List of practice Questions

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2 \lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:

Which index number is used to compare cost of living at two different cities?

The set of value of \(x\) for which the angle between the \(\overrightarrow a = 2x²\hat i + 4x \hat j + \hat k\) and \(\overrightarrow b =7\hat i-2\hat j + x\hat k\) is obtuse is :

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is:

Match List I with List II

Choose the correct answer from the options given below:

A person buys a flat for which he makes down payment of ₹7,50,000 and the balance is to be paid in 10 years by monthly instalments of ₹22,000 each. If the bank charges interest at the rate of 12% per annum, then the actual price of the flat using flat rate system is:

If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:

Two bags of iron ore weight 180 kg 250 gm and 270 kg 50 gm respectively. How much iron ore (in gm) must be taken out from the first bag and added to the second bag so that weight of the first bag may then be two-third of the second bag?

The tangent to the parabola, x² = 2y at the point \((1,\frac{1}{2})\) makes with the x-axis an angle of :

The area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :

If \(x\sqrt{1+y}+y\sqrt{1+x}=0;x\ne y\), then the value of \(\frac{d^2y}{dx^2}+2\frac{dy}{dx}\) at x = 1 is :

The value of 28 mod 3 is.

In the given figure the value of angle ‘x’ is _________

In a polyhedron, the number of faces is 4 and the number of edges is 6, then the number of vertices of that polyhedron is:

Manish goes 8 km in the North from his school. Now, turning to the left, he goes 15 km and again turns to the left and goes to 8 km. How far he is from his school and in which direction?

January 11, 1997 was a Sunday. What day of the week was on January 7, 2000?

A shopkeeper sold \(\frac23\) of his stock of rice at a profit of \( 5\%\) and the remaining stock at a loss of \(2\%\). If his total profit was \( ₹\)\( 1000\), then the cost price of the whole stock of rice is:

If \(A (2,3), B(2,4) C(4,9)\)and \(D (x,8)\) are the vertices of a parallelogram \(ABCD\), then find the value of \(x.\)

A solid hemisphere of radius \(24 cm\) is melted and identical cones each of base radius\( 8 cm\) and height \( 6 cm \) are formed. How many such cones are formed?

For the problem max Z = ax + by, x≥0, y ≥0, which of the following is NOT a valid constraint to make it a linear programming problem?

The value of tan(cos^-1x) is:

Let\[f(x)=\begin{cases} 2x-1, x<1\\ 1, x=1 \\ x^2,x>1 \end{cases}\]then at x = 1

If |\(\vec{a}\)| = 5, |\(\vec{b}\)| = 2 and |\(\vec{a}\) · \(\vec{b}\) | = 8 then the value of |\(\vec{a} \)×\(\vec{b} \)| is:

The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}= \frac{y+17}{4}= \frac{z-6}{2} \space and \space \frac {x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:

If \(A = \begin{bmatrix} 4&5&2\\ 3&-1&7\end{bmatrix}\), then the sum of the elements of the matrix AA^T is: