Class 10

### Which of the following statements in not true? (a)If a point P lies inside a circle, not tangent can be drawn to the circle, passing through p. (b) If a point P lies on the circle, then one and only one tangent can be drawn to the circle at P. (c) If a point P lies outside the circle, then only two tangents can be drawn to the circle form P. (d) A circle can have more than two parallel tangents. parallel to a given line.

Answer: (d) A circle can have more than two parallel tangents. parallel to a given line. Sol: A circle can have more than two parallel tangents. parallel to a given line. This statement is false...

### Which of the following pairs of lines in a circle cannot be parallel? (a) two chords (b) a chord and tangent (c) two tangents (d) two diameters

Answer: (d) two diameters Sol: Two diameters cannot be parallel as they perpendicularly bisect each other.

### In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT =24 cm. If O is the centre of the circle, then length OP = ?

(a) 30 cm                     (b) 28 cm                    (c) 25 cm                     (d) 18 cm Answer: (c) 25 cm Sol: The tangent at any point of a circle is perpendicular to the radius at the...

### In the given figure, a cradle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14cm, BC = 8cm and CA=12 cm. Find the length AD, BE and CF.

BD = 5cm = BE Solving (3) and (4), we get and AD = 9cm

### In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB=6cm, BC=9cm and CD=8 cm. Find the length of side AD.

Sol: We know that when a quadrilateral circumscribes a circle then sum of opposites sides is equal to the sum of other opposite sides. \ AB + CD = AD + BC Þ 6 + 8 = AD = 9 Þ AD = 5 cm...

### Using properties of determinants prove that:

Solution: $\left|\begin{array}{ccc}a & a+2 b & a+2 b+3 c \\ 3 a & 4 a+6 b & 5 a+7 b+9 c \\ 6 a & 9 a+12 b & 11 a+15 b+18 c\end{array}\right|$...

### Evaluate

Solution: We know that expansion of determinant with respect to first row is $a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$. $0(3 \times 6-5 \times 4)-2(2 \times 6-4 \times 4)+0(2 \times 5-4 \times 3)$...

### Evaluate .

Solution: Find determinant $\begin{array}{l} \sqrt{6} \times \sqrt{24-\sqrt{2}} 20 \times \sqrt{5} \\ \sqrt{1} 144-\sqrt{1} 100 \\ =12-10 \\ =2 \end{array}$

### If , find the value of .

Solution: Find the determinant of $A$ and then multiply it by 3 $\begin{array}{l} |A|=2 \\ 3|A|=3 \times 2 \\ =6 \end{array}$

### Find the area of a parallelogram with base equal to 25 cm and the corresponding height measuring 16.8 cm.

Sol: Given: Base = 25 cm Height = 16.8 cm \Area of the parallelogram = Base ´ Height = 25cm ´16.8 cm = 420 cm2

### Mark the tick against the correct answer in the following: Domain of is A. B. C. D.

Solution: Option(C) is correct. To Find: The Domain of $\sec ^{-1}(x)$ Here,the inverse function is given by $y=f^{-1}(x)$ The graph of the function $y=\sec ^{-1}(x)$ can be obtained from the graph...

### Mark the tick against the correct answer in the following: Domain of is A. B. C. D. None of these

Solution: Option(B) is correct. To Find: The Domain of $\cos ^{-1}(x)$ Here,the inverse function of $\cos$ is given by $y=f^{-1}(x)$ The graph of the function $y=\cos ^{-1}(x)$ can be obtained from...

### Mark the tick against the correct answer in the following: Range of is A. B. C. D. None of these

Solution: Option(C) is correct. To Find: The range of $\operatorname{cosec}^{-1}(x)$ Here,the inverse function is given by $\mathrm{y}=\mathrm{f}^{-1}(x)$ The graph of the function...

Solution: Option(C) is correct. To Find:The range of $\sec ^{-1}(x)$ Here,the inverse function is given by $y=f^{-1}(x)$ The graph of the function $y=\sec ^{-1}(x)$ can be obtained from the graph of...
Solution: Option(B) is correct. To Find: The range of $\tan ^{-1} x$ Here, the inverse function is given by $y=f^{-1}(x)$ The graph of the function $y=\tan ^{-1}(x)$ can be obtained from the graph...