{"id":625762,"date":"2023-09-08T02:17:21","date_gmt":"2023-09-08T02:17:21","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=625762"},"modified":"2023-09-08T02:43:55","modified_gmt":"2023-09-08T02:43:55","slug":"kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/","title":{"rendered":"KC Sinha: Exercise 1.1 – Mathematics Solution Class 11 Chapter 1 \u0938\u092e\u0941\u091a\u094d\u091a\u092f"},"content":{"rendered":"\n\n\n\n\n

TYPE-I<\/p>\n\n\n\n

Question 1<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0917\u094d\u0930\u0939\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ? \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092c\u0924\u093e\u0907\u090f
Which of the following collections are sets ? Justify your answer
(i)<\/strong> \u092d\u093e\u0930\u0924 \u0915\u0947 \u0905\u091a\u094d\u091a\u091b\u0947 \u0915\u094d\u0930\u093f\u0915\u0947\u091f \u0916\u093f\u0932\u093e\u0921\u093c\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948,\u0905\u091a\u094d\u091a\u091b\u0947 \u0916\u093f\u0932\u093e\u0921\u093c\u0940<\/p>\n\n\n\n

(ii)<\/strong> \u0935\u093f\u0936\u094d\u0935 \u0915\u0947 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0916\u0924\u0930\u0928\u093e\u0915 \u091c\u093e\u0928\u0935\u0930\u094b \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948<\/p>\n\n\n\n

(iii)<\/strong> \u0906\u092a\u0915\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0938\u092d\u0940 \u0932\u0921\u0915\u093f\u092f\u094b \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :<\/p>\n\n\n\n

\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

(iv)<\/strong> \u0932\u0947\u0916\u0915 \u092e\u0941\u0902\u0936\u0940 \u092a\u094d\u0930\u0947\u092e\u091a\u0928\u094d\u0926 \u0926\u094d\u0935\u093e\u0930\u093e \u0932\u093f\u0916\u093f\u0924 \u0909\u092a\u0928\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

(v)<\/strong> \u0938\u092d\u0940 \u0938\u092e \u092a\u0942\u0923\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

(vi)<\/strong> \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0924\u0932 \u092e\u0947\u0902 \u092a\u094d\u0930\u092d\u0940 \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

(vii)<\/strong> \u0935\u093f\u0936\u094d\u0935 \u0915\u0947 \u0938\u0941\u0928\u094d\u0926\u0930 \u0932\u0921\u093c\u0915\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948<\/p>\n\n\n\n

(viii)<\/strong> \u0935\u093f\u0936\u094d\u0935 \u0915\u0947 \u0935\u093f\u0916\u094d\u092f\u093e\u0924\u0902 \u0917\u0923\u093f\u0924\u091c\u094d\u091e\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948<\/p>\n\n\n\n

(ix)<\/strong> 100 \u0938\u0947 \u0915\u092e \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

(x)<\/strong> \u0907\u0938 \u0905\u0927\u094d\u092f\u093e\u092f \u092e\u0947\u0902 \u0906\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939
Sol :
\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947 \u0939\u0948 \u0964<\/p>\n\n\n\n

Question 2<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u0915\u094b \u0930\u094b\u0938\u094d\u091f\u0930 \u0930\u0941\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093f\u090f
Write the following sets in roster form :
A={x:x \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0924\u0925\u093e -1\u2264x<y}
Sol :
A={-1,0,1,2,3…8}<\/p>\n\n\n\n

B={x:x \u0935\u093f\u0937\u092e \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0924\u0925\u093e x>-2}
Sol :
B={-1,1,3,5,7,9..}<\/p>\n\n\n\n

C={x:x \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u0924\u0925\u093e 5<x\u226426}
Sol :
C={6,7,8,9,10,..26}<\/p>\n\n\n\n

D={x:x \u0907\u0915\u093e\u0908 \u0915\u0947 \u0918\u0928\u092e\u0942\u0932}
Sol :
D={1,w,w2<\/sup>}<\/p>\n\n\n\n

