tag:blogger.com,1999:blog-20809010301270732402024-03-13T11:05:58.717-07:00MathematicsPanini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2080901030127073240.post-18974783173670398702020-05-09T07:01:00.001-07:002020-05-09T07:01:42.142-07:00Class 9th Chapter-1(Number System, Sankhya paddhati[in Hindi]) Ex 1.6 I ...<iframe allowfullscreen="" frameborder="0" height="270" src="https://www.youtube.com/embed/W6EkRBRI8ro" width="480"></iframe>Panini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.com0tag:blogger.com,1999:blog-2080901030127073240.post-3012574774747165312015-08-04T04:36:00.000-07:002015-08-04T04:36:44.451-07:00Basic Mathematics<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: left;">
<span style="color: #0b5394; font-size: small;">Basic Mathematics</span></h2>
Q-1 Angle always measure in --------<br />
(a) Radian (b) Steradion<br />
(c) A&B (d) None<br />
<br />
Q-2 1 right angle = -----------<br />
(a) 400 grade (b) 100 grade<br />
(c) 300 grade (d)) None<br />
<br />
Q-3 1 rad= --------<br />
(a) 56×570 (b) 57×270<br />
(c) 630 (d) None<br />
<br />
Q-4 1min= ----------<br />
(a) 60² (b) 70²<br />
(c) 80² (d) None<br />
<br />
Q-5 Cot (900-f)=?<br />
(a) Sec f (b) Tan f<br />
(c) Cot f (d) None<br />
<br />
Q-6 Cot (1800-f) = -x , find x<br />
(a) Cot f (b) Secf<br />
(c) Tan f (d) None<br />
<br />
Q-7 In 1st quadrant all T- ratio are<br />
(a) + ive (b) -ive<br />
(c) 0 (d) None<br />
<br />
Q-8 Sec f = 1/?<br />
(a) Cos f (b) Sec f<br />
(c) Tan f (d) None<br />
<br />
Q-9 In θ = l/r , l and r are<br />
(a) Arc and radius (b) Arcs<br />
(c) Ratio (d) None<br />
<br />
Q-10 (Newton)0 = ?<br />
(a) Newton (b) 1<br />
(c) 2 (d) None<br />
<br />
Q-11 log¥1=?<br />
(a) 0 (b) 1 (c) 3 (d) None<br />
<br />
Q-12 Sin 1200=?<br />
(a) Ö5/2 (b) Ö3/2 (c) 2 (d) None<br />
<br />
Q-13 Tan 900/Cot 900<br />
(a) ¥ (b) 0 (c) 2¥ (d) None<br />
<br />
Q-14 2×718 is value of -------<br />
(a) 2e (b) e (c) 8e (d) None<br />
<br />
Q-15 If base of log is e then it is<br />
(a) Neperian log (b) Common log<br />
(c) A & B (d) None<br />
<br />
Q-16 log 1050 is<br />
(a) Natural logarithm (b) Common logarithm<br />
(c) A & B (d) None<br />
<br />
Q-17 log (14×7) = log 7×log ……..<br />
(a) 7 (b) 14<br />
(c) 8 (d) 9<br />
<br />
Q-18 In 1975 characteristic is …..<br />
(a) 3 (b) 2<br />
(c) 4 (d) 8<br />
<br />
Q-19 Log7=?<br />
(a) 1×567 (b) 0×8451<br />
(c) 2×871 (d) 4×8451<br />
<br />
Q-20 Antilog 0 would be….<br />
(a) 1 (b) 2<br />
(c) 3 (d) 9<br />
<br />
Q-21 7, 70,700 have mantissa….<br />
(a) 0 (b) 1<br />
(c) 2 (d) 3<br />
<br />
Q-22 d/dx(x15)<br />
(a) 15x143 (b) 15x14<br />
(c) 15x (d) None<br />
<br />
Q-23 By d/dt we mean that<br />
(a) Diff. w. r t t (b) Diff w.r.t x<br />
(c) Diff. w. r. t h (d) None<br />
<br />
Q-24 d/dx (Cosx) = ……..<br />
(a) -Sin x (b) Cos x<br />
(c) Tanx (d) None<br />
<br />
Q-25 d/dx (2009) = ?<br />
(a) 0 (b) 2<br />
(c) 8 (d) 9 <br />
<br />
<br />
<br />
<h3 style="text-align: left;">
<span style="color: #0b5394; font-size: small;">ANSWER and REASONS:-</span></h3>
<br />
1 (a) Radian <br />
2 (b) 100 grade<br />
3 (a) 56×570<br />
4 (a) 60²<br />
5 (b) Tan f<br />
6 (a) Cot f <br />
7 (a) +ive<br />
8 (a) Cos f<br />
9 (a) Arc and radius<br />
10 (b) 1<br />
11 (a) 0 = Log 1 =0<br />
12 (b) Ö3/2<br />
13 (a) ¥ <br />
14 (b) e<br />
15 (a) Neperian log<br />
16 (b) Common logarithm<br />
17 (b) 14<br />
18 (a) 3 =4-1=3<br />
19 (b) 0×8451<br />
20 (a) 1<br />
21 (a) 0<br />
22 (b) 15x14<br />
23 (a) Diff. w. r .t t<br />
24 (a) -Sin x <br />
25 (a) 0</div>
Panini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.com0Nangal, Punjab, India31.36999999999999 76.3831.315776499999991 76.299319 31.424223499999989 76.460681tag:blogger.com,1999:blog-2080901030127073240.post-34537377103153063242015-04-23T06:07:00.000-07:002015-04-23T06:07:41.558-07:00Mathematics 4<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: left;">
<strong><span style="color: #0b5394; font-size: small;">Mathematics </span></strong></h2>
Q-1 If A is a rectangular matrix of order 3 × 4, then rank of a matrix is<br />
(a) Less than equal to 3<br />
(b) > 3<br />
(c) 4<br />
(d) None<br />
<br />
Q-2 If characteristics eq. of a matrix of order 3 × 3 is cubic and it have different three root, then the minimal eq. will be of degree.<br />
(a) 2<br />
(b) 3<br />
(c) 4<br />
(d) 1<br />
<br />
Q-3 In A3 – 7I = 0, Here we use I with 7, what is the reason behind it.<br />
(a) To make it matrix<br />
(b) To make it equal to A2<br />
(c) To make it equal to A3<br />
(d) None<br />
<br />
Q-4 If in a Square Matrix, a row is zero, then it is<br />
(a) Singular matrix<br />
(b) Non singular matrix<br />
(c) Hermition<br />
(d) None<br />
<br />
Q-5 If a matrix of order 3 have three non zero row, then ranks of A is<br />
(a) 2<br />
(b) 3<br />
(c) 4<br />
(d) 9<br />
<br />
Q-6 What is the condition for the matrix to be Involuntary ?<br />
(a) A3 = I<br />
(b) A2 = I<br />
(c) A = I<br />
(d) None<br />
<br />
Q-7 For upper triangular matrix<br />
(a)aij = 0, i = j<br />
(b) aij, i>j<br />
(c) aij = 0, i<j 1="?" li="0," x="y" z="z"> no. of variable<br />(c) a and b<br />(d) None</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-20 2x + 6y = 0 have<br />(a) Unique solution<br />(b) Infinite many solution<br />(c) No solution<br />(d) None</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-21 If A2 = A, then it is<br />(a) Idempotent matrix<br />(b) Nilpotent matrix<br />(c) Involuntary matrix<br />(d) None</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-22 (A + B)1 =?<br />(a) A1 – B1<br />(b) B1 – A1<br />(c) A1 + B1<br />(d) (B1)1</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-23 If 2, 3, 4 are eigen value of A, then eigen value of A2 is<br />(a) (4, 9, 6)<br />(b) 4, 9, 16<br />(c) 5, 9, 16<br />(d) None</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-24 If the upper triangular matrix have diagonal elements 2, 4, 8 then eigen value of this upper triangular matrix is<br />(a) 2, 4, 8<br />(b) 2, 4, 6<br />(c) 7, 5, 6<br />(d) 9, 10, 4</j><br />
<j 1="?" li="0," x="y" z="z"><br />Q-25 If A is matrix of order 5 then its rank is<br />(a) 4<br />(b) 5<br />(c) 9<br />(d) 6<br /></j><br />
<h2 style="text-align: left;">
<j 1="?" li="0," x="y" z="z"><span style="color: #0b5394; font-size: small;">Answers</span></j></h2>
<j 1="?" li="0," x="y" z="z">1(a) Less than equal to 3<br />2(b) 3<br />3(a) To make it matrix<br />4(a) Singular matrix<br />5(b) 3<br />6(b) A2 = I<br />7(b) aij, i > j</j><br />
<j 1="?" li="0," x="y" z="z">8(b) Characteristic eq.<br />9(c) 2<br />10(b) 3<br />11(a) 4<br />12(b) No<br />13(c) A1<br />14(a) Symmetric<br />15(b) Trivial Solution is x = y = z = 0<br />16(a) 4<br />17(b) Skew-Hermition<br />18(a) 4<br />19(a) Rank of A < no. of variable<br />20(b) Infinite many solution<br />21(a) Idempotent matrix<br />22(c) A1 + B1<br />23(b) 4, 9, 16<br />24(a) 2, 4, 8<br />25(c) 9<br /></j><br />
<h2 style="text-align: left;">
<j 1="?" li="0," x="y" z="z"><span style="color: #0b5394; font-size: small;">Reason</span></j></h2>
<j 1="?" li="0," x="y" z="z">2 If roots are different then degree of characteristics eq. & minimal eq. is same<br />4 If any row of matrix is zero, then its A = 0, therefore it is singular matrix<br />11 For this A ¹ 0<br />Rank of A = 4<br />20 For 2x + 6y = 0 but y = K<br />2x + 6K = 0<br />2x = –6k , x = – 3k<br />x = – 3k, y = k,<br />k have so many value</j></div>
Panini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.com0tag:blogger.com,1999:blog-2080901030127073240.post-5323340356444127842015-04-23T05:59:00.000-07:002015-04-23T05:59:43.070-07:00Mathematics <div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: left;">
<span style="color: #0b5394; font-size: small;">Mathematics </span></h2>
Q-1 The radius of 5 (x2 + y2) – 5 (x + y) + 10 = 0 is<br />
(a) Ö6/7 <br />
(b) Ö5/2<br />
(c) Ö7/9<br />
(d) Ö9/16<br />
<br />
Q-2 The radical plane of x2 + y2 + 2x + 6y + 9 = 0 & x2 + y2 + 6x + 9y – 8 = 0 is<br />
(a) 4x + 5y – 18 = 0<br />
(b) 4x + 5y – 17 = 0<br />
(c) 4x + 8y + 19 = 0<br />
(d) None<br />
<br />
Q-3 The center of circle x2 + y2 + 2u1 x + 2v1 y + d = 0 is<br />
(a) (u1 , v1)<br />
(b) ( – u1, – v)<br />
(c) (– u1/2, – v1/2)<br />
(d) None<br />
<br />
Q-4 In y2 = 2x, the vertex is<br />
(a) (0, 1)<br />
(b) (0, 2)<br />
(c) (0, 0)<br />
(d) None<br />
<br />
Q-5 In ( x – 5)2 + ( y – 3)2 = 5<br />
Find the center & radius of a circle.<br />
(a) (5, 3) & Ö5<br />
(b) (5, 4), 5<br />
(c) (5, 2), 6<br />
(d) None<br />
<br />
Q-6 In eq. of circle coefficient of x2 is equal to y2 & it should be equal to<br />
(a) 2<br />
(b) 1<br />
(c) 3<br />
(d) 4<br />
<br />
Q-7 The eq. of tangent to the circle x2 + y2 = 5 at (5, 3) is<br />
(a) 5x + 9y = 10<br />
(b) 5x + 3y = 5<br />
(c) 5x + 9y = 4<br />
(d) None<br />
<br />
Q-8 In the circle x2 + y2 + 2xy + 5z + c = 0, the centre is<br />
(a) (0, 0)<br />
(b) (1, 1)<br />
(c) It is not a circle<br />
(d) (4, 3)<br />
<br />
Q-9 In order to find pt. of intersection two line should be<br />
(a) Intersecting<br />
(b) Parallel<br />
(c) a and b<br />
(c) None<br />
<br />
Q-10 When distance between centre of two circle is equal to sum of their radius, then in this case two circle touch each other<br />
(a) Internally<br />
(b) Externally<br />
(c) Not touch<br />
(d) None<br />
<br />
Q-11 The eq. of circle with end pt. of diameter is (5, 2) & (1, 5) is<br />
(a) x2 + y2 – 6x + 7y – 10 = 0 <br />
(b) x2 + y2 – 6x – 7y + 10 = 0 <br />
(c) x2 + y2 + 6x + 7y – 11 = 0 <br />
(d) x2 + y2 – 6x + 7y – 11 = 0 <br />
<br />
Q-12 If we want to find radical plane, then how many circle we held<br />
(a) 2<br />
(b) 3<br />
(c) 5<br />
(d) 9<br />
<br />
Q-13 If in a equation Ax2 + By2 + 2Hxy + 2Gx + 2Fy + c = 0<br />
B2 – AB = 0, Then is a<br />
(a) Ellipse<br />
(b) Parabola<br />
(c) Hyperbola<br />
(d) None<br />
<br />
Q-14 In x2/a2 + y2/b2 = 1, then value of major axis is<br />
(a) 2a<br />
(b) 2b<br />
(c) 2d<br />
(d) None<br />
<br />
Q-15 In x2/a2 + y2/b2 = 1, then value of minor axis is<br />
(a) 2a<br />
(b) 2b<br />
(c) 2e<br />
(d) None<br />
<br />
Q-16 In x2/25 + y2/16 = 1, the latus rectum is<br />
(a) 32/5<br />
(b) 16/14<br />
(c) 16/9<br />
(d) None<br />
<br />
Q-17 In y2 = 4ax, the eq. of axis is<br />
(a) x = 0<br />
(b) y = 0<br />
(c) x = y= 0<br />
(d) None<br />
<br />
Q-18 If Ratio of distance of any pt. on conic to focus & directrix is 1, then it is<br />
(a) Parabola<br />
(b) Ellipse<br />
(c) Hyperbola<br />
(d) None<br />
<br />
Q-19 If a = b in x2/a2 – y2/b2 = 1, then it is<br />
(a) Rectangle hyperbola<br />
(b) Hyperbola<br />
(c) Ellipse<br />
(d) None<br />
<br />
Q-20 For rectangle hyperbola, the value of l is<br />
(a) Ö2<br />
(b) Ö3<br />
(c) Ö14<br />
(d) Ö5<br />
<br />
Q-21 What is parametric form of x2 + y2 = r 2 ?<br />
(a) x = r cos Ө, y = r sin Ө<br />
(b) x = cos Ө, y = sin<br />
(c) x = r2 cos Ө, y = r2 sin Ө<br />
(d) None<br />
<br />
Q-22 Find the eq. of axis of (x + 1)2/52 + (y + 1)2 /32 = 1<br />
(a) y = 0<br />
(b) y = 1<br />
(c) y = 3<br />
(d) y = 5<br />
<br />
Q-23 What is the focus of parabola y2 = 8x ?<br />
(a) (2,0)<br />
(b) (3,0)<br />
(c) (4,0)<br />
(d) (5,1)<br />
<br />
Q-24 What is the focus of a parabola ?<br />
Y2 = – 36x<br />
(a) (0, – 9)<br />
(b) (0,9)<br />
(c) (0,5)<br />
(d) (0,4)<br />
<br />
Q-25 What is focus of a parabola x2 = 36y ?<br />
(a) (0,4)<br />
(b)(0,9)<br />
(c)(0,5)<br />
(d) None<br />
<br />
<h3 style="text-align: left;">
<span style="font-size: small;">Answers:</span></h3>
1(b) Ö5/2<br />
2(b) 4x + 5y – 17 = 0<br />
3(b) ( – u1, – v1)<br />
4(c) (0, 0)<br />
5(a) (5, 3) & Ö5<br />
6(b) 1<br />
7(b) 5x + 3y = 5<br />
8(c) It is not a circle<br />
9(a) Intersecting<br />
10(b) Externally<br />
