Solutions of JEE (Main)—Mathematics

Newspaper 2013

1 . The circle passing through (1, –2) and touching the

axis of by at (3, 0) also passes throughout the point

(a) (2, –5)

(b) (5, –2)

(c) (–2, 5)

(d) (–5, 2)

2 .

ABCD is known as a trapezium so that AB and CD happen to be parallel and BC ^ CD. In the event that –ADB = q, BC = g and DISC = q, then AB is corresponding to

2

a couple of

2

two

p +q

p & q cos q

(a)

(b) two

2

p cos q + queen sin queen

p cos q & q trouble q

two

2

a couple of

2

( p + q ) cos queen

( s + queen ) sin q

(c)

(d)

two

p cos q & q sin q

( p cos q + q desprovisto q)

3. Given: A group, 2x2 & 2y2 = 5 and a corsa

4 5x.

y2 =

Statement-I: An equation of a prevalent tangent to

these kinds of curves is definitely y sama dengan x & 5.

Statement-II: If the range, y = mx +

5

(m π 0) is

m

their common tangent, then m satisfies

2 + 2 sama dengan 0.

m4–3m

(a) Statement-I is true, Statement-II is true,

Statement-II is not just a correct explanation for

Statement-I

(b) Statement-I is true, Statement-II is bogus.

(c) Statement-I is false, Statement-II is true.

(d) Statement-I is true, Statement-II is true,

Statement-II is a right explanation intended for

Statement-I.

4. A ray of light along back button + a few y = 3 gets reflected

after reaching the x-axis, an formula of the mirrored ray is definitely

(a) = x – 3 (b) 3 times – 3

3y

y=

3y

(c) = back button –1

(d) y sama dengan x &

3

a few. All the registrants of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the pupils. Which of the following

record measures will not change also after the

(a)median

(b)mode

(c)variance

(d)mean

6. In the event that x, con, z are in A. S. and tan–1x, tan–1y and tan–1z are in A. P., then

(a)2x = 3y = 6z

(b)6x = 3y sama dengan 2z

(c)6x = 4y = 3z(d)= z

x=y

5

several

7. If Ú f(x)dx = y(x) then Ú x f(x )dx is definitely equal to

1 3

(a) 3) – Ú x3y (x3) dx + C

x y(x

3

you 3

(b) 3) – Ú x2y (x3) dx + C

x y(x

3

you 3

(c) y(x3) – Ú x3y (x3) dx ] + C

[x

3

one particular 3

(d) y(x3) – Ú x2y (x3) dx ] + C

[x

3

8. An equation from the circle passing through the focii

of the ellipse

x

2

18

+

y

2

being unfaithful

= one particular and having centre in (0, 3) is

(a) –6y & 7 sama dengan 0

by 2+ sumado a 2

(b) x2 + y2 –6y –5 = 0

(c) 2 – 6y + 5 sama dengan 0 (d) x2 & y2 –6y –7 = 0

x2 + con

on the lookout for. The x-coordinate of the incentre of the triangle

that has the coordinates of mid parts of its attributes

as (0, 1), (1, 1) and (1, 0) is

(a)2– 2

(b) you +

a couple of

(c) one particular –

(d) 2 &

2

two

2  JEE (Main)—Mathematics Daily news 2013

10. The intercepts upon x – axis of tangents towards the

x

curve, y =

Ú | t | dt,

x Œ R, which are seite an seite

0

to the range y = 2x, happen to be equal to

(a)

± 2(b)

±3

(c)

± four

(d) ± 1

11. The sum of first 20 terms of the series 0. six, 0. 77,

0. 777,..., is

7

7

(a) – 10–20)(b)(179 + 10–20)

(99

seventy eight

9

six

7

(c) + 10–20)(d) (179 – 10–20)

(99

9

seventy eight

doze. Consider:

Statement-I: (p Ÿ ~ q) Ÿ (~ p Ÿ q) is a fallacy.

Statement-II: (p Æ q) ´ (~ queen Æ ~ p) is actually a tautology.

(a) Statement-I holds true, Statement-II is valid,

Statement-II can be not a correct explanation intended for

Statement-I

(b) Statement-I applies, Statement -II is bogus.

(c) Statement-I is fake, Statement-II applies.

(d) Statement-I is true, Statement-II is ture,

Statement-II is a correct description for

Statement-I

13. The area (in sq . units) bounded by the curves sumado a =

times, 2y – x & 3 sama dengan 0, x-axis and resting in the initial

(a)36

(b)18

27

(c)

(d)9

some

tan A

cot A

+

14. The expression

can be drafted as

you − crib A 1 − tan A

(a)sec A coses A + 1 (b) tan A & cot A

(c)sec A + cosec A (d)sin A cos A & 1

15. The real number k that the formula

2x3 & 3x & k sama dengan 0 offers two distinctive real roots in [0, 1]

(a) lies among 2 and 3

(b) lies between –1 and 0

(c) does not exist

(d) range between you and two

16....