E={x:x2<\/sup>+x..4=0}
Sol :
$E=\\left\\{-\\frac{1-\\sqrt{17}}{2}, \\frac{-1+\\sqrt{17}}{2}\\right\\}$<\/p>\n\n\n\n

F={x:x, 24 \u0938\u0947 \u091b\u094b\u091f\u0940 \u0905\u092d\u093e\u091c\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948}
Sol :
F={2,3,5,7,11,13,17,19,23}<\/p>\n\n\n\n

G={x:x \u0926\u094b \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0905\u0902\u0915\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 4 \u0939\u0948}
Sol :
G={13,22,31,40}<\/p>\n\n\n\n

H={x:x \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x2<\/sup><40}
Sol :
H={1,2,3,4,5,6}<\/p>\n\n\n\n

Question 3<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u0915\u094b \u0938\u093e\u0930\u0923\u0940 \u0930\u0941\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093f\u090f
Write the following sets in roster form(tabular form)
A={x:x\u2208Z and |x|<5}
Sol :
A={-4,-3,-2,-1,0,1,2,34}<\/p>\n\n\n\n

B={x:x \u0936\u092c\u094d\u0926 proportion \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}
Sol :
B={p,r,o,t,i,n}<\/p>\n\n\n\n

C={x:x3<\/sup>=-1,x\u2208R}
Sol :
x3<\/sup>=-1
x3<\/sup>=(-1)3<\/sup>
x=-1
C={-1}<\/p>\n\n\n\n

E={x:x$=\\frac{n}{n+1}$,n\u2208N}
Sol :
E={$\\frac{1}{2},\\frac{2}{3},\\frac{3}{4},\\frac{4}{5},\\dots$}<\/p>\n\n\n\n

Question 4<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u0915\u0947 \u0938\u092d\u0940 \u0905\u0935\u092f\u0935\u094b\u0902 \u0915\u094b \u0938\u0942\u091a\u093f\u092c\u0927 \u0915\u0940\u091c\u093f\u090f
List all the elements of the following sets
A={x:x \u0936\u092c\u094d\u0926 LOYAL \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}
Sol :
A={L,O,Y,A}<\/p>\n\n\n\n

B={x:x \u0938\u092e \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948}
Sol :
B={2,4,6,8,10..}<\/p>\n\n\n\n

C={x:x \u0905\u0902\u0917\u094d\u0930\u0947\u091c\u0940 \u0935\u0930\u094d\u0923\u092e\u093e\u0932\u093e \u0915\u093e \u090f\u0915 \u0935\u094d\u092f\u0902\u091c\u0928 \u0939\u0948 \u091c\u094b p \u0938\u0947 \u092a\u0939\u0932\u0947 \u0906\u0924\u093e \u0939\u0948}
Sol :
C={b,c,d,f,g,h,j,k,l,m,n}<\/p>\n\n\n\n

D={x:x \u0935\u0930\u094d\u0937 \u0915\u093e \u090f\u0915 \u0910\u0938\u093e \u092e\u0939\u0940\u0928\u093e \u091c\u093f\u0932\u092e\u0947 31 \u0926\u093f\u0928 \u0928\u0939\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948}
Sol :
D={\u092b\u0930\u0935\u0930\u0940,\u0905\u092a\u094d\u0930\u0948\u0932,\u091c\u0942\u0928,\u0938\u093f\u0924\u092e\u094d\u092c\u0930,\u0928\u0935\u092e\u094d\u092c\u0930}<\/p>\n\n\n\n

Question 5<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b  \u0915\u094b \u0930\u094b\u0938\u094d\u091f\u0930 \u0930\u0941\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093f\u090f
Write the following sets in roster form
(i)<\/strong> A={x:x \u0905\u092d\u093e\u091c\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u091c\u094b 60 \u0915\u093e \u092d\u093e\u091c\u0915 \u0939\u0948}
Sol :
A={2,5}<\/p>\n\n\n\n

(ii)<\/strong> B=ALGEBRA \u0936\u092c\u094d\u0926 \u0915\u0947 \u0938\u092d\u0940 \u0905\u0915\u094d\u0937\u0930\u094b \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948
Sol :
B={A,L,G,E,B,R}<\/p>\n\n\n\n

(iii)<\/strong> C={x:x \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x2<\/sup><4}
Sol :
C={-1,0,1}<\/p>\n\n\n\n

(iv)<\/strong> D={x:x \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 -3<x<7}
Sol :
D={-2,-1,0,1,2,3,4,5,6}<\/p>\n\n\n\n

(v)<\/strong> E={x:x \u0926\u094b \u0905\u0902\u0915\u094b \u0915\u0940 \u0910\u0938\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u091c\u093f\u0932\u0915\u0947 \u0905\u0902\u0915\u094b \u0915\u093e \u092f\u094b\u0917\u092b\u0932 9 \u0939\u0948}
Sol :
E={18,27,36,45,54,63,72,81,90}<\/p>\n\n\n\n

(vi)<\/strong> F={x:x2<\/sup>+x-2=0}
Sol :
x2<\/sup>+x-2=0
x2<\/sup>+2x-x-2=0
x(x+2)-1(x+2)=0
(x+2)(x-1)
F={-2,-1}<\/p>\n\n\n\n

(vii)<\/strong> G={x:x BETTER \u0936\u092c\u094d\u0926 \u0915\u0947 \u0938\u092d\u0940 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 }
Sol :
G={B,E,T,R}<\/p>\n\n\n\n

(viii)<\/strong> H={x:x, 6 \u0938\u0947 \u091b\u094b\u091f\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948}
Sol :
H={1,2,3,4,5}<\/p>\n\n\n\n

Question 6<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u0915\u094b \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0930\u0941\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093f\u090f
Write the following sets in the set builder form
(i)<\/strong> A={-1,0,1,2,3,…8}
Sol :
A={x:x\u2208I,-1\u2264x\u22649}
={x:x\u2208Z,-1\u2264x\u22648}<\/p>\n\n\n\n

(ii)<\/strong> B={3,6,9,12..}
Sol :
B={x:x=3n;n\u2208N}<\/p>\n\n\n\n

(iii)<\/strong> C={1,-1,i,-i}
Sol :
x4<\/sup>=1
x4<\/sup>-1=0
(x2<\/sup>)2<\/sup>-(12<\/sup>)2<\/sup>=0
(x2<\/sup>-12<\/sup>)(x2<\/sup>+12<\/sup>)=0
$\\begin{array}{l|l}x=1=0& x+1=0\\\\x=1&x=-1\\end{array}$<\/p>\n\n\n\n

x2<\/sup>+1=0
x2<\/sup>=-1<\/p>\n\n\n\n

x=\u00b1\u221a-1<\/p>\n\n\n\n

x=\u00b1i<\/p>\n\n\n\n

C={x:x4<\/sup>=1}<\/p>\n\n\n\n

Question 7<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u0915\u094b \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0930\u0941\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093f\u090f
Write the following sets in set builder form
(i)<\/strong> $A=\\left\\{\\frac{1}{3}, \\frac{2}{4}, \\frac{3}{5}, \\frac{4}{6}, \\frac{5}{7}, \\frac{6}{8}, \\frac{7}{9}, \\frac{8}{10}\\right\\}$
Sol :
A={x:x$=\\frac{n}{n+2}$,n\u2208N \u0924\u0925\u093e n\u22648}<\/p>\n\n\n\n

(ii)<\/strong> B={1,4,9,16}
Sol :
B={x:x=n2<\/sup>;n\u2208N}<\/p>\n\n\n\n

(iii)<\/strong> C={2,5,10}
Sol :<\/p>\n\n\n\n

C={x:x=n2<\/sup>+1;n\u2208N}<\/p>\n\n\n\n

(iv)<\/strong> D={5,7,11,13,17,19,23,29}
Sol :<\/p>\n\n\n\n

D={x:x \u0905\u092d\u093e\u091c\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u0914\u0930 5\u2264x\u226429}<\/p>\n\n\n\n

