Mathematics Test

Result

Mathematics Test - 10

Score
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Weekly Quiz Competition

Question 1
1 / -0

A
2

B
5

C
4

D
6

Solution
Question 2
1 / -0

A
5/6

B
5/16

C
1/6

D
1

Solution
Question 3
1 / -0

One of the diameter of the circle circumscribing rectangle ABCD is 4y = x + 7. If A and B are the points (−3,4) and (5,4) respectively, then the area of the rectangle is -

A
16

B
32

C
8

D
None of these

Solution

Points A and C are the point of tangency for the first circle and similarly points B and D are the point of tangency for the second circle. AB and CD are known as lengths of the direct common tangents and they will be same.
Question 4
1 / -0

A
$\frac{π}{6}$

B
$\frac{π}{4}$

C
$\frac{π}{3}$

D
$\frac{π}{2}$

Solution
Question 5
1 / -0

A
$π$

B
$\frac{π}{2}$

C
$\frac{π}{3}$

D
$\frac{π}{4}$

Solution
Question 6
1 / -0

A

B

C

D

Solution

A differential equation when expressed in the form of a polynomial involves the derivatives and dependent variable in the first power and there are no product of these, and also the coefficient of the various terms are either constants or functions of the independent variable, then it is said to be linear differential equation. Otherwise, it is a non - linear differential equation.

Linear differential equation of first order:

Concept 1 :
Solution of differential equations

Solution of differential equation in many type form of equation.

(1) Differential equation of the first order and first degree.

(2) Equation in which the variables are separable.

(3) Differential equation reducible to the variable separable type.

(4) Homogeneous differential equation.

(5) First order liner differential equation.

(6) Exact differential equation.

(7) Bernoulli’s equation.
Question 7
1 / -0

A
-2

B
2

C
3

D
-1

Solution

Consider a point P in space. The position of the point P is given by triad (x, y, z) where x, y, z are sensed(i.e. algebraic) distance from YZ-plane, ZX-plane and XY-plane respectively.

If we assume are unit vectors along OX, OY, OZ respectively, then position vector of point P is

Note :

• Point on x- axis is (x, 0, 0)

• Point on y-axis is (0, y, 0)

• Point on z-axis is (0, 0, z)

• Point on yz plane is (0, y, z)

• Point on zx plane is (x, 0, z)

• Point on xy plane is (x, y, 0)
Question 8
1 / -0

A
x < 2 or x > 1

B
x < -2 or x > -1

C
x < -1 or x > 1

D
None of these

Solution

Monotonicity in Calculus A function f is said to be monotonic in an interval if it is either increasing or decreasing in that interval.
Question 9
1 / -0

A
2

B
k

C
1/2

D
1

Solution

Here, x is a dummy variable, it can be replaced by any other variable t, u,....

ie, The value of a definite integral does not change with change of variable of integration provided the limits of integration remains the same

2. Interchanging the limits of the definite integral does not change the absolute value but change the sign of the integral
Question 10
1 / -0

A
1

B
-1

C
i

D
no real values of $α$

Solution

Integer Powers of Matrices The positive integral powers of a matrix A are defined only when A is a square matrix.