (OP)^2 +(OQ)^2+ (OR)^{} isequal to

Discussion

1629.	If f(x) is defined in [a, b] where a,b ≥ 0, then find the even extension of f(x).
Answer» If f(x) is defined in [a, b] where a,b $\geq$ 0, then find the even extension of f(x).

Discussion

1630.	In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.
Answer» In the given figure, A, B and C are three points on a circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle other than the arc ABC, find $∠ A D C$ .

Discussion

1631.	Question 1 (ii)Form the pair of linear equations in the following problems, and find their solutions graphically.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 that of one pen.
Answer» Question 1 (ii) Form the pair of linear equations in the following problems, and find their solutions graphically. 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 that of one pen.

Discussion

1632.	The area of the bounded by the curve y = sin x between the ordinates x = 0, x=π2 and the x-axis is _____________.
Answer» The area of the bounded by the curve y = sin x between the ordinates x = 0, $x = \frac{π}{2}$ and the x-axis is _____________.

Discussion

1633.	If A and B are acute angles such that tan A=12, tan B=13 and tan A+B=tan A+tan B1-tan A tan B, find A + B.
Answer» If A and B are acute angles such that $\tan A = \frac{1}{2}, \tan B = \frac{1}{3} and \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$ , find A + B.

Discussion

1634.	Question 86 In the following question, state whether the given statement is true (T) or false (F). The highest common factor of two or more numbers is greater than their lowest common multiple.
Answer» Question 86 In the following question, state whether the given statement is true (T) or false (F). The highest common factor of two or more numbers is greater than their lowest common multiple.

1634.

Question 86 In the following question, state whether the given statement is true (T) or false (F). The highest common factor of two or more numbers is greater than their lowest common multiple.

Answer»

Question 86

In the following question, state whether the given statement is true (T) or false (F).

The highest common factor of two or more numbers is greater than their lowest common multiple.

Discussion

1635.	A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of ₹1008. If she had sold the saree at 10% profit and the sweater at 8% discount , she would have got ₹ 1028 . Find the cost price of the saree and the list price (price before discount) of the sweater.
Answer» A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of ₹1008. If she had sold the saree at 10% profit and the sweater at 8% discount , she would have got ₹ 1028 . Find the cost price of the saree and the list price (price before discount) of the sweater.

Discussion

1636.	Find the HCF of 24, 32 and 36.
Answer» Find the HCF of 24, 32 and 36.

Discussion

1637.	If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part of the cone and the entire cone is:
Answer» If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part of the cone and the entire cone is:

Discussion

1638.	Question 3 (ii)A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.(i) Find the volume of the cone.
Answer» Question 3 (ii) A cloth having an area of $165 m^{2}$ is shaped into the form of a conical tent of radius 5 m. (i) Find the volume of the cone.

Discussion

1639.	Which of the following is a reduced form of the equation (2x−1)2 = x2 + 2?
Answer» Which of the following is a reduced form of the equation $(2 x - 1)^{2}$ = $x^{2}$ + 2?

Discussion

1640.	The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 1023 cm. Then, the diameter of the base of the cylinder = 7 cm.
Answer» The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height $10 \frac{2}{3} c m$ . Then, the diameter of the base of the cylinder = 7 cm.

Discussion

1641.

Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below: Find the mean number of heads per toss No. of heads per toss (x): 0 1 2 3 4 5 No. of tosses (f): 38 144 342 287 164 25

Answer» Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below: Find the mean number of heads per toss

No. of heads per toss (x):	0	1	2	3	4	5
No. of tosses (f):	38	144	342	287	164	25

Discussion

1642.	The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden [Length of rectangle is 20 − (3.5 + 3.5) metres]
Answer» The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden [Length of rectangle is 20 − (3.5 + 3.5) metres]

1642.

The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden [Length of rectangle is 20 − (3.5 + 3.5) metres]

Answer»

The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden [Length of rectangle is 20 − (3.5 + 3.5) metres]

Discussion

1643.	Show that any positive odd integers is of the form 4q+1 or 4q+3 where q is a positive integer.
Answer» Show that any positive odd integers is of the form 4q+1 or 4q+3 where q is a positive integer.

Discussion

1644.	Question 11 Two APs have the same common difference. The first term of one of these is – 1 and that of the other is – 8. The difference between their 4th terms is A) -1 B) -8 C) 7 D) -9
Answer» Question 11 Two APs have the same common difference. The first term of one of these is – 1 and that of the other is – 8. The difference between their $4^{t h}$ terms is A) -1 B) -8 C) 7 D) -9

Discussion

1645.	If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = ______ and EF = _______.
Answer» If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = ______ and EF = _______.

Discussion

1646.	Which of the following relation would hold true for the sides of the similar triangles in the given diagram?
Answer» Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

1646.

Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

Answer»

Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

Discussion

1647.	In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is
Answer» In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

1647.

In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

Answer»

In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

Discussion

1648.	The line 4x + 3y – 12 = 0 cuts the coordinate axes at A and B. The area of ΔOAB is _________.
Answer» The line 4x + 3y – 12 = 0 cuts the coordinate axes at A and B. The area of ΔOAB is _________.

Discussion

1649.	Find the common difference for the arithmetic progression 3+2√2, 3+4√2, 3+6√2, 3+8√2
Answer» Find the common difference for the arithmetic progression $3 + 2 \sqrt{2}, 3 + 4 \sqrt{2}, 3 + 6 \sqrt{2}, 3 + 8 \sqrt{2}$

Discussion

1650.

