NDA Mock Test - 1
150 Questions MCQ Test NDA (National Defence Academy) Mock Test Series | NDA Mock Test - 1
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The marked price of a watch is Rs. 800. A shopkeeper gives two successive discounts and sells the watch at Rs. 612. If the first discount is 10%, the second discount is
Suppose ω and ω2 are the complex cube root of unity which are given as
Q.
(1 – ω) (1 – ω2) (1 + ω4) (1 + ω8) is equal to
Correct Answer :- d
Explanation : (1-w)(1-w2)(1+w4)(1+w8)......(1)
w4 = w3 * w
w4 = 1*w = w.......(2)
w8 = w3 * w3 * w2
= w2.........(3)
Put the values of (2) and (3) in eq (1)
(1-w)(1-w2)(1+w)(1+w2)
(1-w)(1+w)(1-w2)(1+w2)
=> (1-w2) (1-w)
From eq(2) w4 = w
1 - w - w2 + w3
As we know that 1 + w + w^2 = 0
w2 + w = -1……..(4)
Putting in eq(4)
= 1 + 1 + 1
= 3
Suppose ω and ω2 are the complex cube root of unity which are given as
Q.
The value of expression
where n
285 is summation of 3 numbers. Ratio between 2nd and 3rd numbers is 6:5. Ratio between 1st and 2nd numbers is 3:7. The 3rdnumber is?
If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0?
If the equation x2 – bx + 1 = 0 does not possess real roots, then which one of the following is correct?
Consider the equation (x – p) (x – 6) + 1 = 0 having integral coefficients. If the equation has integral roots, then what values can p have?
The roots of the equation (x – p) (x – q) = r2, where p, q and r are real, are
is equal toIf A and B are two matrices such that AB = B and BA = A, then A2 + B2 is equal to
A 2 + B2 = AA + BB
=A(BA) + B(AB) (Given AB = B and BA = A)
=(AB)A + (BA)B
=BA + AB
=A + B
then F(α) . F(β) is equal toIf A and B are two matrices of same order, then
Q.
(AB)n = AnBn is / (AB)n = AnBn
If A and B are two matrices of same order, then
Q.
If A and B are symmetric matrices, then (ABA)T is
If each element in a row of a determinant is multiplied by the same factor r, then the value of the determinant
where ω is the cube root of unity?
(cotx+cosecx)-1/(cotx-cosecx+1)
=(cosecx+cotx)-(cosec²x-cot²x)/(cotx-cosecx+1)
=(cosecx+cotx)[1-(cosecx-cotx)]/(cotx-cosecx+1)
=(cosecx+cotx)(cotx-cosecx+1)/(cotx-cosecx+1)
=(cosecx+cotx)
=(1/sinx+cosx/sinx)
=1+cosx/sinx
If cos A + cos B = m and sin A + sin B = n, where m, n ≠ 0, then what is sin (A + B) equal to?
equal to?
If angles A, B and C are in AP, then what is sin A + 2 sin B + sin C equal to?
Since, A, B, C are in AP.
+ cos 
If p = sin (989o) cos (991o), then which one of the following is correct?
Directions : Read the following information carefully and answer the questions given below.
Q.
(α+ β) is equal to
is equal to
From the top of a lighthouse 70 m high with its base at sea level, the angle of depression of a boat is 15o. The distance of the boat from the foot of the lighthouse is
A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60o. The angle of elevation is 30o from a point at a distance y m from the bank. What is the height of the tree?
hen what is the value of sin C?ABC is a triangle in which BC = 10 cm, CA = 6 cm and AB = 8 cm. Which one of the following is correct?
In a ABC, BC = 
AC = 5 and AB = 7. What is the measure of the ∠A?
In a ΔABC, a + b = 3 
cm and a – b = 3 
cm. If ∠A is 30o, then what is the ∠B?
P : x2 – y2 + 2y – 1 = 0
L : x + y = 3
Q.
Equation of the angle bisectors of the pairs of lines P is
P : x2 – y2 + 2y – 1 = 0
L : x + y = 3
Q.
Area of the triangle formed by the angle bisectors of the pair of lines P and the line L (in sq units) is
P : x2 – y2 + 2y – 1 = 0
L : x + y = 3
Q.
If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' is
What is the slope of the line perpendicular to the line x/4 +y/3 = 1?
