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4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 1/12
Test Review : Free Test - 1 Home | Logout [[email protected]]
Correct: | Incorrect: | Partly correct: | Not Answered:
Total Que: 90 | Max Marks: 360 | Attempted: 2 | Correct: 1 | Total Marks Obt: 3 | Negative Marks: -1
Que 61 Straight Objective Type
The mean of five observations is 4 and their variance is 5.2. If three observations are 1, 2, and 6, then the remaining data are
(A) 2 and 9 (B) 3 and 8 (C) 4 and 7 (D) 5 and 6
Hint: No hint available.
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 62 Straight Objective Type
The statement x is an even number implies that x is divisible by 4 means the same as
(A) x is divisible by 4 is necessary condition for x to be an even number
(B) x is an even number is a necessary condition for x to divisible by 4
(C) x is divisible by 4 is a sufficient condition for x to be an even number
(D) x is divisible by 4 implies that x is not always an even number
Hint: No hint available.
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 63 Straight Objective Type
The graph of f(x) = + 5 has
(A) no local extreme, one point of inflection (B)Two local maximum one local minimum, two point of
inflection
(C)One local maximum, one local minimum, one point of
inflection(D)
One local maximum, one local minimum, two point of
inflection
Hint:
Physics (30) Chemistry (30) Maths (30)
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 2/12
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 64 Straight Objective Type
If tan 25 = x, then is equal to
(A) (B) (C) (D)
Hint:
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 65 Straight Objective Type
simplifies to :
(A) (B) (C) (D) none of these
Hint:
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 66 Straight Objective Type
The number of real points at which line 3y 2x = 14 cuts hyperbola = 5 is
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 3/12
(A) 0 (B) 1 (C) 2 (D) 4
Hint:
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 67 Straight Objective Type
The shortest distance between the z -axis and the line, x + y + 2z 3 = 0, 2x + 3y + 4z 4 = 0 is
(A) 1 (B) 2 (C) 3 (D) 0
Hint:
The equation if any plane containing the given line is (x + y + 2z 3) + (2x + 3y + 4z 4) = 0
(1 + 2)x + (1 + 3) y + (2 + 4)z (3 + 4) = 0 ...... (i)
If this plane is parallel to z-axis then
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 68 Straight Objective Type
The number of values of x in the interval satisfying the equation 6sin2x + sin x 2 = 0 is
(A) 9 (B) 10 (C) 11 (D) 12
Hint:
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 4/12
Que 69 Straight Objective Type
Let the angles A, B, C of a triangle ABC be in AP and b : c = , then A =
(A) 15 (B) 75 (C) 105 (D) 115
Hint:
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 70 Straight Objective Type
If z and are two complex numbers such that then locus of is
(A) real axis (B) imaginary axis (C) circle (D) ellipse
Hint:
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 71 Straight Objective Type
System of equations x + 2y + z = 0, 2x + 3y z = 0 and (tan) x + y 3z = 0 has non-trivial solution then number of value(s) of
(, ) is equal to
(A) 0 (B) 1 (C) 2 (D) 3
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 5/12
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 72 Straight Objective Type
If the coefficients of second, third and fourth terms in the expansion of (1 + x)2n are in A.P., then which of the following is true.
(A) n2 9n + 7 = 0 (B) 3n2 9n + 7 = 0 (C) 3n2 + 9n + 7 = 0 (D) 2n2 9n + 7 = 0
Hint:
2nC1 , 2nC2 ,
2nC3 are in A.P
2n2 9n + 7 = 0
Correct Answer : (D) Your Answer : Not Answered Marks: 0 Top
Que 73 Straight Objective Type
The solution of the equation y2x dx + ydx xdy = 0 is
(A) (B) (C) (D)
Hint:
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 74 Straight Objective Type
is equal to
(A) (B) 0 (C) 1 (D) 3
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 6/12
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 75 Straight Objective Type
The interval [a, b] such that the value of is maximum is
(A) [1, 2] (B) [2, 1] (C) [2, 1] (D) [1, 2]
Hint:
The expression 2 + x x2 is non-negative in [1, 2]
2 + x x2 ] [1, 2]
Thus [a, b] should be [1, 2]
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 76 Straight Objective Type
If a, b, c R, a 0 and the equation ax2 + bx + c = 0 has no real root, then
(A) (a + c)2 < b2 (B) (a + c)2 = b2 (C) (a + c)2 > b2 (D) a + c2 = b2
Hint:
b2 4ac < 0 b2 < 4ac
also (a c)2 0 a2 + c2 2ac
2ac a2 + c2
Adding the two inequalities,
b2 + 2ac < a2 + c2 + 4ac b2 < (a + c)2
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 77 Straight Objective Type
If then a equal to
(A) (B) (C) 24 (D) 6
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 7/12
Hint:
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 78 Straight Objective Type
The triangle formed by the tangents and latus rectum to a parabola y2 = 4ax at the ends of the latus rectum is
(A) equilateral (B) isosceles
(C) right-angled isosceles (D) dependent on the value of a for its classification
Hint:
The tangents intersects on the directrix
the triangle is right angled isosceles.
