List of top Mathematics Questions asked in CBSE CLASS XII

The perimeter of a rectangular metallic sheet is 300 cm 300 \, {cm} . It is rolled along one of its sides to form a cylinder. Find the dimensions of the rectangular sheet so that the volume of the cylinder so formed is maximum.
The chances of P P , Q Q , and R R getting selected as CEO of a company are in the ratio 4:1:2 4 : 1 : 2 , respectively. The probabilities for the company to increase its profits from the previous year under the new CEO, P,Q, P, Q, or R R , are 0.3,0.8, 0.3, 0.8, and 0.5 0.5 , respectively. If the company increased the profits from the previous year, find the probability that it is due to the appointment of R R as CEO.
It is given that function f(x)=x4−62x2+ax+9 f(x) = x^4 - 62x^2 + ax + 9 attains a local maximum value at x=1 x = 1 . Find the value of a a , hence obtain all other points where the given function f(x) f(x) attains local maximum or local minimum values.
Evaluate: ∫0π/41sin⁡x+cos⁡x dx \int_{0}^{\pi/4} \frac{1}{\sin x + \cos x} \, dx
Find: ∫x2+1(x2+2)(x2+4) dx \int \frac{x^2 + 1}{(x^2 + 2)(x^2 + 4)} \, dx
Find: ∫2+sin⁡2x1+cos⁡2xex dx \int \frac{2 + \sin 2x}{1 + \cos 2x} e^x \, dx
Solve the following linear programming problem graphically: Maximisez=4x+3y,subjecttotheconstraints: {Maximise } z = 4x + 3y, \quad {subject to the constraints:} x+y≤800,2x+y≤1000,x≤400,x,y≥0. x + y \leq 800, \quad 2x + y \leq 1000, \quad x \leq 400, \quad x, y \geq 0.
Let a⃗ \vec{a} and b⃗ \vec{b} be two non-zero vectors. Prove that ∣a⃗×b⃗∣≤∣a⃗∣∣b⃗∣ |\vec{a} \times \vec{b}| \leq |\vec{a}| |\vec{b}| . State the condition under which equality holds, i.e., ∣a⃗×b⃗∣=∣a⃗∣∣b⃗∣ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| .
If xcos⁡(p+y)+cos⁡psin⁡(p+y)=0 x \cos(p + y) + \cos p \sin(p + y) = 0 , prove that cos⁡pdydx=−cos⁡2(p+y) \cos p \frac{dy}{dx} = -\cos^2(p + y) , where p p is a constant.
Find the position vector of point C C which divides the line segment joining points A A and B B having position vectors i^+2j^−k^ \hat{i} + 2\hat{j} - \hat{k} and −i^+j^+k^ -\hat{i} + \hat{j} + \hat{k} , respectively, in the ratio 4:1 externally. Further, find ∣AB→∣:∣BC→∣ | \overrightarrow{AB} | : | \overrightarrow{BC} | .
Evaluate: ∫0π/2sin⁡2xcos⁡3x dx \int_{0}^{\pi/2} \sin 2x \cos 3x \, dx
Evaluate: sec⁡2(tan⁡−112)+csc⁡2(cot⁡−113) \sec^2 \left( \tan^{-1} \frac{1}{2} \right) + \csc^2 \left( \cot^{-1} \frac{1}{3} \right)
If a line makes an angle of π4 \frac{\pi}{4} with the positive directions of both x x -axis and z z -axis, then the angle which it makes with the positive direction of y y -axis is:
If ∣a∣=2 |a| = 2 and −3≤k≤2 -3 \leq k \leq 2 , then ∣a∣∣k∣∈: |a| |k| \in:
The derivative of 2x 2^x w.r.t. 3x 3^x is:
Let E E and F F be two events such that P(E)=0.1,P(F)=0.3,P(E∪F)=0.4 P(E) = 0.1, P(F) = 0.3, P(E \cup F) = 0.4 . Then P(F ∣ E) P(F \,|\, E) is:
If A A and B B are two skew-symmetric matrices, then AB+BA AB + BA is:
If a⃗=2i^−j^+k^ \vec{a} = 2\hat{i} - \hat{j} + \hat{k} and b⃗=i^−2j^+k^ \vec{b} = \hat{i} - 2\hat{j} + \hat{k} , then a⃗ \vec{a} and b⃗ \vec{b} are:
If α,β \alpha, \beta , and γ \gamma are the angles which a line makes with the positive directions of x,y,z x, y, z axes respectively, then which of the following is not true?
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:
If the sides of a square are decreasing at the rate of 1.5 cm/s 1.5 \, \mathrm{cm/s} , the rate of decrease of its perimeter is:
xlog⁡xdydx+y=2log⁡x x \log x \frac{dy}{dx} + y = 2 \log x is an example of a:
∫−aaf(x) dx=0 \int_{-a}^a f(x) \, dx = 0 , if:
A function f(x)=∣1−x+∣x∣∣ f(x) = |1 - x + |x|| is:
Let R+ \mathbb{R}_+ denote the set of all non-negative real numbers. Then the function f:R+→R+ f : \mathbb{R}_+ \to \mathbb{R}_+ defined as f(x)=x2+1 f(x) = x^2 + 1 is: