14:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@graph\":[{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://www.divinejee.com\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"If Cr equiv 25Cr and C0 5C1 9C2 101C25 225k then k is equal \",\"item\":\"https://www.divinejee.com/question/if-cr-equiv-25cr-and-c0-5c1-9c2-101c25-225k-then-k-is-equal-to\"}]},{\"@type\":\"QAPage\",\"mainEntity\":{\"@type\":\"Question\",\"name\":\"Question If Cr equiv 25Cr and C0 5C1 9C2 101C25 225k then k is equal on Topic\",\"text\":\"If C_r $ \\\\equiv $ ²⁵C_r and
\\nC₀ + 5.C₁ + 9.C₂ + .... + (101).C₂₅ = 2r $ \\equiv $ ²⁵C_r and
\nC₀ + 5.C₁ + 9.C₂ + .... + (101).C₂₅ = 2²⁵.k, then k is equal to _____.","solutionTex":"S = 1.²⁵C₀ + 5.²⁵C₁ + 9.²⁵C₂ + .... + (101)²⁵C₂₅\n

S = (101).²⁵C₂₅ + (97).²⁵C₂₄ + .......... + (1).²⁵C₀\n
_________________________________________\n

2S = 102{²⁵C₀ + ²⁵C₁ + ......+ ²⁵C₂₅}\n

$$ \\Rightarrow $$ S = 51 $$ \\times $$ 2²⁵ = k.2²⁵\n

$$ \\Rightarrow $$ k = 51","answer":"51","options":[],"metaDescription":"If Cr equiv 25Cr and C0 5C1 9C2 101C25 225k then k is equal to ","solutionVideoLink":null,"year":null,"difficulty":"Medium","videoLink":""},"sidebarQuestions":[{"id":"ef92f0a5-5e19-4683-a31d-29f26a7c7214","title":"The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :","difficulty":"Medium","slug":"/question/the-area-enclosed-by-the-curves-xy4y16-and-xy6-is-equal-to-","subject":"Mathematics","topic":"Area of Bounded Region"},{"id":"1f68dfb6-d27f-437c-bf91-53079cae96c4","title":"Consider the following relations:\n\n R = |(x,y)|x,y are real numbers and x = wy for some rational\n\n mumber w/;\n\n S = { ( frac{m}{n},frac{p}{q} )| m,n,p and q are\n\n integers such that n,q X 0 and qm = pm}.\n\n Then","difficulty":"Medium","slug":"/question/consider-the-following-relations-R-xy-xy-are-real-numbers-and-x-wy-for-some-rational-mumber","subject":"Mathematics","topic":"Relation"},{"id":"0a5c649c-0636-497a-8ee6-dc8ab4ca5570","title":"The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to","difficulty":"Medium","slug":"/question/the-area-of-the-region-enclosed-by-the-parabolas-y4x-x2-and-3yx-42-is-equal-to","subject":"Mathematics","topic":"Area of Bounded Region"},{"id":"5ef0d1d0-9c15-4755-985a-6a35ceb69e5f","title":"Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a\n\n relation defined on A X B such that\n\n R = {( ( a_{1},b_{1} ),\n\n ( a_{2},b_{2} )):a_{1} ? b_{2} and\n\n b_{1} ? a_{2}}. Then the number of elements in the set R\n\n is","difficulty":"Medium","slug":"/question/let-A-1-3-4-6-9-and-B-2-4-5-8-10-Let-R-be-a-relation-defined-on-A-X-B-such-that-R-a-1-b-1-a-2-b-2-","subject":"Mathematics","topic":"Relation"},{"id":"60a0167e-a280-4b2b-af11-373062710c73","title":"Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is","difficulty":"Medium","slug":"/question/area-of-the-region-begincasesxyx2y-224x22yendcases-is","subject":"Mathematics","topic":"Area of Bounded Region"},{"id":"5ebde716-3618-4b63-99af-cd43b613d7f1","title":"For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)","difficulty":"Medium","slug":"/question/for-2-leq-r-leq-n-binom-n-r-2binom-n-r-1-binom-n-r-2","subject":"Mathematics","topic":"Permutations and Combinations"},{"id":"67c07089-0568-4939-a715-f4f9efe86591","title":"Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated, is","difficulty":"Medium","slug":"/question/ten-different-letters-of-an-alphabet-are-given-words-with-five-letters-are-formed-from-these-given-l","subject":"Mathematics","topic":"Permutations and Combinations"},{"id":"718028ee-ee4a-4e36-b05a-ec1c97fcfd49","title":"Let P(S) denote the power set of S = { 1,2,3,...,10}.\n\n Define the relations R_{1} and R_{2} on P(S) as\n\n AR_{1}B if\n\n ( A cap B^{C} ) cup ( B cap A^{C} ) = phi\n\n and AR_{2}B if cup B^{C} = B cup\n\n A^{C},forall A,B in P(S). Then","difficulty":"Medium","slug":"/question/let-P-S-denote-the-power-set-of-S-12310-Define-the-relations-R-1-and-R-2-on-P-S-as-AR","subject":"Mathematics","topic":"Relation"},{"id":"9f72ddfd-3092-43e9-991e-3c98c456b11e","title":"The area of the region (x,y):y^2≤4x,x<4,\\frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,x≠3 is","difficulty":"Medium","slug":"/question/the-area-of-the-region-begincasesxyy24xx4fracxyx-1x-2x-3x-40x3endcases-is","subject":"Mathematics","topic":"Area of Bounded Region"},{"id":"95f81c71-79ca-440c-a306-c7747460e6ed","title":"Let R be the set of real numbers.\n\n \n\nend{enumerate}\n\n\n\nStatement-1: A = {(x,y) in R X R:y - x is an integer }\n\nis an equivalence . relation on R.\n\nStatement-2: B = {(x,y) in R X R:x = alpha y for some\n\nrational number } is . an equivalence relation on R.","difficulty":"Medium","slug":"/question/let-R-be-the-set-of-real-numbers-Statement-1-A-xy-in-R-X-Ry-x-is-an-integer-is-an-equivalence-relation-on-R","subject":"Mathematics","topic":"Relation"}],"currentSlug":"if-cr-equiv-25cr-and-c0-5c1-9c2-101c25-225k-then-k-is-equal-to"}]}],"$L1f","$L20"]