Maths Basic Test

1. Maths Basic Test
Question 1.
The values of x and y if (x, 3) = (2, x+y)
Answer:
A. (1, 2)
B. (2, 1)
C. (1, 0)
D. (2, 0)
Question 2.
U = (x + y, x-3) is a zero vector if x and y are
Answer:
A. (3,-3)
B. (-3, 3)
C. (0, 0)
D. (1, 1)
Question 3.
An idempotent matrix A where
Answer:
A. A 2 = A
B. A 2 = I
C. A 2 = -A
D. A 2 = 0

2. Question 4.
Two circles both of radii 4 have exactly one point in common. If A is a point on one circle and
B is a point on the other circle, what is the maximum possible length for the line segment AB
?
Answer:
A. 11
B. 12
C. 14
D. 16
Question 5.
When two congruent equilateral triangles share a common center, their
union can be a star, as shown. If their overlap is a regular hexagon with an area of 60, what
is the area of one of the original equilateral triangles?
Answer:
A. 50
B. 60
C. 70
D. 90

3. Question 6.
A math teacher gave her class two tests. 30% of the class passed both tests and 45% of the
class passed the first test. What percent of those who passed the first test also passed the
second test?
Answer:
A. 25%
B. 30%
C. 45%
D. 66%
Question 7.
In how many different ways can the letters of the word PERIMETER be arranged? Also
arrange the four different letters of the word in a row.
Answer:
A. 100000, 400
B. 30240, 360
C. 30000, 360
D. 20000, 550
Question 8.
For a boy having 6 friends, how many ways are there to invite 1 or more of them to the
lunch?
Answer:
A. 30
B. 40

4. C. 60
D. None of these
Question 9.
Solve, tan x + tan 2x + tan 3x = tan x tan 2x tan 3x
Answer:
A. π/3
B. 2 π/3
C. n π/3
D. π/4
Question 10.
Two boats leave a place at the same time. One travels 56 km in the direction N 50 degrees
E while the other travels 48 km in the direction S80 degrees E. What is the distance between
the boats at this moment?
Answer:
A. 55 km
B. 44.5 km
C. 50 km
D. None of these
Question 11.
The value of limit given is

5. Answer:
A. 1/2
B. 5/3
C. 3/2
D. 1/3
Question 12.
Derivative of √ tan x is,
Answer:
A. sin 2 x/ √ tan x
B. cos 2 x/ 2 √ tan x
C. sec 2 x
D. None of these
Question 13.
∫ (tan 2 x - cot 2 x) dx =?
Answer:
A. tan x + cot x + c
B. tan x - cot x + c
C. cot x - tan x + c
D. sec x - tan x + c
Question 14.
Force F = 2i - 5j + 3k displaces a particle from A to B. Position vectors of A and B are, A = i +
2j + 3k and B = 3i + 5j + 8k. Find the work done by the force on the object.

6. Answer:
A. 6 units
B. 4 units
C. 10 units
D. 12 units
The word dinosaur, which means "terrible lizard," was coined in 1842, but now we know that
dinosaurs aren't lizards, although they share a common ancestor. Lizards as a group are primitive
compared to dinosaurs. Dinosaurs as a group got bigger over time until an extinction event 65 million
years ago wiped out all but bird-like dinosaurs. Scientists don't agree entirely on what happened, but
the extinction likely was a double or triple whammy involving an asteroid impact, choking chemicals
from erupting volcanoes, climate change and possibly other factors. In a nutshell, dinosaurs were big,
green animals that lived a really really long time ago. Of course you couldn't really fit a dinosaur into
a nutshell, not even a coconutshell, because all dinosaurs were huge. A common misconception,
fueled by anti-dinosaur Zionist propaganda such as Jurassic Park, is that there were many varieties of
dinosaur in all shapes and sizes. This is not true at all. Every single dinosaur was a huge, hulking,
brute that spent all day eating plants, sleeping, and sleep-eating. Actually I think the word "brute" may
be a little harsh, because dinosaurs were gentle and caring. The Tyrannosaurus Rex has been
portrayed as a terrible monster by many, but the truth is he would not hurt a fly.Unless the fly was
really badly injured and in a lot of pain and had to be put out of it's misery for it's own sake, in which
case the T-Rex would put the poor fellow to sleep quickly and humanely and would probably cry a
little while doing so.
Scientists classify dinosaurs into two major groups based on the structure of the bones in their hips.
Most of the well-known dinosaurs, including Tyrannosaurus rex, Deinonychus, maniraptors, and
birds, fall into a category known as Saurischian dinosaurs (pronounced sor-ISK-ee-en). These
"reptile-hipped" dinosaurs have a pelvis that points forward, similar to more primitive animals.
Saurischian dinosaurs, often long-necked, have large and sharp teeth, long second fingers, and a first
finger that points strongly away from the rest of the fingers.
Ornithischian (pronounced or-neh-THISK-ee-en) dinosaurs, a group that includes horned and frilled
ceratopsians, Iguanodontids, armored stegosaurs, and duck-billed hadrosaurs, are more mild-
mannered, plant eaters. All have "bird hips," or a backward-pointing pelvis (although ironically they
are not the ancestors of birds), which is more stable and gives them that lumbering look.

7. They also have a beak-like bump on the front of their lower jaws that Saurischians lack, and their
teeth tend to be smaller and blunter.
Saurischians are divided into two groups – four legged herbivores called sauropods and two-legged
carnivores called theropods (living birds are theropods).