List of practice Questions

For the system of linear equations\(\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta\) which one of the following statements is NOT correct ?

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-
A body of mass 200 g is tied to a spring of spring constant 12.5 N/m, while the other end of the spring is fixed at point \( O \). If the body moves about \( O \) in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:

Let αx=exp(xβyγ) be the solution of the differential equation 2x2ydy−(1−xy2) dx = 0, x>0 , y(2)=\(\sqrt {log_e2}\)​.  Then α+β−γ equals :

If \(A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}\), then :

An organic compound $[ A ]\left( C _4 H _{11} N \right)$, shows optical activity and gives $N _2$ gas on treatment with The structure of $A$ is :

In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic analysis ?
Element not present in Nessler’s reagent is
Two different lenses are used in telescope because

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:

The logic operations performed by the given digital circuit is equivalent to:
logic operations
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion (A):- fan spins even after switch is off
Reason (R):- Fan in rotation has rotational inertia.
In the light of the above statements, choose the correct answer from the options given belows
3, 8, 13, ......,373 are in arithmetic series. The sum of numbers not divisible by three is
An object moves x distance with speed \(v_1\) and next \(x\) distance with speed \(v_2\). The average velocity \(v\) is related to \(v_1\) and \(v_2\) as
Given A, B, C represents angles of a  ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?
The following statements are given : 
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced 
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature 
(3) The average kinetic energy of a gas molecule decreases with increases in volume 
(4) Pressure of a gas increases with increase in temperature at constant pressure 
(5) The volume of gas decreases with increase in temperature 
Choose the correct answer from the options given below :
The reaction of $H _2 O _2$ with potassium permanganate in acidic medium leads to the formation of mainly:
Which one of the following is more useful and effective for a quick visualization of a limited amount of information?
In the equation \(y_i = β_0+β_1.X_1+ε_1, \ β_0\) stands for
Given below are two statements about a normally distributed data.
Statement I : 95.45% of the occurrences will lie between \(\bar {X}±3σ\).
Statement II : 68.27% of the occurrences will lie between \(\bar {X}±1σ\).
In the light of the above statements, choose the correct answer from the options given below:
Read the given statements about correlation carefully and identify the correct statements.
A. A positive relation means that the variables vary in the same direction.
B. If two or more variables are related in a statistical way, is sufficient to conclude that a cause and effect relation exists.
C. A negative relation means that the two variables vary in the opposite direction.
D. Pearson's Product-Moment Method is a method used to calculate r.
Choose the correct answer from the options given below:
Match List I with List II :
List I (Method)List II (Characteristic)
(A)Mean(I)Identify what is most common
(B)Median(II)Based on sound mathematics
(C)Mode(III)Square-root of the variance
(D)Standard deviation(IV)Divides into 2 equal parts
Choose the correct answer from the options given below:
Ravi invested certain sum on simple interest. He invested two-third of his sum at 7% p.a and the remaining at 8% p.a. In 3 years he earned ₹1320 as interest. Find the sum invested by him (in ₹).
In what ratio must a grocer mix tea leaves costing Rs.600/kg and rs.650/kg. So that by selling the mixture at Rs.682/kg, he gains 10%?
If sec 5 A = Cosec A, then the value of A is