Inspiring Math

Book Title Inspiring Math

Language English

Section Science

Source RKMHOS

Author/Editor Vivek Sanjivani

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	, a) , b) , c) $\frac{1}{2}\left\{\frac{\sin {8x}}{8}+\frac{\sin {x}}{2}\right\}+c$ , d) $\left\{\frac{\sin {8x}}{8}+\frac{\sin {2x}}{2}\right\}+c$

https://youtu.be/fcTxW3PSAfE?si=zx9JBl-Nc-f0BW-t

Foot Note:

11

$\int {\frac{dx}{{x}^{2}+8x+20}}$ ,

(a) $\frac{1}{2}{\tan }^{-1}{\left(\frac{x-4}{2}\right)+c}$ , (b) $\frac{1}{2}{\tan }^{-1}{\left(\frac{x+4}{2}\right)+c}$ ,

(c) ${\tan }^{-1}{\left(\frac{x+4}{2}\right)+c}$ , (d) $\frac{1}{2}{\tan }^{-1}{\left(\frac{x+2}{2}\right)+c}$

12

$\int {\frac{dx}{\sqrt{15-8{x}^{2}}}}$

a) ,

b), c)

, d) $\frac{1}{2\sqrt{2}}{\sin }^{-1}{(\frac{\sqrt{2}x}{\sqrt{15}})}+c$

MATHEMATICS (Basic) CLASS IX

CHAPTER: LINES, ANGLES AND TRIANGLES MM: 25

S.NO

MCQ

ANSWERS

TYPE OF QUESTION

1

If the difference between any two supplementary angles is equal to one right angle, then find the angles.

(a)	60° (b) 45°
(c)	30° (d) None of these.

45°

U

2

In the figure,

POR and

QOR form a linear pair. If a - b = 80°, find the values of a and b.

(a) a= 130, b=60 (b) a=130, b= 40 (c) a=140, b= 40 (d) a= 130, b=50

a= 130, b=50

A

3

An angle is 14° less than the sum of a right and a straight angle. What is this angle called

a	A straight angle	b	An obtuse angle
c	An acute angle	d	A reflex angle

A reflex angle

K

4

An angle is 20° more than its complement. Find the angle

(a) 45° (b) 35° (c) 55° (d) 60°

55°

U

5

In

ABC, if 3

A = 2

B = 6

C, find out

B.

(a) 90° (b) 60° (c) 40° (d) 30°

90°

A

6

The base BC of triangle ABC is produced both ways and the measure of the exterior angles formed are 94° and 126° then <BAC is equal to

(a) 94° (b) 54° (c) 40° (d) 44°

40°

U

7

The sum of two angles of a triangle is 116° and the difference is 24°. Find the measure of each angle.

(a) 80° ,36° (b) 50° ,56° (c) 50° ,66° (d) 70° ,46°

70° ,46°

A

8

If a transversal cuts two parallel lines, the bisectors of the interior angles form a

(a) Trapezium (b) kite (c) rectangle (d) none of them

rectangle

K

9

If two lines are parallel and one of the alternate interior angles is 30° more than one-third of a right angle, then the value of the other alternate interior angle is:

(a) 45° (b) 30° (c) 90° (d) 60°

60°

K

10

If the angles formed on a line are 5y, 2y and 3y, then find out the value of y.

(a) 28° (b) 20° (c) 36° (d) 18°

18°

U

11

ABC is right angled at B. If BD

AC and

DBA = 40°, then find out the value of

DCB from the figure given below:

(a) 40° (b) 30° (c) 50° (d) 60°

40°

A

12

Find out the value a and b, if a:b = 2:3.

(a) a = 54° and b = 36° (b) a = 18° and b = 82°

(c ) a = 36° and b = 54° (d) a = 54° and b = 54°

a = 36° and b = 54°

A

13

If a point F lies between two points D and E such that DF = FE, then:

1.

DF = 2 DE

2.

DF

DE

3

DF = DE

4

DF =

DE

DF =

DE

K

14

If

PQS = 115°, then the value of

PQR is:

a	60°	b	70°
c	110°	d	65°

60°

A

15

If

PYZ = 2x +3 and x = 70°, then find out the value of

ZYX.

a	37°	b	143°
c	57°	d	140°

37°

K

16

In the figure, if

XYZ = 54° and ray YQ bisects

XYZ, then find out the value of

PYQ.

a	126°	b	63°
c	54°	d	53°

63°

A

17

In

ABD, AC bisects

BAD,

ABC = 50° and

ADE = 120°. Find out the value of

ACB.

a	70°	b	75°
c	35°	d	95°

95°

A

18

Lines PQ and RS intersect each other at point O. If

POR:

ROQ = 5:7, then find out the

POR.

a	65°	b	45°
c	85°	d	75°

75°

U

19

The angles of a triangle are arranged in ascending order of magnitude . if the difference between two consecutive angles is 10°, the largest angle is

a	50°	b	60°
c	70°	d	80°

70°

A

20

Side BC of triangle ABC has been produced to a point D such that <ACD=120° . if <B is half of <A then the value of <A is:

a	80°	b	75°
c	60°	d	90°

80°

K

21

Find out the complement of two-fifth of a right angle.

a	36°	b	54°
c	43°	d	47°

54°

U

22

Find out the supplement of (115 - x)°.

a	(115 + x)°	b	(115 - x)°
c	(65 + x)°	d	(65 - x)°

(65 + x)°

K

23

Find out

DEB from the figure given below, if AC || DB.

a	25°	b	85°
c	95°	d	45°

95°

A

24

If AB || CD and the ratio of values of

1 and

2 is 4:5, find out the value of

1.

a	50°	b	30°
c	90°	d	80°

80°

A

25

If one angle of a triangle is equal to the sum of other two angles then the triangle is .

a

Isosceles triangle

b

Obtuse triangle

c

Equilateral triangle

d

Isosceles right

Triangle.

Isosceles right triangle.

U

Types of questions: K= Knowledge-based, U=Understanding-based, A=Application-based

5	$\int {\frac{dx}{\sqrt{7-6x-{x}^{2}}} }$ , a) ${\sin }^{-1}{\left(\frac{x-3}{4}\right)}+c$ , b) ${\sin }^{-1}{\left(\frac{x+3}{4}\right)}+c$ , c) $\sin {(\frac{x+3}{4})}+c$ , d) $\cos {(\frac{x+3}{4})}+c$
6	$\int {\frac{\sin {(2{\tan }^{-1}{x)}}}{1+{x}^{2}}dx}$ , a) $\frac{1}{2}\left(\frac{1-{x}^{2}}{1+{x}^{2}}\right)+c$ , b) $-\frac{1}{2}\left(\frac{1+{x}^{2}}{1+{x}^{2}}\right)+c,$ c) $-\frac{1}{2}\left(\frac{1+{x}^{2}}{1+{x}^{2}}\right)+c,$ d) $-\frac{1}{2}\left(\frac{1-{x}^{2}}{1+{x}^{2}}\right)+c$
7	$\int {\frac{dx}{\sqrt{8+2x-{x}^{2}}}}$ , a) ${\sin }^{-1}{\left(\frac{x-1}{3}\right)+c}$ , b) ${\sin }^{-1}{\left(\frac{x+1}{3}\right)+c}$ , c) ${\sin }^{-1}{\left(\frac{x-3}{1}\right)+c},$ d) ${\sin }^{-1}{\left(x-1\right)+c}$
8	$\int {{e}^{ax}\sin {bx}dx},$ a) $\frac{{e}^{ax}}{{a}^{2}-{b}^{2}}\left(\mathrm{asin}{bx}-b\cos {bx}\right)+c$ , b) $\frac{{e}^{ax}}{{a}^{2}+{b}^{2}}\left(\mathrm{asin}{bx}-b\cos {bx}\right)+c$ , c) $\frac{{e}^{ax}}{{a}^{2}+{b}^{2}}\left(\mathrm{asin}{bx}+\cos {bx}\right)+c$ d) $\frac{{e}^{ax}}{{a}^{2}+{b}^{2}}\left(\mathrm{asin}{ax}-b\cos {bx}\right)+c$
9	$\int {\frac{dx}{\sqrt{x+1}+\sqrt{x+2}}}$ , a) $\frac{2}{3}\left[{\left(x-2\right)}^{\frac{3}{2}}+{\left(x+1\right)}^{\frac{3}{2}}\right]+c$ , b) $\frac{2}{3}\left[{\left(x+2\right)}^{\frac{2}{3}}-{\left(x+1\right)}^{\frac{3}{2}}\right]+c$ , c) $\frac{2}{3}\left[{\left(x+2\right)}^{\frac{3}{2}}-{\left(x+1\right)}^{\frac{2}{3}}\right]+c$ , d) $\frac{2}{3}\left[{\left(x+2\right)}^{\frac{3}{2}}-{\left(x+1\right)}^{\frac{3}{2}}\right]+c$
10	$\int {\frac{\left(x+1\right){\left(x+\log {x}\right)}^{2}}{x}}dx$ , a) $\frac{{\left(x+\log {x}\right)}^{3}}{3}+c$ , b) $\frac{{\left(x-\log {x}\right)}^{3}}{3}+c$ , c) $\frac{{\left(x+\log {x}\right)}^{3}}{2}+c$ , d) $\frac{{\left({x}^{2}+\log {x}\right)}^{3}}{3}+c$

Foot Note:

Answers:

(b)

(d)

(a)

(b)

(d)

(a)

'श्रीरामकृष्ण' नाम का आरम्भ

यह स्वाभाविक जिज्ञासा उत्पन्न होती है कि गदाधर को 'श्रीरामकृष्ण' नाम से कब एवं कैसे जाना जाने लगा। गदाधर की वंशावली से ज्ञात होता है कि उनके पिता का नाम क्षुदिराम था, तथा उनके चाचा निधिराम एवं कनाईराम थे। उनके दो अग्रजों के नाम रामकुमार एवं रामेश्वर थे। यह विशेष रूप से उल्लेखनीय है कि परिवार के लगभग प्रत्येक पुरुष सदस्य के नाम में 'राम' शब्द का प्रयोग हुआ है। अतः यह सम्भावना प्रबल है कि ‘रामकृष्ण’ नाम गदाधर को उनके परिवार द्वारा ही दिया गया था।

बाएँ– कामारपुकुर में रघुवीर मन्दिर; दाएँ– उनका पारिवारिक निवास (वर्तमान दृश्य)

श्रीरामकृष्ण वचनामृत के प्रारम्भ में, श्री महेन्द्रनाथ गुप्त (श्रीम) ने दक्षिणेश्वर मंदिर की लेखा-पुस्तिका (वर्ष 1858) के एक पृष्ठ की पुनर्प्रस्तुति की है। उस पृष्ठ पर श्रीश्री राधाकान्त मंदिर के पुजारी का नाम “श्रीरामकृष्ण भट्टाचार्य” लिखा हुआ मिलता है।¹ यह उल्लेखनीय है कि उस समय पुजारियों को “भट्टाचार्य” की उपाधि दी जाती थी। अतः यह विश्वसनीय है कि गदाधर दक्षिणेश्वर आगमन से पूर्व ही 'रामकृष्ण' नाम से जाने जाते थे, यद्यपि इस नाम का प्रचलन सीमित था।¹

Foot Note:

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