List of practice Questions

If\( cos 6\theta= sin 3\theta\), then the value of \(\theta\) is:
₹800 becomes ₹956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what will ₹ 800 amount to in 3 years:
The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?
The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:
The feasible region of an LPP is shown in the figure below.
If \( z=3x+9y\), then the minimum value of \(z\) occurs at :
Alternative Text
The function \(f(x)=sinx+cosx,0\leq x\leq 2\pi \) is :
The value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :
Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.
Alternative Text
(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 
The area of the region \(\{(x, y) : x^2 + y^2 \leq 2ax, y^2 > ax, x \geq 0, y \geq 0\} \text{ where } a > 0\) , is :
The random variable X has a probability distribution P(X) of the following form, where k is some number.
\[P(X=x) \begin{cases} k & \quad \text{if  } x=0\\   2k  & \quad \text{if }  \text{ x=1}\\  3k & \quad \text{if }  \text{ x=2} \\   0  & \quad \text{otherwise}  \end{cases}\]
Then P(x≤2) is:
Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:
The interval in which the \(f(x) = sinx-cosx, 0 ≤ x ≤ 2π\) is strictly decreasing is :
The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:
The integral \(\int_0^1x(1-x)^n dx\) is equal to :
Match List I with List II
LIST I LIST II
A.The common region determined by all the linear
constraints of a L.P.P. is called corner point		I.corner point
B.A point in the feasible region which is the intersection
of two boundary lines is called,		II.non-negative
C.The feasible region for an LPP is always aIII.feasible region
D.The constraints \(x, y≥0\) describes that the
variables involved in a LPP are		IV.convex polygon
Choose the correct answer from the options given below:
A 10 m long, 4 m high and 24 cm thick wall is to be built using bricks having dimensions 25 cm × 12 cm × 8 cm. Number of bricks required is :
The order and the degree of the differential equation
\(\frac{d^2y}{dx^2}=(1+\frac{dy}{dx})^{\frac{1}{2}}\)
respectively are :
The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by :
The value of the integral \(\int\frac{1-\sin x}{\cos^2 x}dx\) is :
Value of 248 (mod 15) is :
In △ABC, BD is the internal bisector of ∠B meeting AC at D. If CD = 7 cm and AC = 10.5 cm, then AB : BC is
The difference between length and breadth of a rectangle is 15m. If the perimeter of rectangle is 162 m, then the area of the rectangle (in m2) is
A vehicle whose cost is ₹7,00,000 will depreciate to scrap value of ₹1,50,000 in 5 years. Using linear method of depreciation, the book value of the vehicle at the end of the third year is :
By investing ₹4650 in a \(7 \frac{1}{2} \%\)% stock, a person obtains an income of ₹300. The market price of the stock is:
₹4200 are divided among ‘P’, ‘Q’, ‘R’ and ‘S’ in such a way that the shares of ‘P’ and ‘Q’. ‘Q’ and ‘R’ as well ‘R’ and ‘S’ are in the ratios of 2:3, 4:5 and 6:7 respectively, the share of ‘P’ is :