Mathematics Test

Result

Mathematics Test - 34

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Weekly Quiz Competition

Question 1
3 / -1

The orthocenter of the triangle with vertices

A

B

C

D

Solution
Question 2
3 / -1

A
3/7

B
1/5

C
1/3

D
3/5

Solution
Question 3
3 / -1

The order of a differential equation whose solution is y = a cos x + b sin x, where a and b are arbitrary constants, is

A
1

B
2

C
3

D
Cannot be determined

Solution

The order of differential equation = number of arbitrary constants = 2
Question 4
3 / -1

A
1.404

B
1.336

C
1.487

D
1.527

Solution

We know that amount = P(1+ r/100)ⁿ. Substituting r = 12 and n = 3 in it, we get A = P[1.12]³ or A/P = 1.404.
Question 5
3 / -1

Directions: Refer to the following functions:

A(x, y, z) = Max {max (x, y), min (y, z), min (x, z)}

B(x, y, z) = Max {max (x, y), min (y, z), max (x, z)}

C(x, y, z) = Max {min (x, y), min (y, z), min (x, z)}

D(x, y, z) = Min {max (x, y), max (y, z), max (x, z)}

Max (x, y, z) = Maximum of x, y and z.

Min (x, y, z) = Minimum of x, y and z.

Assume x, y and z as distinct integers.

For what condition, will A(x, y, z) be equal to Max (x, y, z)?

A
When x is maximum

B
When y is maximum

C
When z is maximum

D
Either (1) or (2)

Solution

Let us assign some values to x, y and z.

Put x = 1, y = 2, z = 3.

Now, A(x, y, z) = Max (2, 2, 1) = 1.

B (x, y, z) = Max (2, 2, 2) = 2

C (x, y, z) = Max (1, 2, 1) = 1

D (x, y, z) = Min (2, 3, 1) = 3

Max (x, y, z) = Min (1, 2, 3) = 1

Min (x, y, z) = Max (1, 2, 3) = 3

They will be equal only when z has the minimum value among the three, and x or y has the maximum value.

1. You might have checked by options and option 1 satisfies, but option 2 also satisfies.

2. You might have checked by options and option 2 satisfies, but option 1 also satisfies.

3. We can simply ignore this option as for x = 1, y = 2 , z = 3, it does not satisfy.
Question 6
3 / -1

A
x/√(1+x²)

B
x

C
x√(1+x²)

D
√(1+x²)

Solution
Question 7
3 / -1

The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is

A
4x² + 3y² = 1

B
3x² + 4y² = 12

C
4x² + 3y² = 12

D
3x² + 4y² = 1

Solution
Question 8
3 / -1

The greatest value of λ ≥ 0 for which both the equations 2x² + ( λ − 1)x + 8 = 0 and x² − 8x + λ + 4 = 0 have real roots is

A
9

B
15

C
12

D
16

Solution
Question 9
3 / -1

A
e^sinx + C

B
e^sinx-cosx + C

C
e^sinx+cosx+ C

D
None of these

Solution
Question 10
3 / -1

In a triangle, the lengths of the two larger sides are 10 cm and 9 cm respectively. If the angles of the triangle are in A.P, then the length of the third side (in cm) can be

A
(5 - √6) only

B
(5 + √6) only

C
(5 - √6) or (5 + √6)

D
Neither (5 - √6) nor (6 + √6)

Solution