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JEE Mathematics Solved Question Paper 2013

Multiple Choice Questions

21.
If P = $open square brackets table row 1 straight alpha 3 row 1 3 3 row 2 4 4 end table close square brackets$ is the adjoint of a 3 x3 matrix A and |A| = 4, then α is equal to

4

11

5

5

Given,
$straight P space equals space open square brackets table row 1 straight alpha 3 row 1 3 3 row 2 4 4 end table close square brackets$
|P| = 1(12-12)-α (4-6) +3(4-6)
= 2α -6.
∵ P =adj(A)
∴ |P| = |adj A | = |A|3-1 = |A|2 = 16
[∵ |adj A| = |A|n-1 order is 3 x3
∴ 2α -6 = 16
2α = 22
α = 11

547 Views

22.

If y = sec (tan^-1 x), then dy/dx at x = 1 is equal to

$fraction numerator 1 over denominator square root of 2 end fraction$
$1 half$
1
1

593 Views

23.

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

250 Views

24.

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by $dP over dx space equals space 100 minus 12 square root of straight x$ . If the firm employs 25 more workers, then
the new level of production of items is

2500
3000
3500
3500

147 Views

25.

If the lines

$fraction numerator straight x minus 2 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 1 end fraction space equals space fraction numerator straight z minus 4 over denominator negative straight k end fraction and fraction numerator straight x minus 1 over denominator straight k end fraction space equals space fraction numerator straight y minus 4 over denominator 2 end fraction space equals space fraction numerator straight z minus 5 over denominator 1 end fraction$
are coplanar, then k can have

any value
exactly one value
exactly two values
exactly two values

157 Views

26.

If the vectors AB = 3î + 4k̂ and AC = 5î - 2ĵ + 4k̂ are the sides of a Δ ABC, then the length of the median through A is

√18
√72
√33
√45

174 Views

27.

If ∫f x dx =Ψ (x),then ∫x⁵ f(x³)dx is equal to

$1 third space open square brackets straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx close square brackets space plus straight C$
$1 third space straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus 3 integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus straight C$
$1 third straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus space straight C$
$1 third straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus space straight C$

191 Views

28.

Statement I - The value of the integral $integral subscript straight pi divided by 6 end subscript superscript straight pi divided by 3 end superscript fraction numerator dx over denominator 1 plus space square root of tan space straight x end fraction$ is equal to π/6.
Statement II- $integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx space equals space integral subscript straight a superscript straight b straight f left parenthesis straight a plus straight b minus straight x right parenthesis space dx$

Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
Statement -I is True; Statement -II is False.
Statement -I is True; Statement -II is False.

120 Views

29.

The area (in square units) bounded by the curves y = $straight y space equals space square root of straight x comma$ 2y-x+3 =0, X -axis and lying in the first quadrant is

154 Views

30.

The intercepts on X- axis made by tangents to the curve, $straight y space equals space integral subscript 0 superscript straight x vertical line straight t vertical line space dt comma space straight x space straight epsilon space straight R$ which are parallel to the line y =2x, are equal to