Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

Q.

How to construct a $105°$ angle?

Q.

The two regression lines were found to be$4X–5Y+33=0$ and $20X–9Y–107=0$. Find the coefficient of correlation between $X$ and $Y.$

1. $0.6$

2. $0.16$

3. $0.3$

4. $0.7$

Q. Question 6
If angles A, B, C and D of the quadrilateral ABCD, taken in order are in the ratio 3: 7: 6: 4, then ABCD is a
(A) rhombus
(B) parallelogram
(C) trapezium
(D) kite

Q.

If the equation $12x^2+7xy-p{y}^2-18x+qy+6=0$ represents a pair of perpendicular straight lines, then

1. $p=12,q=1$

2. $p=1,q=12$

3. $p=–1,q=12$

4. $p=1,q=–12$

Q.

The lines $2x+y-1=0$, $ax+3y-3=0$ and $3x+2y-2=0$are concurrent for

1. All $a$

2. $a=4$ only

3. $–1\le a\le 3$

4. $a>0$ only

Q.

If the coordinates of $\mathrm{A}$ and $\mathrm{B}$ be $(1,1)$ and $(5,7)$, then the equation of the perpendicular bisectors the line segment $\mathrm{AB}$ is

1. $2x+3y=18$

2. $2\mathrm{x}-3\mathrm{y}+18=0$

3. $2x+3y-1=0$

4. $3\mathrm{x}-2\mathrm{y}+1=0$

Q.

The construction of a triangle ABC in which AB = 4 cm, $\angle$A = 60${}^{\circ }$ is not possible when difference of BC and AC is equal to:

1. 3.5 cm

2. 4.5 cm

3. 3 cm

4. 2.5 cm

Q.

In the figure, $ABC$ and $AMP$ are two right triangles, right angled at $B$ and $M$ respectively, prove that:

(i) $△ABC~△AMP$

(ii)$\frac{CA}{PA}=\frac{BC}{MP}$

Q.

If the curve $y^2=6x,9x^2+b{y}^2=16$ intersect each other at right angles, then the value of $b$ is:

1. $4$

2. $\frac{9}{2}$

3. $6$

4. $\frac{7}{2}$

Q.

What value of x would make AOB a line in figure, if $\angle AOC=4xand\angle BOC=(6x+{30}^{\circ })$?

Q.

If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ.
$\angle$ PQT = $\angle$ RQU and $\angle$ TQS = $\angle$ UQS. Prove that QT = QU.
[4 MARKS]

Q.

Using any one construction method, divide a line segment AB=12 cm in the ratio 4:3. [2 MARKS]

Q.

If the intercept made by the line between the axis is bisected at the point $\left(5,2\right)$, then its equation is

1. $5x+2y=20$

2. $2x+5y=20$

3. $5x-2y=20$

4. $2x-5y=20$

Q.

Through a point $A$ on the $X-axis$ a straight line is drawn parallel to $Y-axis$ so as to meet the pair of straight lines $a{x}^2+2hxy+b{y}^2=0$ in $B$ and $C$. If $AB=BC$, Then:

1. $h^2=4ab$

2. $8h^2=9ab$

3. $9h^2=8ab$

4. $9h^2=4ab$

Q.

The line perpendicular to the plane $2x-y+5z=4$ passing through the point $(-1,0,1)$ is

1. $\frac{x+1}{2}=–y=\frac{[z–1]}{–5}$

2. $\frac{x+1}{-2}=y=\frac{[z–1]}{–5}$

3. $\frac{x+1}{2}=-y=\frac{[z–1]}{5}$

4. $\frac{x+1}{2}=y=\frac{[z–1]}{–5}$

Q.

In the given figure $AB=AD$ and $AC$ bisects $\angle BAD$. Prove that

(i) $∆ABC\cong ∆ADC$

(ii) $AC$ bisects $\angle BCD$.

Q. Question 9
AD is a median of the $\Delta ABC$. Is it true that AB + BC + CA > 2AD? Give reason for your answer.

Q. Question 6
The perimeter of a triangle with vetices (0, 4), (0, 0) and (3, 0) is:
(A) 5
(B) 12
(C) 11
(D) $7+\sqrt{5}$

Q.

Period of $\cos x·\cos (60°-x)·\cos (60°+x)$ is:

1. $\frac{\mathrm{\pi }}{2}$

2. $\mathrm{\pi }$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{2\mathrm{\pi }}{3}$

Q. Question 10
In figure , ABCD and AEFG are two parallelograms. If $\angle C={55}^{\circ }$, then determine $\angle F$.

Q.

Find the equation of the perpendicular bisector of the line joining the points $\left(1,3\right)$ and $\left(3,1\right)$.

Q.

In $∆ABC,m\angle A=48°andm\angle C=24°.$ What type of triangle is $∆ABC?$

1. Acute triangle

2. Right triangle

3. Obtuse triangle

Q. Question 11 (iv)
State whether the following are true or false. Justify your answer.
(iv) cot A is the product of cot and A.

Q.

If the line $ax+by+c=0$ is normal to the curve $xy=1$, then

1. $a<0,b>0$

2. $a>0,b<0$

3. $a<0,b<0$

4. Data is insufficient.

Q.

$△$ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. If AD: DC = 1:2, then $\frac{{AB}^2}{{BC}^2}$ is:

1. 1: 2

2. 1: 4

3. 4: 1

4. 2: 1

Q. In an acute △ PQR , \angle PQR=45^° .Prove that (PQ)^{2 }=(PR)^{2 }+(QR)^{2 }- 4× area(△ PQR

Q. Question 6
In the below figure, if $\Delta ABE\cong \Delta ACD$, show that $\Delta ADE\sim \Delta ABC$.

Q.

The equation of normal of $x^2+y^2-2x+4y-5=0$ at $(2,1)$ is:

1. $y=3x-5$

2. $2y=3x+4$

3. $y=3x+4$

4. $y=x+1$

Q. A triangle has consecutive integral SIDES. The largest ANGLE is twice the smallest ANGLE. Find its perimeter using sine rule.

Q. The angle between the bisectors of two adjacent supplementary angles is

1. acute angle
2. right angle
3. obtuse angle
4. none of these