11(b) x2 + y2 – 6x – 7y + 10 = 0<br />
12(a) 2<br />
13 (b)Parabola<br />
14(a) 2a<br />
15(b) 2b<br />
16(a) 32/5<br />
17(b) y = 0<br />
18(a) Parabola<br />
19(a) Rectangle hyperbola<br />
20(a) Ö2<br />
21(a) x = r cos Ө, y = r sin Ө<br />
22(a) y = 0<br />
23(a) (2,0)<br />
24(a)(0, – 9)<br />
25(b)(0,9)<br />
<br />
<h4 style="text-align: left;">
<span style="color: #0b5394;">Reason:</span></h4>
1 (x2 + y2) – 5 (x + y) + 10 = 0<br />
First of all divide it by 5 because coefficient of x2 & y2 should be 1<br />
(x2 + y2) – x – y – 2 = 0<br />
( ½, 1/2), d = – 2<br />
radius = Ö(1/2)2 + (1/2)2 + 2<br />
Ö1/4 + ¼ +2<br />
Ö2/4 + 2<br />
Ö1/2 + 2 = Ö 5/2<br />
2 Let S1 = x2 + y2 + 2x + 6y + 9 = 0<br />
S2 = x2 + y2 + 6x + 6y + 9 = 0<br />
Eq. of radical plane is<br />
S1 – S2 = 0<br />
– 4x – 5y + 17 = 0<br />
4x + 5y – 17 = 0<br />
7 Equation of Tangent at (x1, y1)<br />
xy1 + yy1 = 5<br />
But at pt. (5, 3) it is<br />
x(5) + y(3) = 5<br />
5x + 3y = 5<br />
8 It is not a circle because in circle there is not any term which contain xy etc<br />
11 Equation of circle in diameter form is<br />
(x – x1) (x – x2) + (y – y1) (y – y2) = 0<br />
(x – 5) (x – 1) + (y – 2) (y – 5) = 0<br />
x2 – x – 5x +5 + y2 – 5y – 2y + 5 = 0<br />
x2 – 6x + 5 + y2 – 7y + 5 = 0<br />
x2 + y2 – 6x – 7y + 10 = 0<br />
16 Latus rectum is 2b2/a<br />
By x2/25 + y2/16 = 1<br />
a2 = 25, b2 = 16, a = 5, b = 4<br />
Latus rectum = 2b2/a = 2(16)/5 = 32/5<br />
22 For x2/a2 + y2/b2 = 1, the eq. of axis in y = 0<br />
23 Compare y2 = 8x<br />
With y2 = –4ax<br />
4a = 8, a = 2<br />
F (a, 0), i.e F (2, 0)<br />
24 Compare y2 = – 36x<br />
With y2 = –4ax<br />
4ax = 36, a = 9<br />
F (–a, 0) , F (–9, 0)</div>
Panini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.com0Nangal, Punjab, India31.36999999999999 76.3831.315776499999991 76.299319 31.424223499999989 76.460681tag:blogger.com,1999:blog-2080901030127073240.post-62247606241471122612015-04-23T05:55:00.000-07:002015-04-23T05:55:16.665-07:00Mathematics Numbers<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: left;">
<span style="color: #0b5394; font-size: small;">Mathematics Numbers</span></h2>
Q-1 Which prime of the following is smallest even Prime number?<br />
(a) 4 (b) 2 (c) 8 (d) 10<br />
<br />
Q-2 HCF of 7/4, 21/4, 28/12 is<br />
(a) 7/100 (b) 7/24 (c) 7/25 (d) None<br />
<br />
Q-3 LCM of 12/9, 24/18, 36/27 is<br />
(a) 7 (b) 8 (c) 11 (d) None<br />
<br />
Q-4 x/y=2/5, y/z = 8 , find x/z=?<br />
(a) 4/24 (b) 4/25 (c) 4/58 (d) None<br />
<br />
Q-5 12/13x-41/26x=11, find x<br />
(a) 26× 11/17 (b) 26 ×12/9 (c) 26× 18/11 (d) None<br />
<br />
Q-6 How many prime no. are there between 10 to 30?<br />
(a) 7 (b) 6 (c) 8 (d) 9<br />
<br />
Q-7 1/ (n-n)! =?<br />
(a) 2 (b) 1 (c) 3 (d) 5<br />
<br />
Q-8 If Manoj’s age 5 years ago was 23 years, then what will be its present age?<br />
(a) 25 (b) 18 (c) 19 (d) 28<br />
<br />
Q-9 25% of 50 of 3/35 %of 25 of 4=?<br />
(a) 14/11 (b) 15/14 (c) 19/13 (d) None<br />
<br />
Q-10 5 x +7/7x +8 = 9/11, find x<br />
(a) 5/6 (b) 5/11 (c) 5/8 (d) None<br />
<br />
Q-11 1+2+3+4+ --------- 12 = ?<br />
(a) 72 (b) 78 (c) 79 (d) 80<br />
<br />
Q-12 10 +11+12+ ---------- 15= ?<br />
(a) 175 (b) 75 (c) 68 (d) None<br />
<br />
Q-13 (2n) 2 -(2n+2)2 is always divisible by which value?<br />
(a) 5 (b) n (c) 6 (d) None<br />
<br />
Q-14 X2 + 11x+30 =0 find the value of x<br />
(a) - 5, -6 (b) 5, 6 (c) 15/9 (d) None<br />
<br />
Q-15 Find the digit at unit place of 313× 41× 152 ×161<br />
(a) 3 (b) 6 (c) 4 (d) 5<br />
<br />
Q-16 Find the value of x in 53x4, if it is divisible by4<br />
(a) 4 (b) 3 (c) 5 (d) 7<br />
<br />
Q-17 If x +y = 11 and x2+y2=12, find the value of x y<br />
(a) 67 (b) 66 (c) 68 (d) 29<br />
<br />
Q-18 Find H.C.F of 34 × 46× 78, 33× 47× 79<br />
(a) 34 × 46 ×78 (b) 34 × 46 (c) A&B (d) None <br />
<br />
Q-19 99× 99 × 99 <br />
(a) 1000 300 - 30001 (b) 100001 (c) 1001 (d) None<br />
<br />
Q-20 Find the number which have large of divisor?<br />
(a) 11 (b) 17 (c) 21 (d) 29<br />
<br />
Q-21 (X/13) (X/13) = 4, find x<br />
(a) 27 (b) 26 (c) 28 (d) None<br />
<br />
Q-22 ( 703 + 503)/ (70)2 + 502 - (70) (50)<br />
(a) 130 (b) 120 (c) 180 (d) None<br />
<br />
Q-23 If 10 year after the age of Nirmal is 38 year then presently her age will be<br />
(a) 28 (b) 38 (c) 48 (d) None<br />
<br />
Q-24 Find LCM of 2, 8, 16, 32<br />
(a) 16 (b) 32 (c) 2 (d) 8<br />
<br />
Q-25 H.C.F of (4, 16, 32)<br />
(a) 8 (b) 4 (c) 8 (d) None<br />
<br />
<br />
<h3 style="text-align: left;">
<span style="font-size: small;">ANSWERS:-</span></h3>
<br />
1 (b) 2 <br />
2 (b) 7/24<br />
3 (b) 8<br />
4 (b) 4/25 <br />
5 (a) 26× 11/17<br />
6 (b) 6<br />
7 (b) 1 <br />
8 (d) 28<br />
9 (b) 15/14 <br />
10 (c) 5/8 <br />
11 (b) 78<br />
12 (b) 75<br />
13 (b) n <br />
14 (a) - 5, -6<br />
15 (b) 6 <br />
16 (a) 4 <br />
17 (b) 66<br />
18 (a) 34 × 46 ×78<br />
19 (a) 1000 300 - 30001 <br />
20 (c) 21<br />
21 (b) 26<br />
22 (b) 120<br />
23 (a) 28<br />
24 (b) 32<br />
25 (b) 4 <br />
<br />
<br />
<h4 style="text-align: left;">
<span style="color: #0b5394;">REASONS:-</span></h4>
<br />
<br />
2 (b) HCF=HCF of 7,21,28/LCM of 4,8,12=7/24<br />
3 (b) LCM= LCM12,24,36/1CF 9,18,27 <br />
= 72/9 = 8<br />
4 (b) x/y × y/2 = x/2<br />
=2/5×4/18 =4/45<br />
5 (a) (24 -41) x /26 =11 <br />
= 17/26x=11<br />
x=11×26/17<br />
6 (b) 11, 13, 17,19,23,29<br />
7 (b) 1/01<br />
=1=1/1=1<br />
9 (b) 25/100×50×3/35/100×25×4<br />
= 150/35×4<br />
=150/140=15/14<br />
10 (c) 11(5x+7) =9(7x+8)<br />
=55x+77 = 63x+72<br />
= 5 = 8x<br />
5/8 =x<br />
11 (b) 1+2+3----------- +12<br />
= 12(12+1)/2<br />
= 12(13)/2 =78<br />
12 (b) (1+ 2+3+--------+9) + (10+-------- +15) -(1+2+-------+9)<br />
= å 15-åa</div>
Panini Onlinehttp://www.blogger.com/profile/16937376942922880560noreply@blogger.com0Nangal, Punjab, India31.36999999999999 76.3831.315776499999991 76.299319 31.424223499999989 76.460681