EduRev

Get the App Signup / Login

Welcome Back

Forgot Password?

New User? Sign Up

Create your account now

I accept the Terms & Conditions.

Already Have an Account? Login

WBJEE Maths Test - 10

75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Maths Test - 10

Description

Attempt WBJEE Maths Test - 10 | 75 questions in 120 minutes | Mock test for JEE preparation | Free important questions MCQ to study WBJEE Sample Papers, Section Wise & Full Mock Tests for JEE Exam | Download free PDF with solutions

QUESTION: 1

In the expansion of [7^{1 3} + 11^{1 9}]⁶⁵⁶¹, the number of terms free from radicals is

A.
730
B.
715
C.
725
D.
750

Solution:

General term,
t_{r + 1} = ⁶⁵⁶⁴C_r (7^{1 3})^6561-r (11^{1 9})^r
⇒ t_{r + 1} = ⁶⁵⁶¹C_r . 7^{( 6561-r 3 )} . 11^{( r 9 )}
t_{r + 1}
will be free from radical signs, if
( 6561-r 3 ) and ( r 9 )
are integers for
0 ≤ r ≤ 6561
∴ r = 0, 9, 18, 27, ...6561
0, 9, 18, ...6561 is in A.P.
First term, a = 0
Common - difference = 18 - 9 = 9
Last term, t = 6561
l = a + (n - 1)d, where n = number of terms
⇒ 6561 = 0 + (n - 1)9
⇒ 9(n - 1) = 6561
⇒ n - 1 = 729
⇒ n = 729 + 1
⇒ n = 730

QUESTION: 2

If the sum of the coefficients in the expansion of (x+y)ⁿ is 1024, then the value of the greatest coefficient in the the expansion is

A.
356
B.
252
C.
210
D.
120

Solution:

QUESTION: 3

The approx value of (7.995)¹∕³correct to four decimal places is

A.
1.9995
B.
1.9996
C.
1.9990
D.
1.9991

Solution:

QUESTION: 4

A.
16/3
B.
3/16
C.
-3/16
D.
-16/3

Solution:

QUESTION: 5

The equation of the normal to the circle x² + y² + 6x + 4y - 3 = 0 at (1, -2) is

A.
y + 1 = 0
B.
y + 2 = 0
C.
y + 3 = 0
D.
y - 2 = 0

Solution:

QUESTION: 6

Two circles x² + y² - 2x + 6y + 6 = 0 and x² + y² - 5x + 6y + 15 = 0

A.
are concentric
B.
touch internally
C.
touch externally
D.
intersect

Solution:

QUESTION: 7

(1 − ω + ω ²) (1 − ω² + ω⁴ ) (1 − ω ⁴ + ω8 ) (1 − ω ⁸ + ω ¹⁶) =

A.
4
B.
8
C.
12
D.
16

Solution:

QUESTION: 8

If |z₁ + z₂| = |z₁ - z₂|, then the difference of arguments of z₁ and z₂ is

A.
π/4
B.
π/3
C.
π/2
D.
0

Solution:

QUESTION: 9

The area of the curve |x|+|y|=4 is

A.
4 sq.unit
B.
8 sq.unit
C.
16 sq.unit
D.
32 sq.unit

Solution:

QUESTION: 10

A.
π ∕ 2
B.
π ∕ 4
C.
π ∕ 6
D.
π ∕ 8

Solution:

QUESTION: 11

A.
0
B.
(p - q)(q - r)(r - p)
C.
pqr
D.
p + q + r

Solution:

QUESTION: 12

A.
1 /2 log 2
B.
− 1 /2 log 2
C.
log 2
D.
- log 2

Solution:

QUESTION: 13

The singular solution of the differential equation y=px+p³, (p=dy/dx) is :

A.
4y³+27x²=0
B.
4x²+27y³=0
C.
4y²+27x³=0
D.
4x³+27y²=0

Solution:

QUESTION: 14

Solution:

QUESTION: 15

( d dx )(x² + cos x)⁴ =

A.
4(x² + cos x)(2x - sin x)
B.
4(x² + cos x)³.(2x - sin x)
C.
4(x² - cos x)³.(2x - sin x)
D.
4(x² + cos x)³. (2x + sin x)

Solution:

d dx

(x² + cos x)⁴
= 4.(x² + cos x)³ x d dx (x² + cos x)
= 4(x² + cos x)³ x (2x - sin x)

QUESTION: 16

The solution of the differential equation

A.
y = tan^-1x
B.
y - x = C (1 + xy)
C.
x = tan^-1y
D.
tan(xy) = C

Solution:

QUESTION: 17

The radius of the circle passing through the foci of the ellipse ((x²/16) + (^y2/9) = 1), and having its centre (0,3) is

A.
4
B.
3
C.
√12
D.
7/2

Solution:

QUESTION: 18

(d/dx)[tan⁻¹⁽secx+tanx)]=

A.
1
B.
1/2
C.
cosx
D.
secx

Solution:

QUESTION: 19

The tangents to the hyperbola x² - y² = 3 are parallel to the st. line 2x + y + 8 = 0 at the following points

