Lines and Angles

Q.

At the time 4:15, what is the angle between the minute hand and the hour hand of a clock?

1. 37.5⁰

2. 40⁰

3. 30⁰

4. 52.5⁰

5. 67.5⁰

Q. Angle between the hour and minute hand of a clock at 11:15 is___

1. ${120}^{\circ }$
2. ${90}^{\circ }$
3. ${112.5}^{\circ }$
4. ${150}^{\circ }$

Q. A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and minute hand have interchanged their positions. For how much time (approximately) was he out of his house?

1. 55.25 minutes
2. 55.30 minutes
3. 55.34 minutes
4. 55.38 minutes
5. None of these

Q.

In how many ways can 13 people be seated around two round tables with seating capacities of 6 and 7 people respectively?

1. ¹³C₆*6!* 7!

2. ¹³C₆*5!* 7!

3. ¹³C₆*5!* 6!

4. ¹³C₆*7!* 8!

5. ¹³C₆*8!* 9!

Q. AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of $\angle BEF$. If $\angle LEB={35}^{\circ }$ then $\angle CFQ$ will be:

1. ${70}^{\circ }$
2. ${55}^{\circ }$
3. ${110}^{\circ }$
4. ${125}^{\circ }$

Q. In the $\Delta$ PQR, PS is the bisector of $\angle P$ and PT $\perp$ QR, then $\angle TPS$ is equal to

1. ${90}^{\circ }-\frac{1}{2}\angle R$
2. $\angle Q+\angle R$
3. ${90}^{\circ }+\frac{1}{2}\angle Q$
4. $\frac{1}{2}(\angle Q-\angle R)$

Q.

Two variables $x$and $y$are related by the linear equation $ax+by+c=0$ The coefficient of correlation between the two is $+1,$ if

1. $a$ is positive

2. $b$ is positive

3. $a$ and$b$ both are positive

4. $a$ and $b$ are of opposite sign

Q. In the given figure, AB || CD, $\angle ABO={40}^{\circ }$ and $\angle CDO={30}^{\circ }.$ If $\angle DOB=x,$ then find the value of x.

1. ${10}^{\circ }$
2. ${110}^{\circ }$
3. ${70}^{\circ }$
4. ${20}^{\circ }$

Q.

The angle between the minute hand and the hour hand of a clock when the time is 8:40 is:

1. 

2. 

3. 

4. 

Q. AB^ BC, BD^ AC and CE bisects $\angle$C, $\angle$ A = 30${}^{\circ }$. Then what is CED?
(CAT 1995)

1. 30°
2. 45°
3. 60°
4. 65°

Q. Two parallel lines AB and CD are intersected by a transversal EF at M and N respectively.
The lines MP and NP are the bisectors of interior angles $\angle BMN$ and $\angle DNM$ on the same side of the transversal. Then $\angle MPN$ is equal to:

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${120}^{\circ }$

Q. A variable line x/a + y/b = 1 is such that a+b=4. The locus of the midpoint of the portion of the line intercepted between the axes is

1. x+y=4
2. x+y=2
3. x+y=8
4. x+y=1

Q. AB is a straight line and O is a point on AB. If a line OC is drawn not coinciding with OA or OB, then $\angle AOC$ and $\angle BOC$ are:

1. equal
2. supplementary
3. together equal to 100
4. complementary

Q. In the given figure, AB || CD and AC || BD. If $\angle EAC={40}^{\circ },\angle FDG={55}^{\circ },\angle HAB=x^{\circ },$ then find the value of x.

1. ${55}^{\circ }$
2. ${85}^{\circ }$
3. ${75}^{\circ }$
4. ${65}^{\circ }$

Q. Find the equation of the straight line passing through the point (2, 1) and through the point of Intersection of the lines x + 2y = 3 and 2x – 3y= 4.

1. 5x + 3y – 13 = 0
2. 4x – 7y – 1= 0
3. 2x – 7y – 20=0
4. x – 7y + 13 =0

Q. In the given diagram AB || GH || DE and GF || BD|| HI, $\angle FGC={80}^{\circ }$.Find the value of $\angle CHI$ :

1. ${80}^{\circ }$
2. ${120}^{\circ }$
3. ${100}^{\circ }$
4. ${160}^{\circ }$

Q. Three straight lines, $X,YandZ$ are parallel and the angles are as shown in the figure below. What is $\angle AFB$ equal to?

1. ${20}^{\circ }$
2. ${10}^{\circ }$
3. ${15}^{\circ }$
4. ${30}^{\circ }$

Q. What is the angle between the hour hand and the minute hand of a clock at 7:20 a.m. (in degrees)?

Q. A plane figure is bounded by straight lines only. If n is the number of these lines, then the least value of n is :

1. 1
2. 2
3. 3
4. 4

Q.

A line AB makes zero intercepts on x-axis and y – axis and is perpendicular to another line CD, 3x + 4y + 6 = 0. The equation of line AB is

1. y = 4
2. 4x – 3y + 8 = 0
3. 4x – 3y = 0
4. 4x – 3y + 6 = 0

Q. In the given figure XY || PQ, find the value of x:

1. ${45}^{\circ }$
2. ${70}^{\circ }$
3. ${75}^{\circ }$
4. ${15}^{\circ }$

Q. In the given figure, $PQ||ST,TV||RSandTU\perp ST.$ Find $\angle QRS.$

1. None of these
2. ${120}^{\circ }$
3. ${125}^{\circ }$
4. ${135}^{\circ }$

Q. In the adjoining figure AB || CD and PQ, QR intersects AB ad CD both at E, F and G, H respectively. Given that $m\angle PEB={80}^{\circ }$, $m\angle QHD={120}^{\circ }$ and $m\angle PQR=x^{\circ }$, find the value of x:

1. ${40}^{\circ }$
2. ${20}^{\circ }$
3. ${100}^{\circ }$
4. ${30}^{\circ }$

Q. In the adjoining figure, ABCD is a rectangle and DF = CF also, AE = 3BE. What is the value of $\angle EOF,if\angle DFO={28}^{\circ }and\angle AEO={42}^{\circ }?$

1. ${14}^{\circ }$
2. ${42}^{\circ }$
3. ${70}^{\circ }$
4. ${90}^{\circ }$

Q. In the given figure, $AB||CD,\angle ALC={60}^{\circ }$, EC is the bisector of $\angle LCDandEF||AB$. Then, find the measure of $\angle CEF$.

1. ${80}^{\circ }$
2. ${130}^{\circ }$
3. ${150}^{\circ }$
4. ${120}^{\circ }$

Q.

What is the value of the reflex angle formed between the hands of a clock at 10:25?

1. 

2. 

3. 

4. 

5. 

Q.

The measure of the smallest angle of pentagon if the angles are in the ratio 1:2:3:4:5 -

1. 16⁰

2. 26⁰

3. 32⁰

4. 36⁰

5. 46⁰

Q. Given that segment AB and CD are parallel, if lines l, m and n interesect at point O. Find the ratio of $\theta$ to $\angle ODS$.

1. 3 : 2
2. 2 : 3
3. Data insufficient
4. 3 : 4

Q. Find the slope of the line joining the points (7, 5) and (9, 7):

1. 4
2. 1
3. 2
4. 3

Q. In a $\Delta ABC$, a line XY parallel to BC intersects AB at X and AC at Y:
If BY bisects $\angle XYC$, then $\angle CBY$ : $\angle CYB$ is:

1. 5 : 4
2. 4 : 5
3. 1 : 1
4. 6 : 5