In and A.PA. (a) If a = 11, d = 2, n = 10 find T10 and S10(b) If a = 12, d = 3, Tn = 84 find n(c) If d = 4 and T35 = 123 find a(d) If a = 3 and T20 = 60 find dB. (i) How many terms are there in A.P. 4, −1, −6, ………, (−106)(ii) Test whether 25 is a term of the A.P. 3, 6, 9, 12, 15, …….(iii) Test whether 36 is a term of the A.P. 4, 8, 12, 16, …….

Answer»

In and A.P

A. (a) If a = 11, d = 2, n = 10 find T₁₀ and S₁₀

(b) If a = 12, d = 3, T_n = 84 find n

(c) If d = 4 and T₃₅ = 123 find a

(d) If a = 3 and T₂₀ = 60 find d

B. (i) How many terms are there in A.P. 4, −1, −6, ………, (−106)

(ii) Test whether 25 is a term of the A.P. 3, 6, 9, 12, 15, …….

(iii) Test whether 36 is a term of the A.P. 4, 8, 12, 16, …….

Discussion

Explore topic-wise InterviewSolutions in .

What is the solution of the pair of linear equations: 2x−3y=2, x+2y=8?

Is x − 1 a factor of x100 − 1? What about x + 1?

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=80∘,∠BAC is 40∘, find ∠BCD.

A(6, 1), B(8, 2) and C(9, 4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ∆ADE. [CBSE 2015]

2^{2x}+2^{x+3}+2^7-2^{x+5}=0 What isThe sum of roots of this equation

If the angle of elevation of a tower from a distance of 100 metres from its foot is 60o, then the height of the tower is

Question 81 The normal body temperature is 98.6∘ F. When Savitri was ill, her temperature rose to 103.1∘ F. How many degrees above normal was that?

If (h,k) is the midpoint of (x-y, a - b) and (y-x, b-a), find the value of h+k.

Evaluate ∫(4x+3)√x2+10x+27dx(where C is constant of integration)

A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.

Find the L.C.M. of the following expressions by division method.x3 − 3x2y − 18xy2 + 40y3 and x3 − 4x2y − 11xy2 + 30y3

The value of a22−a13, in the matrix A=⎡⎢⎣120−23432−1⎤⎥⎦, (where aij is the representation of element in the matrix A) is

The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A. P.

When x3+3x2−mx+4 is divided by x- 2, the remainder is m + 3 find the value of m.

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

If A and B are square matrices of the same order and AB = BA = A, then B is called ________ matrix.

∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is(a) 7.5 cm(b) 15 cm(c) 22.5 cm(d) 30 cm

A pair of dice is rolled 5 times. f getting a sum 8 is considered to be success.What is the probability of getting failure?

45. What is the ratio of 99/225

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22.

In equation y=x2 cos2 2πbita,* gama/t alpha units of x,alpha,beta are m,s^-1,(ms^-1)-1 respectively .the unit of y and gama are

The equation 3x−5y=15+3x has

The number of cars parked in different parking areas is visually represented as follows:What is the outlier and the mode without outlier of this data?

Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below:What should be dimensions of the rectangles?

Examine, whether the following numbers are rational or irrational:(i) 7(ii) 4(iii) 2 + 3(iv) 3 + 2(v) 3 + 5(vi) (2-2)2(vii) (2-2) (2+2) (viii) (2+ 3)2(ix) 5-2(x) 23(xi) 225(xii) 0.3796(xiii) 7.478478(xiv) 1.101001000100001

108. The line x+y =1 meets the lines represented by the equation y^3+6xy^2 +11x^2y- 6x^3 =0 at the points, P,Q,and R.IF O is the origin, then (OP)^2 +(OQ)^2+ (OR)^{} isequal to

If f(x) is defined in [a, b] where a,b ≥ 0, then find the even extension of f(x).

In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.

Question 1 (ii)Form the pair of linear equations in the following problems, and find their solutions graphically.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 that of one pen.

​The area of the bounded by the curve y = sin x between the ordinates x = 0, x=π2 and the x-axis is _____________.

If A and B are acute angles such that tan A=12, tan B=13 and tan A+B=tan A+tan B1-tan A tan B, find A + B.

Question 86 In the following question, state whether the given statement is true (T) or false (F). The highest common factor of two or more numbers is greater than their lowest common multiple.

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of ₹1008. If she had sold the saree at 10% profit and the sweater at 8% discount , she would have got ₹ 1028 . Find the cost price of the saree and the list price (price before discount) of the sweater.

Find the HCF of 24, 32 and 36.

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part of the cone and the entire cone is:

Question 3 (ii)A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.(i) Find the volume of the cone.

Which of the following is a reduced form of the equation (2x−1)2 = x2 + 2?

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 1023 cm. Then, the diameter of the base of the cylinder = 7 cm.

The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden [Length of rectangle is 20 − (3.5 + 3.5) metres]

Show that any positive odd integers is of the form 4q+1 or 4q+3 where q is a positive integer.

Question 11 Two APs have the same common difference. The first term of one of these is – 1 and that of the other is – 8. The difference between their 4th terms is A) -1 B) -8 C) 7 D) -9

If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = ______ and EF = _______.

Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

The line 4x + 3y – 12 = 0 cuts the coordinate axes at A and B. The area of ΔOAB is _________.

Find the common difference for the arithmetic progression 3+2√2, 3+4√2, 3+6√2, 3+8√2

The area of the bounded by the curve y = sin x between the ordinates x = 0, x=π2 and the x-axis is _____________.

If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = and EF = _.