ECAT Solved Model Past Paper 2024 PDF
PHYSICS
Q. An astronaut in space comes to know of an explosion on a nearby planet. The astronaut came to know about the explosion because:
Answer: B) The astronaut only saw the explosion.
Q. A gate is connected in a configuration shown in the figure. The relationship between Y and X is given by:
Answer: D) Both B and C (Y= $\overline{X}$ ).
Q. You have 20 capacitors available with you, each of 15 F. You need a capacitor of around 1 F in a circuit. You can achieve this value by connecting:
Answer: C) 15 capacitors in series.
Q. A thermistor with positive temperature coefficient is used to measure temperature in a furnace:
Answer: B) Increases.
Q. Which single gate in the following system is equivalent to:
Answer: B) NAND gate.
Q. When you drop a ball it accelerates downward at 9.8 m/s². If you instead throw it downwards then its acceleration immediately after leaving your hand, assuming no air resistance, is:
Answer: A) 9.8 m/s².
Q. Which one of the following is not a vector quantity?
Answer: A) Kinetic energy.
Q. A tight wire is clamped at two points 2.0 m apart. It is plucked near one end. Which are three longest wavelengths present on the vibrating wire?
Answer: B) 4.0 m, 2.0 m, 1.33 m.
Q. A uniform bar AE of weight 9 N is held horizontal by vertical forces. Two additional forces act at A and D as shown in figure. At which point must a vertical force of 6 N act to keep bar in equilibrium:
Answer: C) Point C.
Q. In a competition, fielders are required to throw the cricket hard ball as far as possible. Under ideal conditions, optimum throwing angle is 45°. What should this angle be in (i) strong winds against the direction of throw; and (ii) strong winds in the direction of throw?
Answer: B) (i) less than 45°, (ii) more than 45°.
Q. Three similar light bulbs are connected to a constant voltage DC supply. The filament of one of the bulbs breaks. What happens to the ammeter reading and the brightness of the remaining bulbs?
Answer: D) Ammeter reading decreases, bulb brightness remains unchanged.
Q. Two spheres, each of mass m and velocity v are involved in a perfectly inelastic head-on collision. The percentage loss in kinetic energy due to the collision is:
Answer: D) 100%.
Q. An ambulance moves around a large round-about, with its sirens on. For a person standing at the center, the frequency heard will be:
Answer: A) Equal to the actual siren frequency.
Q. Two satellites are launched. Satellite 1 has mass 10 kg and Satellite 2 has mass 5 kg. The relation between their escape velocities $v_1$ and $v_2$ is:
Answer: B) $v_1=v_2$
Q. Which of the following graphs correctly shows the variations of relative distance, d, between two stones thrown down from a cliff?
Answer: A) Graph A (Linear increase).
Q. A mass of a liquid of density $\rho$ is mixed with an equal mass of another liquid of density $3\rho$. The density of the mixture is:
Answer: C) 1.5ρ.
Q. The accuracy in determination of g in the pendulum experiment is:
Answer: A) Approximately 3%.
Q. Uncertainty in resistor is 2%, potential difference is 1%. The uncertainty in power loss ($P=V^2/R$) is:
Answer: C) Approximately 4%.
Q. With reference to path A→B→C→B, total time and displacement are:
Answer: A) t=(2n+1) sec, d=10 m.
Q. Which statement relating average velocity and instantaneous velocity at point C is true?
Answer: D) The instantaneous velocity at C is greater than the average velocity.
Q. A sphere collides with another. If the collision is perfectly elastic, which statement is correct?
Answer: B) The total kinetic energy before the impact is 3mv².
Q. Two waves of 250 Hz produce a stationary wave where nodes are 2 m apart. The speed is:
Answer: D) 1000 m/sec.
Q. The wavelength of monochromatic light in a diffraction grating (spacing 1.2 μm, angle 30°) is:
Answer: B) 600 nanometers.
Q. Which equation represents the difference in pressure in the two sections of the pipe?
Answer: C) $P_1−P_2=1.5\rho v^2$.
Q. In a diffracted spectrum, the order of red, green and blue light starting from normal is:
Answer: D) Blue, green, red.
Q. Refractive index is 1.5, the wavelength of the refracted ray in glass is:
Answer: A) λ/1.5.
Q. Temperature close to floor is $T_1$ and ceiling is $T_2$:
Answer: B) $T_2>T_1$ because of Charles’s Law.
Q. Current of 1A flows for 5 seconds. Total charge is:
Answer: A) 5 Coulombs.
Q. Current increases from 0 to 5A over 5 seconds. Total charge is:
Answer: C) 12.5 Coulombs.
Q. A current carrying wire loop in a magnetic field will tend to:
Answer: A) Rotate clockwise.
MATHEMATICS
Q. Solving the equation $x^2 +(a+b)x+ab=0$ for x gives:
Answer: C) x=−a,x=−b.
Q. If the roots of a quadratic equation are $2\pm \sqrt3$, then the equation is:
Answer: A) $x^2−4x+1=0$.
Q. The eighth term of the expansion $(2x−1/4x)^{12}$ is:
Answer: B) −188/$x^2$.