If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b?
4x + 3y -1 = 0
x - y + 5 = 0
bx + 5y -3 = 0 are concurrent .
so,
P( 4x + 3y -1) + Q (x - y + 5) + R (bx + 5y -3) = 0
x ( 4P + Q + bR) + y(3P -Q + 5R) + (-P + 5Q -3R) = 0
this is possible when, we think ,
det[{ 4, 1 , b } {3 , -1 , 5 } { -1 , 5 , -3 }] = 0
4(3 - 25) - (-9+5) + b( 15 -1 ) = 0
-88 +4 + 14b = 0
14b - 84 = 0
b = 6
A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
If given points are the ends of diameter, then the equation of circle is
A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
How many tangents can be drawn from the origin to the circle that we get in above question?
A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
The radius of the circle x2 + y2 + x + c = 0 passing through the origin is
A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
What is the equation to circle which touches both the axes and has centre on the line x + y = 4?
Consider the following statements in respect of circles x2 + y2 – 2x – 2y = 0 and x2 + y2 = 1
I. The radius of the first circle is twice that of the second circle.
II. Both the circles pass through the origin.
If f (x) = 2x + 7 and g (x) = x2 + 7, x R, then which value of x will satisfy fog (x) = 25?
Assertion (A) A gun recoils when a bullet is fired from it.
Reason (R) Action and reaction are equal and opposite.
A book is kept on the surface of a table. If the gravitational pull of the earth on the book is the force of action, then the force of reaction is exerted by
Assertion (A) A beaker filled with water at 4oC overflows if the temperature is decreased or increased.
Reason (R) Density of water is maximum at 4oC.
Mosquitoes can lay eggs on the surface of water. But when oil is sprinkled on the surface of water, mosquitoes cannot lay eggs because
Which one among the following statements about thermal conductivity is correct?
Thermal conductivity means that a substance has a capacity to conduct heat and electricity or it just let heat and electricity to pass through its own body .
The correct answer is-
water > steel > wood
• It is so because water is apart from liquid metals, water has the highest thermal conductivity of any liquid.
• Steels thermal conductivity is around 45 watts per kelvin per meter. So this material is a good thermal conductor but comes after water.
• Thermal conductivity declines as the density of the wood decreases or it do not conduct heat and electricity. So it comes at last as thermal conductor.
Which one of the following is the correct sequence in terms of increasing mass?
The type of amino acids that the human body can synthesise are known as
Who among the following is considered to be the father of Ayurveda?
Which one of the following was the official language of Gupta period?
Who laid the foundation of the first independent Turkish kingdom in India?
Babur laid the foundation of Mughal empire in 1526 by defeating
Which of the following opposed Gandhiji's Satyagraha against the Rowlatt Act?
Which one among the following wars ended by the Treaty of Salbai?
Which of the following regions is characterised by high temperature, heavy rainfall and dense vegetation?
Amongst the following Indian States, which one has the minimum total forest cover?
According to Census 2011, which one of the following Indian States has the maximum population in India after Uttar Pradesh?
The Dul Hasti Power Station is based on which one of the following rivers?
In some parts of India, consumption of underground water causes mottled teeth and bone damage. Which one of the following is responsible for this malady?
Consider the following metals:
1. Uranium
2. Radium
3. Plutonium
Q.
Which of these are used in making nuclear weapons?
Match List-I (Disease) with List-II (Organism) and select the correct answer using the codes given below the lists:
Correct Answer :- c
Explanation : a) Vibrio cholerae interacts with many organisms in the environment, including heterotrophic protists (protozoa). Several species of protozoa have been reported to release undigested bacteria in expelled food vacuoles (EFVs) when feeding on some pathogens.
b) Mumps is an acute, self-limited, systemic viral illness characterized by the swelling of one or more of the salivary glands, typically the parotid glands. The illness is caused by the RNA virus, Rubulavirus. Rubulavirus is within the genus Paramyxovirus and is a member of the family Paramyxoviridae.
c) Ringworm is a contagious fungal infection caused by common mold-like parasites that live on the cells in the outer layer of your skin. It can be spread in the following ways: Human to human. Ringworm often spreads by direct, skin-to-skin contact with an infected person.
d) Human African trypanosomiasis, also known as sleeping sickness, is a vector-borne parasitic disease. It is caused by infection with protozoan parasites belonging to the genus Trypanosoma.
