maths

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


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


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)





If tan 25 = x, then is equal to

(A) (B) (C) (D)

Hint:



simplifies to :

(A) (B) (C) (D) none of these

Hint:



The number of real points at which line 3y 2x = 14 cuts hyperbola = 5 is



(A) 0 (B) 1 (C) 2 (D) 4

Hint:

Correct Answer : (B) Your Answer : Not Answered Marks: 0 Top


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



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:





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:



If z and are two complex numbers such that then locus of is

(A) real axis (B) imaginary axis (C) circle (D) ellipse

Hint:



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:





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


The solution of the equation y2x dx + ydx xdy = 0 is

(A) (B) (C) (D)

Hint:



is equal to

(A) (B) 0 (C) 1 (D) 3

Hint:





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]



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



If then a equal to

(A) (B) (C) 24 (D) 6



Hint:



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.



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:





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.



Equation x2 + y2 + x + y + (x2 + y2 2x + 2y + 5) = 0 represents a circle if

(A)R {1} (B) (C) (D)

Hint:



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:





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



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:





If (y2 5y + 3)(x2 + x + 1) < 2x x R then y lies in interval

(A) (, 2] (B) (C) (D)

Hint:



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:





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:



If differentiable function f(x) is inverse of g(x) then f (g(x)) is equal to

(A) (B) 0 (C) (D) 1

Hint:





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



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


Copyright 2011 Texel Graphics Web Solutions

maths

Documents

numberd x

numberb x

tan x y

straight objective typeif

straight objective typelet

zaxis thencorrect answer

negative marks

max marks