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7601.

The bisects of exterior angle at B and C of ΔABC meet at O. If ∠A = x°, then ∠BOC =(a) 90°+x°2(b) 90°-x°2(c) 180°+x°2(d) 180°-x°2

Answer» The bisects of exterior angle at B and C of ΔABC meet at O. If ∠A = x°, then ∠BOC =



(a) 90°+x°2



(b) 90°-x°2



(c) 180°+x°2



(d) 180°-x°2
7602.

What is the collective term for aces, jacks, queens and kings in cards? __

Answer»

What is the collective term for aces, jacks, queens and kings in cards?


__
7603.

88.A sector of a circle of radius R metres is bounded by an Arc A and by two radii OA and OB at an angle beeta radian given that the perimeter of the sector is 18m and that the area of a sector is 8 m square calculate the numerical values of R and beeta

Answer» 88.A sector of a circle of radius R metres is bounded by an Arc A and by two radii OA and OB at an angle beeta radian given that the perimeter of the sector is 18m and that the area of a sector is 8 m square calculate the numerical values of R and beeta
7604.

Prove the theorem of intersecting chords.

Answer» Prove the theorem of intersecting chords.
7605.

State whether the following statements are true or false. Justify your answers.(i) Every irrational number is a real number.(ii) Every point on the number line is of the form √m, where ′m′ is a natural number.(iii) Every real number is an irrational number.

Answer»

State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

(ii) Every point on the number line is of the form m, where m is a natural number.

(iii) Every real number is an irrational number.

7606.

Circumference of the base of a cylinder open at the top is 132cm. The sum of the radius and slant height of the cylinder is 41cm. Find the cost of polishing the outer surface of cylinder at the rate of ₹400 per m​​​​​​2.

Answer» Circumference of the base of a cylinder open at the top is 132cm. The sum of the radius and slant height of the cylinder is 41cm. Find the cost of polishing the outer surface of cylinder at the rate of ₹400 per m​​​​​​2.
7607.

The number of dimensions of a surface are(a) 1(b) 2(c) 3(d) 0

Answer» The number of dimensions of a surface are

(a) 1

(b) 2

(c) 3

(d) 0
7608.

Question 13Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1, how many such lines can we find?

Answer» Question 13

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1, how many such lines can we find?
7609.

Question 12Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.

Answer» Question 12

Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
7610.

Question 4In the figure, BD and CE intersect each other at the point P. Is ΔPBC∼ΔPDE? Why?

Answer» Question 4

In the figure, BD and CE intersect each other at the point P. Is ΔPBCΔPDE? Why?






7611.

Question 1 (v)Classify 2π as rational or irrational.

Answer»

Question 1 (v)

Classify 2π as rational or irrational.





7612.

Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45∘. Also, find the circumradius of the triangle measures.

Answer» Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45. Also, find the circumradius of the triangle measures.
7613.

Question 73Fill in the blanks to make the statements true.If all sides of a quadrilateral are equal, it is a .

Answer» Question 73

Fill in the blanks to make the statements true.




If all sides of a quadrilateral are equal, it is a .
7614.

Question 8In the figure, l∥m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points of l and m, respectively.

Answer» Question 8

In the figure, lm and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points of l and m, respectively.


7615.

Locate the position of the ball lying on the given number line.

Answer»

Locate the position of the ball lying on the given number line.






7616.

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Answer» There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.




7617.

In the given figure, seg AB≅ seg CB and seg AD≅ seg CD. Prove that △ABD≅△CBD.

Answer» In the given figure, seg AB seg CB and seg AD seg CD. Prove that ABDCBD.


7618.

In the given figure, line AB || line CD and line PQ is transversal. Measure of one of the angles is given. Hence find the measures of the following angles. (i) ∠ART(ii) ∠CTQ(iii) ∠DTQ(iv) ∠PRB

Answer»


In the given figure, line AB || line CD and line PQ is transversal. Measure of one of the angles is given. Hence find the measures of the following angles.





(i) ∠ART


(ii) ∠CTQ


(iii) ∠DTQ

(iv) ∠PRB





7619.