(v)<\/strong> E={5,9,13,17,21..}
Sol :
E={x:x=4n+1,n\u2208N}<\/p>\n\n\n\n

(vi)<\/strong> F={14,21,28,35,42,..98}
Sol :<\/p>\n\n\n\n

F={x:x=7n,n\u2208N \u0914\u0930 2\u2264n\u226414}<\/p>\n\n\n\n

(vii)<\/strong> G={1,5,10,15…}
Sol :
G={x:x=5n,n\u2208N \u0914\u0930 x=1}<\/p>\n\n\n\n

Question 8<\/h4>\n\n\n\n

\u092c\u093e\u0908 \u0913\u0930 \u0930\u094b\u0938\u094d\u091f\u0930 \u0930\u0941\u092a \u092e\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u092a\u094d\u0930\u0924\u092f\u0947\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u0926\u093e\u0908 \u0913\u0930 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0930\u0941\u092a \u092e\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0938\u0947 \u0938\u0939\u0940 \u092e\u093f\u0932\u093e\u0928 \u0915\u0940\u091c\u093f\u090f
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
(i) {P,R,I,N,C,A,L} (a) {x:x  \u090f\u0915 \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0924\u0925\u093e 18 \u092d\u093e\u091c\u0915 \u0939\u0948}
(ii) {0} (b) {x:x \u090f\u0915 \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x2<\/sup>-9=0}
(iii) {1,2,3,6,9,18} (c) {x:x \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x+1=1}
(iv) {-3,3} (d) {x:x \u0936\u092c\u094d\u0926 PRINCIPAL  \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}<\/p>\n\n\n\n

Sol :
(i)\u2194d
(ii)\u2194c
(iii)\u2194a
(iv)\u2194b<\/p>\n\n\n\n

Question 9<\/h4>\n\n\n\n

\u092c\u093e\u0908 \u0913\u0930 \u0930\u094b\u0938\u094d\u091f\u0930 \u0930\u0941\u092a \u092e\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u092a\u094d\u0930\u0924\u092f\u0947\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u0926\u093e\u0908 \u0913\u0930 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0930\u0941\u092a \u092e\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0938\u0947 \u0938\u0939\u0940 \u092e\u093f\u0932\u093e\u0928 \u0915\u0940\u091c\u093f\u090f
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
(i) {1,3,5,7,9} {x:x \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x2<\/sup>-4=0}
(ii) {2,-2} {x:x \u0936\u092c\u094d\u0926 MATHEMATICS \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}
(iii) {M,A,T,H,E,I,C,S} {x:x \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0914\u0930 12 \u0915\u093e \u092d\u093e\u091c\u0915 \u0939\u0948}
(iv) {1,2,3,6,12} {x:x 10 \u0938\u0947 \u091b\u094b\u091f\u0940 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948}
Sol :
(i)\u2194d<\/p>\n\n\n\n

Question 11<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u092e\u0947 \u092c\u0924\u0932\u093e\u0907\u090f A=B \u0939\u0948 \u0905\u0925\u0935\u093e \u0928\u0939\u0940\u0902
In the following sate whether A=B or not :
(i)<\/strong> A={4,8,12,16}, B={8,4,16,18}
Sol :
A\u2260B<\/p>\n\n\n\n

(ii)<\/strong> A={x:x, 10 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948},B\u2260{10,15,20,25,30..}
Sol :
A\u2260B<\/p>\n\n\n\n

(iii)<\/strong> A={2,46,8,10},B={x:x,x \u0938\u092e \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0939\u0948 \u0914\u0930 x\u226410}
Sol :
A=B<\/p>\n\n\n\n