A.
(2, 1) or (1, 2)
B.
(2, -1) or (-2, 1)
C.
(-1, -2)
D.
(-2, -1)

Solution:

QUESTION: 20

The equation of the ellipse in the form of ((x²/a²) + (^y2/b2) = 1), given the eccentricity to be 2/3 and latus rectum 2/3, is

A.
25x² + 45y² = 9
B.
25x² - 4y² = 9
C.
25x² - 4y² = -9
D.
25x²+ 4y² = 1

Solution:

QUESTION: 21

The function f(x) = sin ⁴x + cos ⁴x increases if

A.
0 < x < π 8
B.
π 4 < x < 3 π 8
C.
3 π 4 < x < 5 π 8
D.
5 π 8 < x < 3 π 4

Solution:

f ′ x > ⇒ 4 sin 3 x . cos x − 4 cos 3 x . sin x > 0

⇒ sin x . cos x sin 2 x − cos 2 x > 0
o r sin 2 x . cos 2 x < 0 o r sin 4 x < 0
∴ π < 4 x < 2 π o r 3 π < 4 x < 4 π
∴ π 4 < x < π 2 o r 3 π 4 < x < π .

QUESTION: 22

The st. line lx + my + n = 0 touches the hyperbola x²/a²- y2/_^b² = 1 if

A.
a²l² - b2m² = n²
B.
a²l² + m² = n²b²
C.
a² + b² = n²(l² + m²)
D.
a²l² + b²m² = n²

Solution:

QUESTION: 23

A.
1
B.
e ^{b − a}
C.
e ^{a − b}
D.
e b

Solution:

QUESTION: 24

tan⁻¹(x/y) - tan⁻¹(x - y/x + y) is

A.
π/2
B.
π/3
C.
π/4
D.
- 3π/4

Solution:

QUESTION: 25

If A and B are two square matrices such that B = -A⁻¹ BA, then (A + B)² =

A.
0
B.
A² + B²
C.
A² + 2AB + B²
D.
A + B

Solution:

QUESTION: 26

The strength of a beam varies as the product of its breadth b and square of its depth d. A beam cut out of a circular log of radius r would be strong when

A.
b = d = r /2
B.
C.
D.

Solution:

QUESTION: 27

|(1)/(2 + i)² −(1)/(2 − i)² | =

A.
√8/5
B.
25/8
C.
5/√8
D.
8/25

Solution:

QUESTION: 28

The focus of the parabola x²-8x+2y+7=0 is

A.
(0,-1/2)
B.
(4,9/2)
C.
(4,4)
D.
(-4,-9/2)

Solution:

QUESTION: 29

The axis of the parabola 9y²-16x-12y-57=0 is

A.
3y=2
B.
x+3y=3
C.
2x=3
D.
y=3

Solution:

QUESTION: 30

If ⁿP₄:ⁿP₃=1:2, then n=

A.
4
B.
5
C.
6
D.
7

Solution:

QUESTION: 31

Number of divisors of n = 38808 (except 1 and n) is

A.
70
B.
68
C.
72
D.
74

Solution:

Factorizing the given number, we have
38808 = 2³ . 3² . 7² . 11
Therefore the total number of divisors
= (3 + 1) (2 + 1) (1 + 1) - 1 = 71
But this includes the division by the number itself
Hence, the required number of divisors
= 71 - 1 = 70

QUESTION: 32

The number of straight lines that can be formed by joining 20 points of which 4 points are collinear is

A.
183
B.
186
C.
197
D.
185

Solution:

Number of straight lines = ²⁰C₂ - ⁴C₂ + 1

QUESTION: 33

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A.
2/3
B.
3/4
C.
8/21
D.
9/21

Solution:

QUESTION: 34

A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement the probability that second drawn ball is white, is

A.
4/7
B.
1/7
C.
4/49
D.
12/49

Solution:

QUESTION: 35

Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal, is

A.
165/216
B.
177/216
C.
51/216
D.
90/216

Solution:

QUESTION: 36

If b,c and sinB are given such that ∠B is acute and b<c sinB, then

A.
No triangle is possible
B.
One triangle is possible
C.
Two triangle are possible
D.
One right angled triangle is possible

Solution:

When two sides and angle opposite to one of then be given. In this case, the triangle is not always uniquely determined. It is quite possible to have no triangle, one triangle and two triangles with this type of data.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b² = c² + a² - 2ac cos B
⇒ a² - 2ac cos B = b² - c²
⇒ a² - 2ac cos B + c² cos² B
= b² - c² + c² cos² B
⇒ (a - c cos B)² = b² - c² (1 - cos² B)
= b² - c² sin² B

This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no solution.