In the given figure PQ || BC, ∠4 = ∠5 and QB bisects ∠PQC. Find ∠1. 60

Answer» In the given figure PQ || BC, 4 = 5 and QB bisects PQC. Find 1.

  1. 60
7620.

Question 10Rationalize the denominator of the following(i)23√3(ii)√40√3(iii)3+√24√2(iv)16√41−5(v)2+√32−√3(vi)√6√2+√3(vii)√3+√2√3−√2(viii)3√5+√3√5−√3(ix)4√3+5√2√48+√18Thinking processFor rationalizing the denominator multiplying numerator by the conjugate of the denominator term and simplify it to get the result.

Answer» Question 10

Rationalize the denominator of the following

(i)233(ii)403(iii)3+242(iv)16415(v)2+323(vi)62+3(vii)3+232

(viii)35+353

(ix)43+5248+18

Thinking process

For rationalizing the denominator multiplying numerator by the conjugate of the denominator term and simplify it to get the result.


7621.

The population of Delhi State in different census years is as given below: Census year 1961 1971 1981 1991 2001 Population in Lakhs 30 55 70 110 150

Answer»

The population of Delhi State in different census years is as given below:





















Census year 1961 1971 1981 1991 2001
Population in Lakhs 30 55 70 110 150
7622.

The two lines represented by the equations: 6x - 3y + 10 = 0 and 2x - y + 9 = 0, are _______.

Answer»

The two lines represented by the equations: 6x - 3y + 10 = 0 and 2x - y + 9 = 0, are _______.



7623.

What are the derivations for the formula of mode and median in statistics?

Answer» What are the derivations for the formula of mode and median in statistics?
7624.

Question 20 The mean of 25 observation is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is: A) 23 B) 36 C) 38 D) ​​​​​​​40

Answer» Question 20
The mean of 25 observation is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is:

A) 23
B) 36
C) 38
D) ​​​​​​​40
7625.

The hypotenuse of a right angled triangle is 3.5 metres long and another of its sides is 2.5 metres long.Calculate its perimeter correct to centimetres.

Answer»

The hypotenuse of a right angled triangle is 3.5 metres long and another of its sides is 2.5 metres long.



Calculate its perimeter correct to centimetres.





7626.

Prove the following identities (1-16)1+cot x+tan x sin x-cos xsec3 x-cosec3 x=sin2 x cos2 x

Answer» Prove the following identities (1-16)



1+cot x+tan x sin x-cos xsec3 x-cosec3 x=sin2 x cos2 x
7627.

If the point C(− 2, 3) is equidistant from the points A(3, − 1) and B(x, 8), find the value of x. Also, find the distance BC.

Answer» If the point C(− 2, 3) is equidistant from the points A(3, − 1) and B(x, 8), find the value of x. Also, find the distance BC.
7628.

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.

Answer»

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.



7629.

The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is(a) 60°(b) 75°(c) 120°(d) 150°

Answer» The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is



(a) 60°



(b) 75°



(c) 120°



(d) 150°
7630.

Factorise:40 + 3x – x2

Answer» Factorise:

40 + 3x – x2
7631.

Question 6 In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.

Answer» Question 6
In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.

7632.

Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4cm. Find the length of the common chord

Answer» Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4cm. Find the length of the common chord
7633.

Choose the correct statements.

Answer»

Choose the correct statements.


7634.

If a particular number system having base B, such that(√21)B=(3)10Then the value of B is _____4

Answer» If a particular number system having base B, such that

(21)B=(3)10

Then the value of B is _____
  1. 4
7635.

A cylindrical pillar is 50cm in diameter and 3.5m in height. Find the coat of painting the curved surface of the pillar at the rate of ₹12.50 per m×m.

Answer» A cylindrical pillar is 50cm in diameter and 3.5m in height. Find the coat of painting the curved surface of the pillar at the rate of ₹12.50 per m×m.
7636.

