Engineering & CS Scholarship Test

Find the incorrect part of the sentence: Hardly had he left the house when it begins to rain.

Choose the word that best fits the blank: The government’s new policies aim to _______ economic growth and reduce unemployment.

Select the correct word: Despite his vast experience, he remained _______ in his approach, always open to learning new things.

Choose the grammatically correct sentence:

Choose the antonym of ‘obfuscate’:

Choose the synonym of ‘laconic’:

Choose the best analogy: Battery is to flashlight as fuel is to

Select the correct word: The manager’s speech was so _______ that everyone left the room feeling inspired.

Complete the sentence: The ancient ruins were remarkably well-preserved, offering historians a _______ glimpse into the past.

Read the passage and answer: The author describes the protagonist as a ‘tenacious warrior’ who never gives up. What does ‘tenacious’ most likely mean in this context?

Choose the best analogy: Ocean is to fish as forest is to

Identify the error in the sentence: The committee have decided to postpone the event due to unforeseen circumstances.

Identify the error in the sentence: Neither the teacher nor the students was aware of the sudden schedule change.

Complete the sentence: The professor’s lecture was so _______ that most students struggled to stay awake.

Find the incorrect part of the sentence: The book, along with the notes, were placed on the table.

Choose the antonym of ‘intransigent’:

Read the passage and answer: The scientist’s groundbreaking discovery revolutionized the field of medicine. He had spent years testing various hypotheses before finally reaching a conclusion. What quality best describes the scientist?

Choose the word that best fits the blank: The detective was known for his _______ attention to detail, solving even the most complicated cases.

Choose the synonym of ‘trenchant’:

Choose the grammatically correct sentence:

Which of the following expression is true considering Eᴬ < Eᴮ < Eᶜ?

The energy levels of the hydrogen spectrum is shown in figure. There are some transitions A, B, C, D and E. Transition A, B and C respectively represent:

A hall has the dimensions 10m x 12m x 14m. A fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement?

If a stationary bar magnet is placed near a coil at rest so maximum lines of forces passes through the coil, the galvanometer shows:

The process is adiabatic, the value of n in the equation PVⁿ = C is

A pipe carries an ideal fluid at a constant flow rate. If the radius of the pipe is halved, by what factor does the velocity change?

The velocity-time plot for a moving particle has constant slope. This means:

1 joule of work done in C.G.S system is equal to:

Certain neutron stars are believed to be rotating at about 1 rev /sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be (Take π² ≈ 10 ):

A cell of e.m.f E is connected with an external resistance R, then p.d. across cell is V. The internal resistance of cell will be:

If R₁ ​ and R₂ ​ are respectively the filament resistances of a 200 watt bulb and 100 watt bulb designed to operate on the same voltage, then:

What happens to the capacitive reactance if the frequency of the supply increases?

The phase difference between oscillatory motion of two points separated by a distance of λ/2 ​ is (where λ is the wavelength):

The body is moving at twice the distance as radius of earth from the surface then what will be the value of ‘g’?

A heat engine absorbs 500 J of heat from a hot reservoir at 600 K and expels 300 J to a cold reservoir at 300 K. What is the efficiency of this engine?

The De-Broglie wavelength of an electron moving with a velocity of 1.5 × 1 0⁸ m / s is equal to that of photon. The ratio of K.E of the electron to that of photon ( C = 3 × 1 0⁸ m / s )

A source emits sound of frequency 900 Hz wile moving towards a stationary observer with the speed v / 3, v is speed of sound in air. What is the frequency of sound heard by observer?

Flux Density of 1.3 × 10 ⁻⁵ T is measured at a distance of 0.1m form a straight conductor carrying a current of 6.5 A. Calculate the force per unit length on a similar parallel conductor placed at a distance of 0.1 m from the first and carrying current of 3 A.

Two racing cars of masses m 1 ​ and m 2 ​ are moving in circles of radii r 1 and r 2 ​ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is:

Which of the following is NOT an assumption of Bernoulli’s equation?

The maximum range of a gun on horizontal terrain is 16 k m 16km. If g = 10 m / s² . What must be the muzzle velocity of the shell?

A particle performs uniform circular motion with an angular momentum L. If the frequency of particle motion is doubled and its K.E is halved, the angular momentum becomes:

Half-life of radioactive substance is 100 years. The mass of sample disintegrates after 300 years is:

Which of the following logic gate is an universal gate?

The peak voltage of an AC supply is 325 V. What is the RMS voltage?

Dimensions of one or more pairs are same. Identify the pairs:

In a multiple graded index fiber, periphery as compared to the central core has a:

At what temperature will the velocity of sound in air reduces to half of its value at 0⁰ C?

For a point P(x,y), x shows

f(x)=x^4 +x ^2 is a _____ function.

Find x if ∣1 a b1 x b1 c x∣ = 0 ​

Equation of tangent to the parabola y² = 8 x at (−2,−4) is

If ₙC₂ = 16, then n=

When x² +2x² −x −k is divided by x−2, the remainder is 4. Find k k.

Sarah is scheduling the first four periods of her school day. She needs to fill those periods with calculus, art, literature, and physics, and each of these courses is offered during each of the first four periods. How many different schedules can Sarah choose from?

The 21st term of the arithmetic sequence 4 , − 1 , − 6,… is

If f (x) = 1/x and 0

If f f is a linear function and f(1)=−2 and f(−2)=1. Find the value of x x, for which f(x)=1.5?

The parabola with the equation y=4x − 1/2 ​x² has how many points where both (x,y) coordinates are both positive integers?

For any integer k , what is value of ωⁿ if n = 3 k ?

The roots of a quadratic equation will be irrational if Δ=b 2 −4ac is

sin(−135°)=

What is the area of a triangle with vertices (1,1), (3,1), and (5,7)?

If A is a 4×7 matrix and B is a 5×4 matrix, then the order of matrix BA will be

In which of the following cases is a triangle not possible?

Find the inverse of the following matrix: (3 52 4)

The center of the circle x² + y² − 10x + 3y + 1 = 0 is in the ___ quadrant.

sin⁻¹(4/3)=

The y-intercept of 2y=3x+1 is

If a straight line f ( x ) bisects the first and third quadrants, what will be the value of f(x) when x=a?

Sarah is scheduling the first four periods of her school day. She needs to fill those periods with calculus, art, literature, and physics, and each of these courses is offered during each of the first four periods. How many different schedules can Sarah choose from?

If f(x)=3x−1, and n n represents the slope of the line with the equation y=f⁻¹ (x), and p represents the slope of a line that is perpendicular to the line y=f(x) then np=

tan(1110°)=

The set 1,−1,i,−i is closed w.r.t

Harmonic mean between 2 and 8 is

sin⁻¹(4/3)=

Which of the following is a hyperbola?

If a point A(3,5) is located on a circle centered at origin in the coordinate plane, which of the following points lies outside this circle?

For the given arithmetic progression 1,3,5,7,…, the least number of terms required to make a sum exceeding 4000 4000 is

If three fair coins are tossed simultaneously, then probability of getting at least two heads is

sin(α−β)=