﻿ The equation esinx-e-sinx -4 = 0 has from Mathematics Class 12 JEE Year 2012 Free Solved Previous Year Papers

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# JEE Mathematics 2012 Exam Questions

#### Multiple Choice Questions

1.

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

• 5π/6

• π/6

• π/4

• 3π/4

B.

π/6

3 sin P + 4 cos Q = 6 ...... (1)
4 sin Q + 3 cos P = 1 ...... (2)
From (1) and (2) ∠P is obtuse.
(3 sin P + 4 cos Q)2+ (4 sin Q + 3 cos P)2= 37
⇒9 + 16 + 24 (sin P cos Q + cos P sin Q) = 37
⇒ 24 sin (P + Q) = 12

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2.

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

• 29/5

• 5

• 6

• 11/5

C.

6

Line L : 2x +y = k passes through the point (say P) which divides a lie segment (say AB) in ratio 3:2 where A (1,1) and B (2,4).
Using section formula, the coordinates of the point P which divides AB internally in the ratio 3:2 are

Also, since the line L passes through P, hence substituting the coordinates of   in the equation of line L: 2x +y = k,
we get

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3.

Let x1, x2, ......, xn be n observations, and let be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ2.
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4.

• Statement 1 is false, statement 2 is true

• 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

D.

Statement 1 is true, statement 2 is false

is the AM and σ2 is the variance of n observations x1, x2, x3......xn
AM of 2x1, 2x2, 2x3, .......2xn

Hence, it prove that statement 2 is false.

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4.

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: , for any natural number n.

• Statement 1 is false, statement 2 is true

• 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

B.

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Statement 1 has 20 terms whose sum is 8000 And statement 2 is true and supporting statement 1.
kth bracket is (k – 1)2 + k(k – 1) + k2 = 3k2 – 3k + 1.

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5.

The negation of the statement “If I become a teacher, then I will open a school” is

• I will become a teacher and I will not open a school

• Either I will not become a teacher or I will not open a school

• Neither I will become a teacher nor I will open a school

• I will not become a teacher or I will open a school

A.

I will become a teacher and I will not open a school

Let us assume that
p: I become a teacher' and
q: I will open a school

Then, we can easily as certain that
Negation of (p →q)

~(~p ∨ q) = p ∧ ~q
Which means that ' l' will become a teacher and I will not open a school.

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6.

The equation esinx-e-sinx -4 = 0 has

• infinite number of real roots

• No real root

• exactly one real root

• exactly four real roots

B.

No real root

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7.

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

•  –150

• 150

• times its 50th term

• 0

D.

0

The 150 th term of this AP
Let a be the first term and d be the common difference of the given AP, then
T100 =  a+ (100-1)d = a + 99d
T50 = a +(50-1)d = a +49 d
T150 = a + (150-1) d = a +149 d
Now, according to the question,
100 x T100 = 50 x T50
⇒ 100 (a +99d) = 50(a +49d)
2(a +99d) = (a+ 49d)
2a +198 d =a +49d
a +149d = 0

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8.

If n is a positive integer, then  is

• an irrational number

• an odd positive integer

• an even positive integer

• a rational number other than positive integers

A.

an irrational number

Adding both the binomial expansions above, we get
It is the irrational number because of odd power of  appears in each of the terms.

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9.

Statement I An equation of a common tangent to the parabola  and the ellipse 2x2 +y2 =4 is .
Statement II If the line  is a common tangent to the parabola  and the ellipse 2x2 +y2 =4, then m satisfies m4 +2m2 =24

• Statement 1 is false, statement 2 is true

• 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

C.

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

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10.

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

• x – 2y + 2z – 3 = 0

• x – 2y + 2z + 1 = 0

• x – 2y + 2z – 1 = 0

• x – 2y + 2z + 5 = 0

A.

x – 2y + 2z – 3 = 0

Perpendicular distance of the plane ax +by + cz +d =0 from the point
(x,y,z) is d =
Equation of plane parallel to x – 2y + 2z – 5 = 0 is x – 2y + 2z + k = 0 ...... (1)

perpendicular distance from O(0, 0, 0) to (1) is 1

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