(iv)<\/strong> A={a,b,c,d},B={d,c,b,d}
Sol :
A=B<\/p>\n\n\n\n

(v)<\/strong> A={2,3},B={x:x2<\/sup>+5x+6=0}
Sol :
x2<\/sup>+5x+6=0
x2<\/sup>+3x+2x+6=0
x(x+3)+2(x+3)=0
(x+3)(x+2)=0
$\\begin{array}{l|l}x+3=0&x+3=0\\\\x=-3&x=-2\\end{array}$
B={-3,-2}
A\u2260B<\/p>\n\n\n\n

Question 12<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u092e\u0947 \u0915\u094c\u0928 \u0930\u093f\u0915\u094d\u0924, \u090f\u0915\u0932 \u0914\u0930 \u092f\u0941\u0917\u094d\u092e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948, \u0909\u0928\u092e\u0947 \u0915\u094c\u0928 \u0938\u092e\u093e\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ?
Which of the following sets are empty, singleton set and pair set.Which of them are equal?
A={x:2x=10,x2<\/sup>-7x+10=0}<\/p>\n\n\n\n

B={x:x2<\/sup>-16x+55=0 and x2<\/sup>=25}<\/p>\n\n\n\n

C={x:$-\\frac{1}{2} \\leq x \\leq \\frac{1}{2}$}<\/p>\n\n\n\n

D={x;0\u22644x2<\/sup>\u22641}<\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n
\"\"\/<\/a><\/figure>\n\n\n\n

Question 13<\/h4>\n\n\n\n

\u0915\u094d\u092f\u093e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0938\u092e\u093e\u0928 \u0939\u0948
Are the following sets equal ?
(i)<\/strong> A={1,2},B={1,2},
C={x:x2<\/sup>-3x+2=0}
Sol :<\/p>\n\n\n\n

(ii)
(iii)
(iv)
<\/a><\/p>\n\n\n\n

Question 14<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947 \u0915\u094c\u0928 \u0905\u092a\u0930\u093f\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ?
Which of the following sets are infinite sets
(i)<\/strong> x \u0905\u0915\u094d\u0937 \u0915\u0947 \u0938\u092e\u093e\u0928\u093e\u0928\u094d\u0924\u0930 \u0938\u092d\u0940 \u0930\u0947\u0916\u093e\u090f\u0901
Sol :
\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(ii)<\/strong> \u092e\u0942\u0932 \u092c\u093f\u0928\u094d\u0926\u0941 \u0935\u0943\u0924\u094b\u0902 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f
Sol :
\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(iii)<\/strong> 100 \u0938\u0947 \u092c\u0921\u0940 \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0915 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f
Sol :
\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(iv)<\/strong> \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u0913 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u091c\u094b 5 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948
Sol :
\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(v)<\/strong> 99 \u0938\u0947 \u091b\u094b\u091f\u0940 \u0905\u092d\u093e\u091c\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f
Sol :<\/p>\n\n\n\n

\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(vi)<\/strong> \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0928\u094d\u0926\u0941 \u0938\u0947 \u0917\u0941\u091c\u0930\u0928\u0947 \u0935\u093e\u0932\u0940 \u0930\u0947\u0916\u093e\u0913 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f
Sol :<\/p>\n\n\n\n

\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(vii)<\/strong> \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u091c\u094b 42 \u0915\u094b \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948
Sol :<\/p>\n\n\n\n

\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(viii)<\/strong> {x:x\u2208Z \u0914\u0930 x>6}
Sol :<\/p>\n\n\n\n

\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(ix)<\/strong> {x:x \u0939\u093f\u0928\u094d\u0926\u0940 \u092c\u094b\u0932\u0928\u0947 \u0935\u093e\u0932\u0947 \u092d\u093e\u0930\u0924 \u0915\u0947 \u0932\u094b\u0917 \u0939\u0948}
Sol :<\/p>\n\n\n\n

\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(x)<\/strong> \u092a\u0943\u0925\u094d\u0935\u0940 \u092a\u0930 \u0930\u0939\u0928\u0947 \u0935\u093e\u0932\u0947 \u091c\u093e\u0928\u0935\u0930\u094b \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f
Sol :<\/p>\n\n\n\n

