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# JEE Mathematics Solved Question Paper 2012

#### 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) = 12 163 Views

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 224 Views

3.

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 1 457 Views

4.

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

263 Views

5.

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.

178 Views

6.

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.

208 Views

7.

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 312 Views

8.

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 1 197 Views

9.

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.

213 Views

10.

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.

170 Views