QUESTION: 37

If k be the perimeter of the Δ A B C then b cos² C/ 2 + c cos² B /2 is equal to

A.
k
B.
2k
C.
k 2
D.
none of these

Solution:

QUESTION: 38

If x²+ax+10 = 0 and x²⁺bx-10=0 have a common rooot,then a²-b² is equal to

A.
10
B.
20
C.
40
D.
50

Solution:

QUESTION: 39

The range of values of a so that the equation x³ - 3x + a = 0 has three real and distinct roots is

A.
− ∞ , − 2 ∪ 2, ∞
B.
(-2,0)
C.
(-2,3)
D.
(-2,2)

Solution:

⇒ a − 2 a + 2 < 0 or ⇒ − 2 < a < 2
Thus the given equation would have real and distinct roots is a ∈ (-2,2)

QUESTION: 40

If (1 -p) is a root of quadratic equation x² + px + (1 -p) = 0 then its roots are

A.
0, -1
B.
-1, 1
C.
0, 1
D.
-1, 2

Solution:

QUESTION: 41

The number of terms common to two A.P.'s 3, 7, 11, ..., 407 and 2, 9, 16,...., 709 is

A.
14
B.
21
C.
28
D.
none of these

Solution:

QUESTION: 42

If a, b, c are in A.P., , mb, c are in G.P.then a, m²b, c are in

A.
A.P.
B.
G.P
C.
H.P.
D.
none of these

Solution:

QUESTION: 43

2^1/4 4^1/8 8^1/16 16^1/32 ... upto ∞ is equal to

A.
1
B.
2
C.
3/2
D.
5/2

Solution:

QUESTION: 44

The sum of all 2-digit odd numbers is

A.
2475
B.
2530
C.
4905
D.
5049

Solution:

QUESTION: 45

Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is

A.
128
B.
216
C.
240
D.
160

Solution:

QUESTION: 46

In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is

A.
80 percent
B.
40 percent
C.
60 percent
D.
70 percent

Solution:

QUESTION: 47

The equation of a line passing through (1,2) and perpendicular to 3x+4y+5=0 is

A.
4x-3y+2=0
B.
4x-3y+3=0
C.
4x-3y+4=0
D.
4x+3y-2=0

Solution:

QUESTION: 48

A line L passes through points (1,1) and (2,0) and Line L' passes through [(1/2),0] and perpendicular to L, then the area triangle formed by L, L' and y-axis is

A.
15/8
B.
25/4
C.
25/8
D.
25/16

Solution:

QUESTION: 49

If α,β are the roots of x²+ax+b=0, α³+β³=

A.
-(a³+3ab)
B.
(a³+3ab)
C.
-a³+3ab
D.
(a³-3ab)

Solution:

QUESTION: 50

If 2tan²θ=sec²θ, the general value of θ is

A.
nπ + (π/4)
B.
nπ - (π/4)
C.
nπ + (π/4)
D.
2nπ + (π/4)

Solution:

QUESTION: 51

Consider the equation 3 . The parameter 'a' so that the given equation has a solution which satisfies

A.
1 3 ≤ a ≤ 1
B.
1 2 ≤ a < 7
C.
1 2 < a < 7
D.
None of these

Solution:

QUESTION: 52

The sum to infinity of the series

A.
3
B.
4
C.
6
D.
2

Solution:

QUESTION: 53

Let f x be an odd function in the interval with a period T, then

A.
Periodic with period T
B.
Non-periodic
C.
Periodic with period 2T
D.
Periodic with period aT

Solution:

QUESTION: 54

Let α , β be any two positive values of x for which 2 cos x , | cos x | and 1 − 3 cos 2 x are in G.P., then the minimum value of | α − β | is

A.
π /3
B.
π/ 4
C.
π /2
D.
None of these

Solution:

QUESTION: 55

If ω is cube root of unity, then the value of is equal to

A.
+1
B.
0
C.
+ω
D.

Solution:

QUESTION: 56

The range of value of β such that (0, β ) lie on or inside the triangle formed by the lines y + 3x + 2 = 0, 3y − 2x − 5 = 0, 4x + x − 14 = 0 is:

A.
5 < β ≤ 7
B.
1 2 ≤ β ≤ 1
C.
5 3 ≤ β ≤ 7 2
D.
None of these

Solution:

QUESTION: 57

If the line x cos θ + y sin θ = 2 is the equation of a transverse common tangent to the circles

A.
5π /6
B.
2π/ 3
C.
π /3
D.
π/ 6

Solution:

QUESTION: 58

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C , then :

A.
A=C
B.
B=C
C.
A ∩ B = φ
D.
A=B

Solution:

QUESTION: 59

The solution of the differential equation

Solution:

QUESTION: 60

Let P(3, 2, 6) be a point in space and Q be a point on the line

Then the value of μ for which the vector is parallel to the plane x - 4y+3z = 1 is

A.
1 4
B.
− 1/ 4
C.
1/ 8
D.
− 1/ 8

Solution:

QUESTION: 61

If a ‸ , b ‸ and c ‸ are three unit vectors, such that a ‸ + b ‸ + c ‸ is also a unit vector and θ 1 , θ 2 and θ 3 are angles between the vectors a ‸ , b ‸ ; b ‸ , c ‸ and c ‸ , a ‸ respectively then among θ 1 , θ 2 and θ 3