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Ute bere hott Merete ek vd, , } Nucleus Tutorials, , Pioneer Tustitute of Gcience, , D4 an ee & Advanced),NEET, |.Sc./B.Sc/l.Com, , , , 1. Let S be the set of all real numbers and R be a relation defined by aRb iff, la — b| <= 1. Then Ris, (a) Reflexive and symmetric but not transitive., (b.) Reflexive and transitive but not symmetric., (c.) | Symmetric and transitive but not reflexive., (d.) An equivalence relation., 2. Let Z be the set of all integers then the operation + on Z defined by a*tb=a+b-ab, is, (a) Commutative but not associative., (b.) Associative but not commutative., (c.) Neither commutative nor associative., (d.) Both commutative and associative., , = (n+ 1); when n is odd, , , , 3. Let f:N + N: f(n) =}? Then f is, fh ahi @) =; when n is even. f, (a) One -one and into. (b.) one -one and onto., (c.) many one and into a. ) many one and onto., 4. Let f R-{=}= r-}: 609 =. Then, f*0) =?, ay ay, @s xs bs oa Oss (d.) none of these., 5. If to==*, x # Ethen (fof)(x) =?, (a) x (b.) (2x-3) — (c) = (d) none., 6. The value of cos-? (cos) is, @m= we (= (ae, 7. The principal value of cot! (—y3) is, @= (b) = oF @=, 8. tant aay =?, @s w= oz @2, 9. tan{cos™* : +tan™* j=, @Me we oz (2, 2x-y -1 0, 10. “ZS”, =+ul* [5 13] then, , (a) z= 3, w=4 (b) z=4,w=3

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(c)z=1w=2 (d)z =2, w=-1, 11. IfAisa square matrix such that |A] #0; and A? + 2/ = O then A“=?, , (@i-A) — () +A) (FU-A) (d= +A), , , , , , , , 1 ww w, 12. If w isa complex cube rootofunitythen]q@ q@? 1/=?, jw 1 w, (a)1 (b)-1 (c) 0 (d) none of these, at+ib c+ib, 3 ia a ibn?, (a) (a? + b? — c* — d*) (b) (a? — b? +c? — d?), (c) (a? + b? +c? +d?) (d) none of these, b+c a a, 14.) b c+a bb |=?, c c atb, (a) 4abe (b) 2(a+ b+ c) (c) (ab+ be+ ca) (d) none of these, , at+x a-x a-x, ja-~x atx a~x| =0is, jaa—-x a-x atx, , 15. The solution set of the equation, , , , (a) {a , 0} (b) {3a ,0} (c) {a , 3a} (d) none of these, 16. If A is an invertible square matrix then |A~'| =?, (a)|Al oF (c)1 (d)0, 17. If A is singular then A (adj A) =?, (a) a unit matrix (b) a null matrix, (c) a symmetric matrix (d) none of these, 18. 1f (x +y) = sin (x+ y) then =?, 1—cos(x+y), (a) -1 (b) 1 Oman (d)none of these, , 19. Ifx” = y* then=?, , , , , , , , (a) Se (b) an © eee) (d)none of these, 20. If y =cos~* &) then 2 =?, , Ms Oss Ons (d) none of these, 21. Ifx = asec 0, y = btan@ then =?, , (a) seco (b}? cosec 4 (c)Pcota (d) none of these, , 1-cos 4x, , 22. If the function f(x) = {= x #0, k,x=0, , (a1 (b)2 r @>, , is continuous at x= 0 then k=?

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keosx, , 23. If the function f(x) = 4 "2 ., 3, when x = 7, , when x # = 7, be continuous at x = > then the value, , of kis, (a)3 (b)-3 (c)-5 (d)6, , 24. The function f(x) = x3 — 6x + 15x — 12 is, (a) strictly decreasing on &, (b) strictly increasing on R, (c) increasing in (—o , 2] and decreasing in (2 ,), (d) none of these, 25. f(x) = (sinx — cos x) is decreasing in, , (a(o= (b) (4.4) (©)(=. 2m) (d)none of these, 26. The minimum value of f (x) = 3x* — 8x3 — 48x + 25 on [0,3] is, , (a) 16 (b) 25 (c)-39 (d) none of these, 27. The maximum value of f (x) = (x — 2)(x — 3)? is, , (a2 (b)3 jos (a) 0, 28.1fy = x*"* then 2?, , (a) (sin x) . x(8in2-2) (b) (sin x cos x) .xB*-)), , (c) x8in= Je] (d) none of these, 29. f(x) = (x + 133 (x — 3) is increasing in, , (a)(—%, 1) (b) (-1, 3) (c) ((3, 0) (d) (—99, 0), 30. f (x) = [x(x — 3)} is increasing in, , (a) (0) (b) (—©, 0) © (3) (4)(0,2) v 3,2), , 31.1f £R— Rhe given by (4) = (3—28)3, then Hix) is, , (A)x¥3 (BY ae (C) x (D) (3 - 9), 32. If f: N — R be a function defined as /(x)= 4x24+12x+15 then inverse of, fisamap g: Range /-N given by, , Weo-=2 @ew=- @em==== CWMNone., , i ay _, 33.1f x/T+y+yv14+x=0, then =?, x -1 -1, O= Ms (c)1 Oger, , it¢tx, 34. If y = (sin~! x)?, then the value of (1 — x2)y2—xy1 is:, (A) 2 (B)1 (C) -—2 (D) 0, 35. The equation of the normal to the curve y=x?+4x+1 at the point where x=3 is, (A) x+10y—223=0 (B) 10x—y — 278 = 0, (C) x+10y+223=0 (D) 10x—y + 278 = 0