Classify the following numbers as rational or irrational (i) √23 (ii) √225(iii) 0.3796

Answer» Classify the following numbers as rational or irrational

(i) 23

(ii) 225

(iii) 0.3796
7637.

Question 185In the following figure, AB∥DC and AD=BC. Find the value of x.

Answer» Question 185

In the following figure, ABDC and AD=BC. Find the value of x.


7638.

A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is(a) 1 : 1(b) 1 : 2(c) 2 : 1(d) 1 : 3

Answer» A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is



(a) 1 : 1



(b) 1 : 2



(c) 2 : 1



(d) 1 : 3
7639.

If ABCD (in order) is a quadrilateral inscribed in a circle, then which of the following is/are always true?

Answer»

If ABCD (in order) is a quadrilateral inscribed in a circle, then which of the following is/are always true?

7640.

Marks obtained by 5 students in a class test out of 25 are 12, 15, 12, 20 and 17 respectively. Find the mode of the given number of observations.

Answer»

Marks obtained by 5 students in a class test out of 25 are 12, 15, 12, 20 and 17 respectively. Find the mode of the given number of observations.



7641.

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is the diagonal. Show that(i) SR || AC and SR=12AC(ii) PQ = SR(iii) PQRS is a parallelogram.

Answer» ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is the diagonal. Show that

(i) SR || AC and SR=12AC

(ii) PQ = SR

(iii) PQRS is a parallelogram.


7642.

In the adjoining figure, AD and BE are the medians of ΔABC and DF || BE. Show that CF=14AC.

Answer»

In the adjoining figure, AD and BE are the medians of ΔABC and DF || BE. Show that CF=14AC.

7643.

What should be the generic form of the following equation? (5x+y)7=2

Answer»

What should be the generic form of the following equation?
(5x+y)7=2

7644.

The diameters of two cones are equal. If their slant heights are in the ratio 3:4, then find the ratio of their curved surface areas.

Answer»

The diameters of two cones are equal. If their slant heights are in the ratio 3:4, then find the ratio of their curved surface areas.



7645.

Prove that root 2 is an irrational number

Answer» Prove that root 2 is an irrational number
7646.

In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ADC=120∘ then ∠BAC=? (a) 60∘ (b) 30∘ (c) 20∘ (d) 45∘

Answer»

In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ADC=120 then BAC=?

(a) 60

(b) 30

(c) 20

(d) 45

7647.

What's the cost of painting a box which is in the shape of a cuboid of dimensions 3 m×4 m×5 m at a rate of ₹ 5/m2?

Answer»

What's the cost of painting a box which is in the shape of a cuboid of dimensions 3 m×4 m×5 m at a rate of 5/m2?

7648.

Tap on the option that completes the given pattern.

Answer»

Tap on the option that completes the given pattern.


7649.

How are the following dealt with while preparing the final accounts for the year ended 31st , 2019? RECEIPTS AND PAYMENTS ACCOUNT (AN EXTRACT) for the year ended 31st March, 2019 Dr. Cr. Receipts ₹ Payments ₹ By Payments for Sports Material 1,40,000 BALANCE SHEET (AN EXTRACT) as at 1st April, 2018 Liabilities ₹ Assets ₹ Creditors for Sports Materials 6,000 Sports Materials 8,000 Additional information :Sports Materials in Hand on 31st March, 2019 – ₹ 22,000.

Answer» How are the following dealt with while preparing the final accounts for the year ended 31st , 2019?











































RECEIPTS AND PAYMENTS ACCOUNT (AN EXTRACT)

for the year ended 31st March, 2019
Dr. Cr.
Receipts Payments




By Payments for Sports Material 1,40,000



















































BALANCE SHEET (AN EXTRACT)

as at 1st April, 2018

Liabilities


Assets






Creditors for Sports Materials 6,000 Sports Materials 8,000



Additional information :

Sports Materials in Hand on 31st March, 2019 – ₹ 22,000.
7650.

If two isosceles triangles have a common base, then prove that the line joining their vertices bisects them at right angles.

Answer» If two isosceles triangles have a common base, then prove that the line joining their vertices bisects them at right angles.