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# JEE Mathematics 2010 Exam Questions

#### Multiple Choice Questions

11.

Let A be a 2 × 2 matrix with non-zero entries and let A2 = I, where I is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.
Statement-1: Tr(A) = 0.
Statement-2: |A| = 1.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is false, Statement-2 is true.

C.

Statement-1 is true, Statement-2 is false.

A satisfies A2 -Tr(A). A + (det A) l = 0
on comparing with A2-I = 0,
we get
Tr (A) = 0, |A| = - 1

152 Views

12.

If two tangents drawn from a point P to the parabola y2= 4x are at right angles, then the locus of P is

• X = 1

• 2x +1 = 0

• x = -1

• 2x-1 = 0

C.

x = -1

We know that the locus of point P from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola.
Hence, the required locus is x = -1

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13.

let f : (-1, 1) → R be a differentiable function
with f(0) = -1 and f'(0) = 1.
Let g(x) = [f(2f(x) + 2)]2. Then g'(0) =

• 4

• -4

• 0

• -2

B.

-4

g(x) = (f(2(f(x) + 2))2
g'(x) 2f (2f (x) 2) f '(2f (x) 2) 2f '(x)
g'(0) 2f (2f (0) 2) f '(2f (0) 2) 2f '(0)
= 4f(0) × (f '(0))2– 4

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14.

The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

• less than 4

• 5

• 6

• atleast 7

D.

atleast 7

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15.

Let f : R → R be a positive increasing function with

• 1

• 2/3

• 3/2

• 3

A.

1

Since f(x) is a positive increasing function.
⇒ 0< f(x)<f(2x)<f(3x)
⇒ 0<1<

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16.

Let f : R → R be defined by

If f has a local minimum at x = - 1 then a possible value of k is

• 1

• 0

• -1/2

• -1

C.

-1/2

k – 2x > 1 k + 2 = 1
k > 1 + 2x k = -1
k > 1 + 2(-1)
k > -1

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17.

The equation of the tangent to the curve, that is parallel to the x-axis, is

• y = 0

• y = 1

• y = 3

• y =2

C.

y = 3

On differentiating w.r.t, we get
dy/dx = 1-8/x3
since the tangent is parallel to X-axis, therefore
⇒ x3 = 8
⇒ x = 2 and y = 3
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18.

Let f : R → R be a continuous function defined
by f(x) = 1/ex + 2e-x
Statement - 1: f(c) = 1/3, for some c ∈ R.
Statement-2: 0 < f(x)≤ , for all x ∈ R.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is false, Statement-2 is true.

A.

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement I us true and statement I as for some 'c'
f(c) = 1/3
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19.

Statement-1: S3 = 55 × 29.
Statement-2: S1 = 90 × 28 and S2 = 10 × 28.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is false, Statement-2 is true.

C.

Statement-1 is true, Statement-2 is false.

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20.

Consider the system of linear equation
x1 + 2x2 + x3 = 3
2x1 + 3x2 + x3 = 3
3x1 + 5x2 + 2x3 = 1
The system has

• infinite number of solutions

• exactly 3 solutions

• a unique solution

• no solution

D.

no solution

Subtracting the Eq. (ii) – Eq. (i)
We get x1 + x2 = 0
Subtract equations
Eq. (iii) – 2 × eq. (ii)
x1 + x2 = 5

Therefore, no solutions

146 Views