iit pattern maths paper

MATHS PAPER 1SECTION 1 (+4/-1) SINGLE CORRECTQ1 is equal to(a) (b) (c)(d) none of these Q2If then it (where { } FP of x) is.(a)1(b) 2(c)e(d) none of these Q3Suppose be a function defined by f(x) = max(sin x, tan2 x) then no. of points where f(x) is non differentiable is:(a)2(b) 3(c)4(d) none of these Q4If for a complex number z = x + iy amp, then maximum value of |z| is (A) 1 –(B) 1 + (C) (D) 2 Q5A,B and C are points represented by complex numbers z1, z2 and z3. If the circumcentre of the triangle ABC is at the origin and the altitude AD of the triangle meets the circumcircle again at P, then P represents the complex number (A) – (B) –(C) –(D) Q6If the equation |z – z1|2 + | z – z2|2 = k represents the equation of a circle, where z1 2+ 3i, z2 4 + 3i are the extremities of a diameter, then the value of k is (A)(B)4(C)2(D)None of these Q7If ||z + 2| |z 2|| = a2, z C is representing a hyperbola for a S, then S contains(A)[1, 0](B)(, 0](C)(0, )(D)none of these Q8The function f(x) = max {1 – x, 1 + x, 2}, x (- , ) is (A) continuous at all points (B) differentiable at all points (C) differentiable at all points except at x = 1 and x = -1 (D) continuous at all points except at x = 1 and x = -1, where it is continuous. Q9 Let f(x) = [tan2x][cot2x] where [] denotes greatest integer function then number of points at which function f(x) is discontinuous in (0, 2)(A) 0(B) 3(C) 4(D) 7 SECTION-2(+4/-1)COMPREHENSION1Read the following writeup carefully:If f(x) = max(|x2 – 1|, |x – 1|) and g(x) = ; x R.Now answer the following questions:Q10The value of f(x) is (A) f(x) = (B) f(x) = (C) f(x) = (D) f(x) = Q11The function f(x) is continuous for x belongs to(A) R – {0, 1}(B) R – {– 2, 0, 1}(C) R(D) none of these Q12The function g(x) is differentiable for (A) R – {0, 1}(B) R – {–2, 0, 1}(C) R(D) none of these COMPREHENSION2Read the following writeup carefully:In argand plane |z| represent the distance of a point z from the origin. In general |z1 – z2| represent the distance between two points z1 and z2. Also for a general moving point z in argand plane, if arg(z) = , then z = |z|ei, where ei = cos + i sin.Now answer the following questions Q13.The equation |z – z1| + |z – z2| = 10 if z1 = 3 + 4i and z2 = – 3 – 4i represents(A) point circle(B) ordered pair (0, 0)(C) ellipse(D) none of theseQ14||z – z1| – |z – z2|| = t, where t is a real parameter always represents (A) ellipse (B) hyperbola (C) circle(D) none of these Q15If |z – (3 + 2i)| = , then locus of z is (A) circle(B) parabola (C) ellipse (D) hyperbola Q16If z1 = 4ei/3 and z2 = 2ei5/6, then |z1 – z2| equals (A) 20(B) (C) (D) SECTION3Q17 COLUMN MATCHING(each matching 2 marks)(multiple match)Column 1Column2(A) (p) continous in (-2,2)(B) (q) non differentiable at 3 points in (-2,2)(C) (r) monotonically increasing in (-2,2)(D) (s) discontinous at 2 points in (-2,2)SECTION 4SUBJECTIVE (+3/0) Q18 If is purely real, find the locus of z.Q19 Find the right hand derivative of f (x) = [x] sin x at x = n, where n I.Q20 f(x) = find the value of k so that function becomes continuous at all x I.