[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143481-105":59,"doc-detail-143481-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","mscit-entrance-test-paper-sample","M.Sc.(IT) Entrance Test Paper - Sample","","M.Sc. (IT) entrance test sample paper featuring Section-A with 100 MCQs, total time of 2 hours and total marks 200. The questions cover calculus and differential concepts including derivatives, Leibniz and Rolle’s/Mean Value Theorems, series expansion, polar curve intersection and orthogonality, curvature, envelopes, and partial derivatives. It also includes probability via defective notebook selection, Jacobians, Jacobian-based relations, and implicit differentiation problems.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mscit-entrance-test-paper-sample/143481/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mscit-entrance-test-paper-sample/143481.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",22,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the structure and total scoring of the M.Sc. (IT) entrance test sample paper?","Question",{"text":113,"@type":114},"The paper contains Section-A with Mathematics MCQs, 100 questions in total, total time of 2 hours, and total marks of 200.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which calculus topics are included in the Mathematics MCQs?",{"text":118,"@type":114},"The questions include derivatives of functions, Leibniz rule, Rolle’s theorem and its interpretation, Mean Value Theorem, curvature and envelopes, Taylor/Maclaurin series, and implicit/parametric differentiation.",{"name":120,"@type":111,"acceptedAnswer":121},"Does the sample paper include non-calculus concepts as well?",{"text":122,"@type":114},"Yes. It includes probability based on defective notebooks supplied by different companies and also includes topics like Jacobians and related coordinate transformation ideas.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},143481,1787695355,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","M.Sc. (IT) Entrance Test Paper (Sample)  \nName: Roll Number:  \nTotal Time :-2 Hours Questions: 100 MCQs Total Marks :-200  \nSECTION-A  \nMATHEMATICS QUESTIONS  \n1. The first and second derivatives of a quadratic Polynomial at x = 1 are 1 and 2 respectively. Then the value off(1)– f(0) Is given by?  \na. 3⁄2 b. 1⁄2 c. 1 d. 0  \n2. nth derivative of Sinh(x) is  \na. 0.5(ex – e-x) b. 0.5(e-x – ex) c. 0.5(ex –(-1)n e-x) d. 0.5((-1)-n e-x-ex)  \n3. Let f(x) = sin(x)/1+x2. Let y(n) denote the nth derivative of f(x) at x = 0 then the value of y(100) + 9900y(98) is  \na. 0 b. -1 c. 100 d. 1729  \n4. Let f(x) = ex sin(x2)⁄x Then the value of the fifth derivative at x = 0 is given by  \na. 25 b. 21 c. 0 d. 5  \n5. Leibniz rule gives the  \na. Nth derivative of addition of two function  \nb. Nth derivative of division of two functions  \nc. Nth derivative of multiplication of two functions  \nd. Nth derivative of subtraction of two function  \nsin(x)  \n6. For the function f(x) = x2 , How many points exist in the interval [0, 7π] Such that f'(c) = 0.  \na. 8 b. 0 c. 7 d. 6  \n7. Rolle’s Theorem is a special case of  \na. Lebniz Theorem  \nb. Mean Value Theorem  \nc. Taylor Series ofa function  \nd. Leibnit’x Theorem  \n8. For the function f(x) = x2 – 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?  \na. 3⁄2 b. 1⁄2 c. 5⁄2 d. 1  \n9. Mean Value Theorem tells about the  \na. Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable  \nb. Existence of point c in a curve where slope of a tangent to curve is equal to zero  \nc. Existence of point c in a curve where curve meets y axis  \nd. Existence of point c in a curve where curve meets x axis  \n10. The Mclaurin Series expansion of sin(ex) is?  \nx cos(1) 􀁦 􀁦 xn .(􀀐1)a (2a􀀎1)n  \na. sin(1)+  1!  +  0  n!  􀁵  (2a􀀎1)! ex e3x e5x  \nb. ~~ ~~ 􀀎  􀀎 ~~ ~~  􀁦 1! 3! 5! ex e3x e5x  \nc. 􀀐  􀀎 ~~ ~~ 􀀐 ~~ ~~  􀁦 1! 3! 5!  \n􀁦 􀁦 xn .(􀀐1)a (2a􀀎1)n  \nd.  0  n!  􀁵  (2a􀀎1)!  \n11. Find lxim􀁯􀁦(1 􀀎 x2~~ ~~􀀎~~ ~~12x~~ ~~􀀎1)x2 􀀎3x􀀎1  \na. e b. 1 c. e2 d. 1⁄e  \n12. Angle of intersection of two polar curves is equal to the angle between the tangents drawn at the point of intersection of the two curves then What is the condition for the two curves intersecting orthogonally for the below mentioned figure?  \na. tan􀁍1.tan 􀁍3 􀀠 1  \nb. tan􀁍1.tan 􀁍3 􀀠􀀐 1  \nc. tan(􀁍1􀀎􀁍3) 􀀠  1   2  \nd. tan(􀁍1􀀐􀁍3) 􀀠  1   2  \nx   ds  \n13. For the curve y 􀀠 alog sec( ) what is the value of ? (where φ is the angle made by tangent to  \na dx  \nthe curve with x-axis)?  \na. cos φ b. sec φ c. tan φ d. cot φ  \n14. The curvature of a function f(x) is zero. Which of the following functions could be f(x)?  \n[a. ax](a. ax) + b [b. ax](b. ax2)[2](b. ax2) + bx + c c. sin(x) d. cos(x)  \n15. Envelope of a family of curves can be defined as    \na. A curve which touches 50% of the family of curves  \nb. A curve which is a straight line  \nc. A curve which touches each member of the family of curves  \nd. A curve which surrounds the family of curves  \n􀂧􀀐1 􀀐1 2 􀂷  \n3 􀂨  \n16. Find the value of A where A= 􀂨 0 1  \n􀂩􀂨 2 2  \n􀂸  \n􀀐1 􀂸  \n1 􀂹􀂸  \n􀂧 3  \n􀂨 a. 􀂨 􀀐2  \n􀂨  \n􀂩􀀐2  \n5  \n􀀐9  \n􀀐4  \n􀀐1􀂷􀂸  \n2 􀂸􀂸  \n􀀐5 􀂹  \n􀂧 3  \n􀂨  \nb. 􀂨 1  \n􀂨  \n􀂩􀀐2  \n5  \n􀀐9  \n􀀐4  \n􀀐1􀂷􀂸  \n1 􀂸􀂸  \n􀀐5 􀂹  \n􀂧 3  \n􀂨 c. 􀂨 􀀐2  \n􀂨  \n􀂩􀀐2  \n5  \n􀀐9  \n􀀐4  \n􀀐1􀂷􀂸  \n1 􀂸􀂸  \n􀀐5 􀂹  \n􀂧 3  \n􀂨 d. 􀂨 􀀐1  \n􀂨  \n􀂩􀀐2  \n5  \n􀀐9  \n􀀐4  \n􀀐1􀂷􀂸  \n1 􀂸􀂸  \n􀀐5 􀂹  \n17. Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A?  \na. 44⁄69 b. 25⁄69 c. 13⁄24 d. 11⁄24  \n18. Find the derivative of: f (x) 􀀠 x  \na. 􀀐  1  b.  1  c.  1  d. x  \n2 x x 2 x  \n19. The pth derivative of a qth degree monic polynomial,","cbCaiq7Sc47UNZf8","https://ap.wps.com/l/cbCaiq7Sc47UNZf8","pdf",618674,15,"English","# Section-A\n## Mathematics Questions","[{\"question\":\"What is the structure and total scoring of the M.Sc. (IT) entrance test sample paper?\",\"answer\":\"The paper contains Section-A with Mathematics MCQs, 100 questions in total, total time of 2 hours, and total marks of 200.\"},{\"question\":\"Which calculus topics are included in the Mathematics MCQs?\",\"answer\":\"The questions include derivatives of functions, Leibniz rule, Rolle’s theorem and its interpretation, Mean Value Theorem, curvature and envelopes, Taylor/Maclaurin series, and implicit/parametric differentiation.\"},{\"question\":\"Does the sample paper include non-calculus concepts as well?\",\"answer\":\"Yes. It includes probability based on defective notebooks supplied by different companies and also includes topics like Jacobians and related coordinate transformation ideas.\"}]","M.Sc.(IT) Entrance Test Paper - Sample | PDF",38]