List of practice Questions

Fill in the blank with the correct Article:
_______ town is famous for its hot springs.
Fill in the blank with the correct Article:
We decided to go boating on __________ Dal lake
From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty$, the potential at the centre of the cavity thus formed is ($G =$ gravitational constant)
Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is
Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :
Determination of the molar mass of acetic acid in benzene using freezing point depression is affected by :
Arrange the following amines in the order of increasing basicity.
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R << L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is $T$ and its distance from the galaxy's axis is $r$, then :
A pendulum made of a uniform wire of cross sectional area $A$ has time period $T$. When an additional mass $M$ is added to its bob, the time period changes to $T_M$. If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ is equal to ( $g =$ gravitational acceleration)
A simple harmonic oscillator of angular frequency $2 \,rad \,s^{-1}$ is acted upon by an external force $F= \sin\, t \,N$. If the oscillator is at rest in its equilibrium position at $t\, =\, 0$, its position at later times is proportional to :
A ball is projected up at an angle $\theta$ with horizontal from the top of a tower with speed $v$. It hits the ground at point $A$ after time $t_{A}$ with speed $v_{A}$ . Now, this ball is projected at same angle and speed from the base of the tower (located at point $P$) and it hits ground at point $B$ after time $t_{B}$ with speed $v_{B}$. Then
A man covers half of his journey by train at 90 km/hr, one-third of the remainder by bus at 30 km/hr and the rest by cycle at 10 km/hr. The average speed during the entire journey is ______ .
Mr. Suresh went into a restaurant and had a happy lunch for Rs.162. He paid for the same using a 500 rupee note. He was so happy with the meal and hence purchased a mini snack box for Rs. 37 and paid for the same using a 100 rupee note. Mr. Suresh ensured that he collected the balance from the cashier in both cases. Although he was satisfied with the service, he did not pay any tips to the server. The next day when the cashier went and deposited the money in the bank, it was found by the banker that only the two currency notes which were given by Mr. Suresh were counterfeit notes. As per policy, the bank immediately tore both the notes using their shredding machine. What is the total loss to the restaurant in this transaction ?
A dishonest seller sells his grocery items using a false weight and thus gains 5% for a kilogram, he uses the weight of approximately _______ .
A man sold \(\frac 35^{th}\) of his articles at a gain of 20% and the remaining at cost price. Find the percentage gain earned in the transaction.
A batsman was having 32 runs per innings as his average after 15th innings. His average increased by 2 runs after 16th inning. Then what was his score in the 16th inning?
A, B and C can do a work in 6, 8 and 12 days respectively. If they do the work together and earn Rs. 2700, what is the share of C in that amount ?
Three pipes A, B and C can fill a tank in 12 hours. All the pipes started working together and after 3 hours, C is closed. If A and B can fill the remaining part in 10 hours, then the number of hours taken by C alone to fill the tank is.
Ajit, Ravi and Hari were trying to hit a target. If Ajit hits the target 5 times in 8 attempts, Ravi hits it 3 times in 5 attempts and Hari hits it 2 times in 4 attempts. What is the probability that the target is hit by at least 2 persons?
In a competitive exam there were 5 sections. 10% of the total number of students cleared the cut off in all the sections and 5% cleared none of the sections. From the remaining candidates 30% cleared only section 1, 20% cleared only section 2, 10% cleared only section 3 and remaining 1020 candidates cleared only section 4. How many students appeared in the competitive exam ?
Three candidates "A", "B", "C" participated in an election. "A" gets 40% of the votes more than "B". "C" gets 20% votes more than "B". "A" also overtakes "C" by 4000 votes. If 90% voters voted and no invalid or illegal votes were cast, then what will be the number of voters in the voting list?
A bottle contains 50 liters of milk. From this bottle 5 liters of milk was taken out and replaced the water. This process was repeated further for three times. How much milk is now contained in the bottle ?
In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school.
A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ?
How many zeros would be there in \(1024!\) ?