Q. Which of the following statements is true?
Answer: D) All of these.
Q. If $x^2−6x+8=0$, then the valid values of x are:
Answer: A) (4, 2).
Q. What is the value of x if $\log_9 729=x$?
Answer: C) 3/4.
Q. On simplifying $\frac{3\log_y y+1}{4−2\log_y 1}$, the result is:
Answer: B) 1.
Q. For line y=mx+c, if x=0,y=4 and x=5,y=14, then:
Answer: A) m=2,c=4.
Q. The expression $(x^2−1)/(x−1)$ is:
Answer: A) x+1.
Q. Find the angle between -360° and 180° when sinx=1/2:
Answer: C) 30°, -150°.
Q. If Ax=B with matrices A and B given, X is:
Answer: A) [13].
Q. Given AB=C, find matrix B:
Answer: B) B=[2−1].
Q. On simplifying $(1−\cos2\theta)/\sin2\theta$, the result is:
Answer: C) tanθ.
Q. Evaluate $\lim_{x→1}(x^2+x−2)/(x^2−1)$:
Answer: A) f(x)=1.5.
Q. Differentiating $(x−1)(x+2)$ gives:
Answer: C) 2x+1.
Q. The gradient of $y=ax^2+bx$ at (2,5) is 2. Find a,b:
Answer: C) a=−2,b=10.
Q. Points on $y=2x^3−4x^2+x+1$ where slope is -1:
Answer: C) Both A & B.
Q. If dy/dx=3, then y is given by:
Answer: B) 3x+c.
Q. Evaluate $\int_0^2 f(x)dx+\int_2^3 f(x)dx$ if total is 3 and $\int_0^3=K$:
Answer: C) K=3.
Q. Given $\int_0^3 f(x)dx=3$, evaluate $\int_0^3 [3f(x)+4]dx$:
Answer: A) K=21.
Q. Given $y=x^3−1$, evaluate the integral from 1 to 2:
Answer: C) 9/4.
Q. Valid roots of $3x^3−8x^2−5x+6$:
Answer: D) Both A and B (-1 and 3).
Q. Lines M:y=3x+1 and N:y=−x+2:
Answer: D) M and N intersect at a single point.
Q. If $f(x)=3x+1$ and $g(x)=x−1$, fg(x) is:
Answer: C) 3x−2.
Q. y-intercept and slope of $2y+3x−2=0$:
Answer: A) y-intercept = 1, Slope = -1.5.
Q. Solving $x^2−3x^{1/2}+2=0$ yields:
Answer: A) (1, 4).
Q. Area enclosed by y=cosx from 0 to π/2 is same as:
Answer: A) $\int_0^{\pi/2}\sin xdx$.
Q. Given $(x^2−25)/(x−5)=8$, x is:
Answer: B) 3.
Q. Complex number 1+i expressed in polar form:
Answer: C) $\sqrt2(\cos45^\circ+isin45^\circ)$.
Q. For $A+A^T=2I$, values of p and k are:
Answer: D) 1 and 0.
CHEMISTRY
Q. In an alkaline battery, the anode, cathode, and electrolyte are:
Answer: C) Zinc, Manganese dioxide, potassium hydroxide.
Q. Lead acid batteries discharge because of:
Answer: C) Both A and B (Deposition of $PbSO_4$ at both electrodes).
Q. A crystal system where all axes are equal but angles are not 90°:
Answer: B) Rhombohedral.
Q. Correct electronic configuration of Nitrogen (Z=7):
Answer: B) $1s^2,2s^2,2p^3$.
Q. Configuration representing an element forming a +3 ion:
Answer: A) $1s^2,2s^2,2p^6,3s^2,3p^1$.
Q. Complete the reaction: $KMnO_4+FeSO_4+H_2SO_4 \rightarrow$
Answer: D) $K_2SO_4+MnSO_4+Fe_2(SO_4)_3+H_2O$.
Q. To ensure ethanol is not used for drinking, it is converted to methylated spirit by adding:
Answer: A) 10% methanol and a little acetone.
Q. Pickle (Achaar) when placed in the path of current:
Answer: A) Will conduct current.
Q. Steel is manufactured by open hearth process from:
Answer: D) All of the above.
Q. Which ion has more electrons than protons and more protons than neutrons?
Answer: D) $OH^−$.
Q. Alkanes or paraffins are made up of:
Answer: D) Carbon and hydrogen.
Q. Volume of gas at 0°C is 100 cm³, volume at 273°C (assuming constant P):
Answer: B) 200 cm³.
Q. When water freezes, it occupies:
Answer: A) 9% more space.
Q. At Murree hills, water will boil at about:
Answer: C) 98°C.
Q. The noble gases have:
Answer: C) No electron pair interaction.
Q. The transition elements:
Answer: D) All of the above.
Q. Potassium permanganate is:
Answer: B) A powerful oxidizing agent.
Q. Functional group present in both aldehydes and ketones:
Answer: A) Carbonyl.
Q. Which of the following is an alcohol?
Answer: A) $CH_3−CH_2−OH$.
Q. Alkanes are non-polar compounds that are insoluble in:
Answer: A) Polar solvent.
