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IIT-JEE-Mathematics–Screening-2000
SCREENING
Time : Two hours
Max. Marks : 100
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PART A
1. Let f (θ) = sin θ (sin θ + sin 3 θ). Then f (θ) :
(A) ≥ 0 only when θ ≥ 0 (B) ≤ 0 for all real θ
(C) ≥ 0 for all real θ
(D) ≤ 0 only when θ ≤ 0
2. If x + y = k is normal to y2
= 12 x, then k is :
(A) 3
(B) 9
(C) –9
(D) –3
4. If a and β (α < β) are the roots of the equation x2 + bx + c = 0 , where
c < 0 < b, then :
(A) 0 < α < β
(B) α < 0 < β < │α│
(C) α < β < 0
(D) α < 0 < │α│< β
5. Let f : R → R be any function. Define g : R → R by g (x) = │f
(x) │for all x.
Then g is :
Onto if f is onto
One-one is f one-one
Continuous if, f is continuous
Differentiable if f is differentiable
6. The domain of definition of the function y (x) is given by the equation 2x+ 2y = 2 is :
(A) 0< x≤1
(B) 0≤x≤1
(C) -∞ < x ≤0
(D) -∞< x<1
7. If x2+ y2=1, then :
(A) yy'" - 2(y ' )2+1=0
(B) yy'' + (y ' )2+1=0
(C) yy " = (y ' )2-1=0
(D) yy''+2(y ' )2+1=0
8. If a,b, c, d are positive real numbers such that a + b + c + d = 2, then M =
(a + b) (c + d) satisfies the relation :
(A) 0 ≤ M ≤ 1
(B) 1 ≤ M ≤ 2
(C) 2 ≤ M ≤ 3
(D) 3 ≤ M ≤ 4
9. If the system of equations x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has
a non-zero solution, then possible values of k are :
(A) –1, 2
(B) 1, 2
(C) 0, 1
(D) –1, 1
10. The triangle PQR is inscribed in the circle x2+
y2=25. If Q and R have
coordinates (3, 4) and (–4, 3) respectively, then ∠PQR is equal to:
(A) π/2
(B) π/3
(C) π/4
(D) π/6
11. In a triangle ABC, 2ac sin 1/2 (A – B + C) =
(A) a2+b2-c2
(B)
c2+a2-b2
(C) b2-c2-a2
(D)
c2-a2-b2
12. For x Є
R, limn→∞((x-3)/(x+2))x =
(A) e
(B) e-1
(C) e-5
(D) e5
13. Consider an infinite geometric series with first term and common ratio r. If
its sum is 4 and the second term is 3/4, then :
(A) a=4/7, r=3/7
(B) a =2, r = 3/8
(C) a = 3/2, r = 1/2
(D) a = 3, r = 1/4
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