Engineering & CS Scholarship Test

sin(−135°)=

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?

If ₙC₂ = 16, then n=

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

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

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

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

Find x if ∣1 a b1 x b1 c x∣ = 0 ​

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?

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

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

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.

Harmonic mean between 2 and 8 is

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?

sin(α−β)=

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

Which of the following is a hyperbola?

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

The set 1,−1,i,−i is closed w.r.t

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

sin⁻¹(4/3)=

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

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

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

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

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

sin⁻¹(4/3)=

If f (x) = 1/x and 0

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

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=

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?

tan(1110°)=

Choose the grammatically correct sentence:

Choose the antonym of ‘obfuscate’:

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

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

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

Choose the grammatically correct sentence:

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

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?

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

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

Choose the antonym of ‘intransigent’:

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

Choose the synonym of ‘laconic’:

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

Choose the synonym of ‘trenchant’:

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?

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

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

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

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

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

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

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 )

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

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

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

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:

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

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

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

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:

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:

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?

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

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?

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

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

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:

Which of the following logic gate is an universal gate?

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?

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.

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?

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

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

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?

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 ):