From 6 different novels and 3 different dictionaries, 4 novels an

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

1.

For each t ∈R, let [t] be the greatest integer less than or equal to t. Then

limx0+ x1x+2x+......+15x

  • does not exist (in R)

  • is equal to 0

  • is equal to 15

  • is equal to 120


2.

If the tangent at (1, 7) to the curve x2 = y – 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is

  • 95

  • 195

  • 185

  • 85


3.

If α, β ∈ C are the distinct roots, of the equation x2 -x + 1 = 0, then α101 + β107 is equal to

  • 2

  • -1

  • 0

  • 1


4.

PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45o, 30o and 30o, then the height of the tower (in m) is

  • 50√2

  • 100

  • 50

  • 100√3


Advertisement
5.

The sum of the coefficients of all odd degree terms in the expansion of x + x3 -15 + x - x3-15, (x>1) is

  • 2

  • -1

  • 0

  • 1


6.

Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of △PTQ is

  • 36√5

  • 45√5

  • 54√3

  • 60√3


Advertisement

7.

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is

  • At least 750 but less than 1000

  • At least 1000

  • Less then 500

  • At least 500 but less than 750


B.

At least 1000

Number of ways of selecting 4 novels from 6 novels
= 6C4
Number of ways of selecting 1 dictionary from
3 dictionaries = 3C1
Required arrangements = 6C4 × 3C1 × 4! = 1080
=> At least 1000


Advertisement
8.

Two sets A and B are as under:

A = {(a-b)∈ RxR:|a-5|<1 and |b-5|<1}

B = {(a,b)∈ Rx R: 4(a-6)2 + 9 (b-5)2 ≤ 36},then

  • Neither A ⊂ B nor B ⊂ A

  • B ⊂ A

  • A ⊂ B

  • A ∩ B = ∅


Advertisement
9.

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the
parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and,∠CPB = θ then a value of tan θ is

  • 4/3

  • 1/2

  • 2

  • 3


10.

The Boolean expression ~ (p v q )v (-p ∧q ) is equivalent to

  • ~q

  • ~ p

  • p

  • q


Advertisement