Mathematics - Class 12 Mock Test 7

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Question 1 of 10

1. A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. What is the equation of such curve passing through (0, k)?

2x² + y² = k²

x² - y² = k²

x² + y² = k²

x² + 2y² = k²

Question 1 of 10

Question 2 of 10

2. If, A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant length k. What kind of curve is passing through (0, k)?

Ellipse

Parabola

Hyperbola

Circle

Question 2 of 10

Question 3 of 10

3. Which of the following is the condition for two vectors to be Collinear?

The vectors should have the magnitude 1 and 0 respectively

The vectors should have the same initial point

The vectors should have the same magnitude

The vectors should be parallel to the same line

Question 3 of 10

Question 4 of 10

4. If k is any scalar and \(\vec{a}\), \(\vec{b}\) be vectors then k (\(\vec{a}\)+ \(\vec{b}\))= ________

\(\vec{a}\) + \(\vec{b}\)

k\(\vec{a}\) + \(\vec{b}\)

\(\vec{a}\) + k\(\vec{b}\)

k\(\vec{a}\) + k\(\vec{b}\)

Question 4 of 10

Question 5 of 10

5. What will be the value of the differential equation dy/dx = (x + y)²/(x + 2)(y – 2)?

ke^2Y/X where, X = x + 2 and Y = y – 2

ke^2X/Y where, X = x - 2 and Y = y + 2

ke^Y/X where, X = x + 2 and Y = y – 2

ke^2Y/X where, X = x and Y = 2y

Question 5 of 10

Question 6 of 10

6. Find \(|\vec{a}+\vec{b}|\), if \(|\vec{a}|=3 \,and \,|\vec{b}|=4 \,and \,\vec{a}.\vec{b}=6\).

\(\sqrt{23}\)

\(\sqrt{37}\)

Question 6 of 10

Question 7 of 10

7. What will be the value of C if C the constant of the coefficient of the solution of the given equation (D + 1)²y = 0 given y = 2 log_e 2 when x = log_e 2 and y = (4/3) log_e3 when x = log_e3?

-4

-2

Question 7 of 10

Question 8 of 10

8. What is the value of the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?

-2c/3

3c/2

2c/3

-c/3

Question 8 of 10

Question 9 of 10

9. Find the projection of vector \(\vec{a}=8\hat{i}-\hat{j}+6\hat{k}\) on vector \(\vec{b}= 4\hat{i}+3\hat{j}\).

\(\frac{29}{\sqrt{5}}\)

\(\frac{29}{5}\)

\(\sqrt{\frac{29}{5}}\)

\(\frac{\sqrt{29}}{5}\)

Question 9 of 10

Question 10 of 10

10. A scalar quantity has only magnitude and no direction.

True

False

Question 10 of 10