Directions : The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Arabian Nights are (a) / a collection of (b) / very interesting episodes of adventure. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
I hope to visit (a) / my uncle only next year (b) / during summer vacations. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Ration has run out (a) / and the District Magistrate (b) / has been informed (c) / No error (d)
It should be "ran" instead of "run" because there in the sentence "has" which is in past tense and so the "ran"
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
The number of vehicles (a) / plying on this road (b) / is more than on the main road. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
May I (a) / know who you want (b) / to see please. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Our is the only country (a) / in the world that can boast of (b) / unity in diversity. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
The doctor referred the patient (a) / for the OPD (b) / without examining him. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
I do not understand (a) / why (b) / he is so angry at me. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Because of his innocence (a) / he can not distinguish (b) / a cheat for an honest person. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Not she is intelligent (a) / nor hard working (b) / and still she expects to secure first class. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
I was surprised (a) / to see her speak (b) / with somewhat anger. (c) / No error (d)
(c) Replace ‘somewhat’ by ‘some’.
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Privatisation offers the most ideal situation (a) / for consumers because private sector (b) / is very conscious of quality. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
It were the students (a) / who wanted the teacher (b) / to declare holiday. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
Everyone of the new Nursing Homes (a) / coming up in the Urban areas (b) / need a lot of improvement. (c) / No error (d)
The sentences given below, have three parts, indicated by (a), (b) and (c). Read each sentence to find out whether there is an error. If a sentence has no error, choose part (d), which stands for 'No error'. (Ignore the errors of punctuation, if any).
Q.
He will be likely (a) / to take part in the ceremony (b) / provided he is granted leave. (c) / No error (d)
Directions : Each of the following items consists of a sentence followed by four words or group of words. Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
His CANDID remarks impressed the authorities.
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
The guilty appealed to the jury to CONDONE his punishment.
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
His family SEVERED ties with him for marrying intercaste.
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
It is easy to understand his FUZZY thoughts.
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
He drove his car through SLIMY road to reach your office.
slimy means covered with slime means a thick unpleasant liquid. SO its antonym will be clean,
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
There was a fire this morning. They were lucky to ESCAPE it.
Select the antonym of the word occurring in the sentence in capital letters as per the context.
Q.
His ELOQUENT speech helped him bag the award.
Directions : Each of the following items consists of a sentence followed by four words or group of words. Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
Trees that BLOCK the view of oncoming traffic should be cut down.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
We saw a SCINTILLATING fireworks display.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q. Europe, America and Japan have taken to the field of science with SINGULAR vigour and activity.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
Ant is believed to be the most INDUSTRIOUS creature.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
As I look around I see the crumbling ruins of a proud civilisation strewn like a vast heap of FUTILITY.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
By 1918, Gandhiji had established himself as a leader with a UNIQUE way of protesting exploitation and injustice.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
Your INTERVENTION was required.
Select the synonym of the word occurring in the sentence in capital letters as per the context.
Q.
It is difficult to DISCERN the sample on the slide without adjusting the microscope.
Directions : Pick out the most effective word from the given words to fill in the blank to make the sentence meaningfully complete.
Q.
The lions in the Gir forest are protected as they come under ….. species.
The teacher's counsel had a ……. effect on the mischievous student's conduct.
The Director pointed out in favour of the manager that the profitability of the plant had …… since he taken over.
We cannot go on strike every year. Now that we have gone on strike we must …….. this issue.
I was totally ……. by his line of thinking and could not put forth any argument.
Man is ………., however, he is more in need of mental companionship than of physical companionship.
He is the best man for this job. He has mental …….. to carry it out.
His party is solely to be blamed for the political …… in the country.
The Earth is at present in great danger of becoming uninhabitable because of ……. environmental pollution, which is going on at an incredible rapid pace.
Directions : In the questions given below, a part of the sentence is underlined. Below are given alternatives to the underlined part which may improve the sentence. Choose the correct alternative. In case, no improvement is needed, option (d) is the answer.
Q.
Not a word they spoke to the unfortunate wife about it.
With a thundering roar the huge rocket soared up from the launching pad.
My opinion for the film is that it will bag the national ward.
My opinion about the film is that it will bag the national award.
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