Q. Aqua regia is formed when HCl and HNO₃ are mixed in ratio:
Answer: D) 3:1.
Q. Benzene is extraordinarily stable because of:
Answer: A) Delocalized electron cloud.
Q. Which of the following is NOT used as fertilizer?
Answer: B) Sodium hydroxide.
Q. Ethanol can be prepared by fermenting glucose in the:
Answer: D) Absence of oxygen.
Q. Periodic table helps study properties of:
Answer: C) Elements and their compounds.
Q. The oxidation states of Boron are:
Answer: D) +3, +1.
Q. Which amino acids can be synthesized by our body?
Answer: D) Non-essential amino acids.
Q. Formaldehyde is used in silvering of mirrors because:
Answer: A) It reduces Tollen’s reagent.
Q. Coagulant used in water treatment:
Answer: D) Alum (Phitkari).
Q. Which of the following is a natural polymer?
Answer: B) Polysaccharide (Starch/Cellulose).
ENGLISH
Passage:
Science, engineering and technology disciplines are dictating the turn of events in the world today. Nations which are leading in these disciplines are also leading the world politically and militarily. The powers accompanying the progress in these disciplines is causing scientists, engineers and technologists to disbelieve Allah subtly if not openly. They have started believing that they can predict the future, make machines comparable to Allah’s creations and have become oblivious of the day of judgment and of the life in the hereafter.
Science, engineering and technology revolve around observation of Allah’s creations. Since Allah almighty has created Adam (AS) as superior of all creations and blessed him with the knowledge of natural phenomenon rightly described in the Quran as “Allah taught all names to Adam”, it is obvious that Adam’s offsprings, the human race, has been bestowed with the ability to observe nature of Allah’s creations, understand and utilize the principles of natural phenomenon, termed as scientific laws, to their own benefit in a very restricted domain.
Why restricted domain? Because, for example human beings can extract iron from iron ore and wood from trees using scientific laws but cannot make iron ore nor can make trees. Human being can bandage an injury or sew it or working of natural phenomenon, but cannot create sand, neither the elements used in making electronics circuits nor the electric circuit laws that govern their working. They can make different machines, using their knowledge of scientific laws, integrated it skillfully programmed computers, all made from Allah’s creations and working according to Allah’s laws. These machines cannot work by themselves but need electric power or fossil fuel to function. Any form of power source is again a blessing of Allah. The fact is as Allah has rightly pointed out in the Quran that nobody can make even a fly nor can anybody take back anything picked up by a fly. Human beings are in reality totally dependent on the blessing and provisions of Allah restricted within the bounds set by him.
With the wealth of knowledge gained from observance of Allah’s creations and appreciating their total dependence on Allah, Scientists, engineers and technologists should have been in the forefront of believers in Allah. They know that they cannot make a machine that runs maintenance-free for a long time with minimal input nor can they make a machine which is self-growing, but they observe a heart beating for so many years with minimal input, they see Allah’s creations multiplying with little input, a weak child growing and attaining physical powers with so little input, they observe a single seed giving tons of grain.
They extract or use energy from natural resources like petroleum, gas, water, sunlight which are available in enormous quantities for feeding whole mankind’s lust for energy to run their machines but can they make these natural resources themselves? No, they look for alternate natural resources to compensate the loss. They observe space, an untapped frontier. They observe the massive size and the mind-boggling distances of space objects, the fascinating and awe-striking heavenly bodies all serenely population the apparently infinite space and held in place by invisible forces of Allah. Doesn’t this awesome spectacle make us realize how small a non-entity we are? Doesn’t it strengthen our belief in Allah and convince us to submit to Allah?
Unfortunately, most of the scientists, engineers and technologists instead of bowing to Allah’s commands have chosen to disobey them and live in a make-believe world revolving around their animal desires and lust for power. No matter how powerful they may be or be in custody of unmatched wealth and resources, they will finally return to Allah and death will overtake them at the appointed time. Don’t they see death daily? Can they negate it or avoid it using their scientific knowledge and power?
Q. Death:
Answer: D) All of above.
Q. Humans utilize natural phenomena in a “restricted domain” because:
Answer: D) Humans cannot create the basic elements (like silicon) from sand.
Q. Scientist cannot make energy themselves because:
Answer: C) They cannot make natural resources themselves.
Q. Distances of heavenly objects are “mind boggling” because:
Answer: A) Of their sheer magnitude which baffles imagination.
Q. A heart that beats for years with minimum input is proof:
Answer: A) It is an example of Allah’s creation.
Q. If a natural energy resource becomes unavailable, scientists:
Answer: B) Look for alternate resource to compensate the loss.
Q. Scientists cannot make a machine that:
Answer: D) Both A and C (Like a fly that grows/reproduces).
Q. Adam (AS) was taught all names, implying:
Answer: B) That humans have been bestowed with ability to understand nature.
Q. The crux of the passage is:
Answer: B) That Allah alone is the creator. Humans merely utilize these creations.
Q. While reading the passage, we learn that:
Answer: C) Silicon which is used to fabricate integrated circuits is extracted from sand.
