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General — JEE Mathematics MCQs

Master General for JEE Main with free mathematics MCQs. Each question includes a detailed solution and instant feedback — practice at easy, medium, and hard difficulty levels to build exam-ready confidence.

13 practice questions with instant feedback and solutions.

3 \times 3

M

with entries from

\{0,1,2\}

are there, for which the sum of the diagonal entries of

M^{T} M

5 ?

Let the functions

f: \mathbb{R} \rightarrow \mathbb{R}

g: \mathbb{R} \rightarrow \mathbb{R}

f(x)=e^{x-1}-e^{-|x-1|} \quad \text { and } \quad g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)

Then the area of the region in the first quadrant bounded by the curves

y=f(x), y=g(x)

x=0

O

be the origin and let

P Q R

be an arbitrary triangle. The point

S

\overrightarrow{O P} \cdot \overrightarrow{O Q}+\overrightarrow{O R} \cdot \overrightarrow{O S}=\overrightarrow{O R} \cdot \overrightarrow{O P}+\overrightarrow{O Q} \cdot \overrightarrow{O S}=\overrightarrow{O Q} \cdot \overrightarrow{O R}+\overrightarrow{O P} \cdot \overrightarrow{O S}

Then the triangle

P Q R

S

The area of the region

\left\{(x, y): x y \leq 8,1 \leq y \leq x^{2}\right\}

a, b

denote the distinct real roots of the quadratic polynomial

x^{2}+20 x-2020

c, d

denote the distinct complex roots of the quadratic polynomial

x^{2}-20 x+2020

. Then the value of

a c(a-c)+a d(a-d)+b c(b-c)+b d(b-d)

S

be the set of all complex numbers

Z

|z-2+i| \geq \sqrt{5}

. If the complex number

Z_{0}

\frac{1}{\left|Z_{0}-1\right|}

is the maximum of the set

\left\{\frac{1}{|z-1|}: z \in S\right\}

, then the principal argument of

\frac{4-z_{0}-\overline{z_{0}}}{Z_{0}-\overline{z_{0}}+2 i}

y=y(x)

satisfies the differential equation

8 \sqrt{x}(\sqrt{9+\sqrt{x}}) d y=(\sqrt{4+\sqrt{9+\sqrt{x}}})^{-1} d x, \quad x>0

y(0)=\sqrt{7}

y(256)=

f: \mathbb{R} \rightarrow \mathbb{R}

is a twice differentiable function such that

f^{\prime \prime}(x)>0

x \in \mathbb{R}

f\left(\frac{1}{2}\right)=\frac{1}{2}, f(1)=1

Medium•General

f:(0, \infty) \rightarrow \mathbb{R}

be a differentiable function such that

f^{\prime}(x)=2-\frac{f(x)}{x}

x \in(0, \infty)

f(1) \neq 1

Medium•General

b_{i}>1

i=1,2, \ldots, 101

\log _{e} b_{1}, \log _{e} b_{2}, \ldots, \log _{e} b_{101}

are in Arithmetic Progression (A.P.) with the common difference

\log _{e} 2

a_{1}, a_{2}, \ldots, a_{101}

are in A.P. such that

a_{1}=b_{1}

a_{51}=b_{51}

t=b_{1}+b_{2}+\cdots+b_{51}

s=a_{1}+a_{2}+\cdots+a_{51}

Medium•General

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Medium•General

S=\{1,2,3, \ldots, 9\}

k=1,2, \ldots, 5

N_{k}

be the number of subsets of

S

, each containing five elements out of which exactly

k

N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=

Medium•General

The least value of

\alpha \in \mathbb{R}

4 \alpha x^{2}+\frac{1}{x} \geq 1

x>0