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 79 Straight Objective Type
A letter is known to have come either from "KRISHNAGIRI" or "DHARMAPURI". On the post mark only the two consecutive
letters "RI" are visible. Then the chance that it came from KRISHNAGIRI is:
(A) 3/5 (B) 2/3 (C) 9/14 (D) none of these
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 8/12
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 80 Straight Objective Type
Out of 8 sailors on a boat, 3 can work only on one side and 2 only on the other side. The number of ways the sailors can be
arranged on the boat is-
(A) 17000 (B) 1720 (C) 1728 (D) 1736
Hint:
Sailors required for each side = 8/2 = 4
Since 5(= 3 + 2) sailors can work only on specified sides, the remaining 3 (= 8 5) sailors would work on the boat so that there
are 4 sailors on each side.
No. of such selections = 3C1 = 3
No. of ways of arranging all sailors = 3 4 ! 4 ! = 1728.
Correct Answer : (C) Your Answer : Not Answered Marks: 0 Top
Que 81 Straight Objective Type
Equation x2 + y2 + x + y + (x2 + y2 2x + 2y + 5) = 0 represents a circle if
(A)R {1} (B) (C) (D)
Hint:
Correct Answer : (D) Your Answer : Not Answered Marks: 0 Top
Que 82 Straight Objective Type
The equation of an ellipse, whose axes are the coordinate axes, minor axis is equal to distance between the focii and latus
rectum equals to 10, is
(A) x2 + y2 = 100 (B) 4x2 + y2 = 50 (C) 4x2 + y2 = 36 (D) x2 + 2y2 = 100
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 9/12
Correct Answer : (D) Your Answer : Not Answered Marks: 0 Top
Que 83 Straight Objective Type
Let A = {p, q, r}. Which of the following is an equivalence relation in A ?
(A) R1 = {(p, q), (q, r), (p, r), (p, p)} (B) R2 = {(r, q), (r, p), (r, r), (q, q)}
(C) R3 = {(p, p), (q, q), (r, r), (p, q)} (D) None of these
Hint:
R1 is not reflexive, because (q, q), (r, r) R1.
R1 is not an equivalence relation.
R2 is not symmetric because (q, r)(p, r) R2.
R2 is not an equivalence relation
R3 is not symmetric, because (p, q) R3 but (q, p) R3
Correct Answer : (D) Your Answer : Not Answered Marks: 0 Top
Que 84 Straight Objective Type
Let f : R R and g : R R be two one-one and onto functions such that they are the mirror images of each other about the
line y = a. If h(x) = f(x) + g(x), then h(x) is
(A) one-one and onto (B) one-one and into (C) many-one onto (D) many-one and into
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 10/12
Correct Answer : (D) Your Answer : Not Answered Marks: 0 Top
Que 85 Straight Objective Type
If (y2 5y + 3)(x2 + x + 1) < 2x x R then y lies in interval
(A) (, 2] (B) (C) (D)
Hint:
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 86 Straight Objective Type
If a, b, c are in H.P. then which of the following is not true.
(A) are in H.P. (B) are in H.P.
(C) are in G.P. (D) e1/a, e1/b, e1/c are in G.P.
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 11/12
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 87 Straight Objective Type
Number of integral solutions of equation (x + 2)(x + 3)(x + 8)(x + 12) = 4x2 is
(A) 4 (B) 2 (C) 0 (D) 1
Hint:
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 88 Straight Objective Type
If differentiable function f(x) is inverse of g(x) then f (g(x)) is equal to
(A) (B) 0 (C) (D) 1
Hint:
4/7/2014 Review Test Paper
http://jee.raoiit.com/main/rold.php?paperid=1 12/12
Correct Answer : (A) Your Answer : Not Answered Marks: 0 Top
Que 89 Straight Objective Type
A question paper consists of two parts A and B. Part A has 4 questions with an alternative and part B has 3 questions without
any alternative. The number of ways to attempt paper when at least one question must be attempted for each part is (are)
(A) 561 (B) 560 (C) 648 (D) 127
Hint:
Required ways = (34 1)(23 1) = 560
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
Que 90 Straight Objective Type
Two sides of a rhombus are parallel to the lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at the point
(1, 2) and the vertex A lies on the y-axis and coordinate of A are (0,) then can be
(A) 1 (B) 5/2 (C) 3/2 (D) 1
Hint:
Distance between AB and CD = distance between AD and BC
Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top
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