\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

(xi)<\/strong> \u0938\u0902\u0916\u094d\u092f\u093e\u0913 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u091c\u094b 5 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948
Sol :<\/p>\n\n\n\n

\u0905\u092a\u0930\u093f\u092e\u093f\u0924<\/p>\n\n\n\n

Question 15<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0926\u093f\u092f\u0947 \u0917\u092f\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b \u092e\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u091a\u0941\u0928\u093f\u092f\u0947
From the sets given below select equivalent sets
A={1,2,3,5},B={5,10},
C={x:x2<\/sup>-5x+4=0}
D={x:x \u0936\u092c\u094d\u0926 LOVE \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}
E={x:x\u0936\u092c\u094d\u0926 WOLF \u0915\u093e \u090f\u0915 \u0905\u0915\u094d\u0937\u0930 \u0939\u0948}
Sol :
A={1,2,3,5},B={5,10},
C={1,4}
D={L,O,V,E}
E={W,O,L,F}<\/p>\n\n\n\n

A,D,E \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 \u0964
B \u0914\u0930 C \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 \u0964<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 11 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

TYPE-I Question 1 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0917\u094d\u0930\u0939\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ? \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092c\u0924\u093e\u0907\u090fWhich of the following collections are sets ? Justify your answer(i) \u092d\u093e\u0930\u0924 \u0915\u0947 \u0905\u091a\u094d\u091a\u091b\u0947 \u0915\u094d\u0930\u093f\u0915\u0947\u091f \u0916\u093f\u0932\u093e\u0921\u093c\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939Sol :\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948,\u0905\u091a\u094d\u091a\u091b\u0947 \u0916\u093f\u0932\u093e\u0921\u093c\u0940 (ii) \u0935\u093f\u0936\u094d\u0935 \u0915\u0947 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0916\u0924\u0930\u0928\u093e\u0915 \u091c\u093e\u0928\u0935\u0930\u094b \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939Sol :\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0928\u0939\u0940 \u0939\u0948 (iii) \u0906\u092a\u0915\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0938\u092d\u0940 \u0932\u0921\u0915\u093f\u092f\u094b \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939Sol : […]<\/p>\n","protected":false},"author":302,"featured_media":625764,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[919],"tags":[],"boards":[],"class_list":["post-625762","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-11","entry"],"yoast_head":"\nKC Sinha: Exercise 1.1 - Mathematics Solution Class 11 Chapter 1 \u0938\u092e\u0941\u091a\u094d\u091a\u092f - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"TYPE-I Question 1 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0917\u094d\u0930\u0939\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ? \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092c\u0924\u093e\u0907\u090fWhich of the following collections are sets ? Justify your\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 1.1 - Mathematics Solution Class 11 Chapter 1 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\" \/>\n<meta property=\"og:description\" content=\"TYPE-I Question 1 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0917\u094d\u0930\u0939\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ? \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092c\u0924\u093e\u0907\u090fWhich of the following collections are sets ? Justify your\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-08T02:17:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-08T02:43:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-8-1-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1600\" \/>\n\t<meta property=\"og:image:height\" content=\"901\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"KC Sinha: Exercise 1.1 – Mathematics Solution Class 11 Chapter 1 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\",\"datePublished\":\"2023-09-08T02:17:21+00:00\",\"dateModified\":\"2023-09-08T02:43:55+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\"},\"wordCount\":827,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-8-1-scaled.jpg\",\"articleSection\":[\"class 11\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/\",\"name\":\"KC Sinha: Exercise 1.1 - Mathematics Solution Class 11 Chapter 1 \u0938\u092e\u0941\u091a\u094d\u091a\u092f - IndCareer Schools\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-1-1-mathematics-solution-class-11-chapter-1-samuchchay\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-8-1-scaled.jpg\",\"datePublished\":\"2023-09-08T02:17:21+00:00\",\"dateModified\":\"2023-09-08T02:43:55+00:00\",\"description\":\"TYPE-I Question 1 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0917\u094d\u0930\u0939\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 ? \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092c\u0924\u093e\u0907\u090fWhich of the following collections are sets ? 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